Patent Publication Number: US-2021162602-A1

Title: Rotation connecting mechanism, robot, robot arm, and robot hand

Description:
TECHNICAL FIELD 
     The present disclosure relates to a rotation connecting mechanism used in a joint of a robot capable of making a motion close to a human, and a robot, a robot arm, and a robot hand, in which the rotation connecting mechanism is used. 
     BACKGROUND ART 
     A humanoid robot including a body, arms, legs, and a head similarly to a human is being developed. In a conventional humanoid robot, typically a motor and a gear are disposed in a joint and a joint intersection is disposed on an axis of the gear. In such a humanoid robot, it is necessary to dispose the gear in the joint by a rotational degree of freedom, and the joint becomes large. Patent Document 1 proposes a biped walking robot in which a skeleton is connected by the joint and the joint is driven with two rotational degrees of freedom by expansion and contraction of a link by two actuators for each joint. Patent Document 2 proposes a robot that drives the joint with two rotational degrees of freedom by expansion and contraction of the link by two actuators and drives an ankle, a wrist, and a neck with three rotational degrees of freedom in which one rotary actuator is added to the two actuators. Patent Document 3 proposes a parallel link mechanism including one fixed length link, in which one end is connected to a bearing with three degrees of freedom provided on a fixed side member while the other end is connected to a movable side member, and three variable length links, in each of which one end is connected to the fixed side member by a bearing with three rotational degrees of freedom while the other end is connected to the movable side member by a bearing with three degrees of freedom. 
     A closed worm gear type finger joint unit that can be used in a hand part or a robot hand of a humanoid robot has been proposed (Patent Document 4). The closed worm gear type finger joint unit illustrated in Patent Document 4 has one joint shaft. Nothing is disclosed about application of a worm gear mechanism to a finger including a plurality of finger joints. 
     CITATION LIST 
     Patent Document 
     Patent Document 1: Japanese Patent Laid-Open No. 2004-202676 
     Patent Document 2: National Patent Publication No. 2011-527641 
     Patent Document 3: Japanese Patent Laid-Open No. 2003-172418 
     Patent Document 4: WO 2007/077698 
     SUMMARY OF INVENTION 
     Technical Problems 
     The joint can be made compact using the actuator. However, when the joint has two rotational degrees of freedom, for example, motion accompanied by twist cannot be performed by a wrist. When the motion accompanied by torsion cannot be made, sometimes the motion close to a human cannot be made. 
     A structure of the three-rotational-degree-of-freedom joint described in Patent Document 2 is complicated. An ankle and the wrist cannot be thickened because a shape similar to a human is required to be obtained, and an interval of a distance between the joint that is a fulcrum and a connection point of the link that is an action point is narrowed. For this reason, it is considered that sometimes the robot cannot output enough power. 
     In the parallel link mechanism of Patent Document 3, it is necessary to provide a connecting unit having two rotational degrees of freedom at both ends of each of three variable length links. A movable member 5 is connected to a base member 1 at a total of four points including a connecting rod 4 and three expansion mechanisms 7. That is, in the parallel link mechanism of Patent Document 3, the positions of the four points of the movable member 5 in the three-dimensional space are determined. Because a plane in a space is determined by three points, controlling of load distribution and positioning of the four points is difficult in the parallel link mechanism of Patent Document 3 in which the positions of the four points are determined. 
     In order to put the robot into practical use, it is necessary to have a technique that enables the robot that can be manufactured at low cost as much as possible in addition to being able to perform the motion close to a human as in the past. The connecting unit having at least two rotational degrees of freedom is more expensive than the connecting unit having one rotational degree of freedom. Desirably the number of connecting units having at least two rotational degrees of freedom is decreased in the joint having two rotational degrees of freedom, and three-point support is adopted to facilitate the control in the joint having three rotational degrees of freedom. 
     The present disclosure has been made to solve the above problems, and an object of the present disclosure is to obtain a rotation connecting mechanism that is lower in cost than conventional one. 
     Solution to Problems 
     According to one aspect of the present disclosure, a rotation connecting mechanism includes: a joint to connect a second member rotatably to a first member with at least two rotational degrees of freedom; a first actuator; and a second actuator. The first actuator includes: a first link having four rotational degrees of freedom or five rotational degrees of freedom; a second-member first attaching unit provided in the second member and having a fixed positional relationship with respect to the joint, one end of the first link being attached rotatably to the second-member first attaching unit with at least two rotational degrees of freedom; a first-member first attaching unit to which the other end of the first link is attached rotatably with at least two rotational degrees of freedom; and a first power source to generate force changing a distance between the second-member first attaching unit and a first reference point provided in the first member and having a fixed positional relationship with respect to the joint. 
     The second actuator includes: a second link having three rotational degrees of freedom, four rotational degrees of freedom, or five rotational degrees of freedom; a first-link second attaching unit provided on the first link having a fixed positional relationship with respect to the second-member first attaching unit, one end of the second link being attached rotatably to the first-link second attaching unit with at least one rotational degree of freedom; a first-member second attaching unit to which the other end of the second link is attached rotatably with at least two rotational degrees of freedom; and a second power source to generate force changing a distance between the first-link second attaching unit and a second reference point provided in the first member and having a fixed positional relationship with respect to the joint. 
     According to another aspect of the present disclosure, a rotation connecting mechanism includes: a joint to connect a second member rotatably to a first member with at least two rotational degrees of freedom; a first actuator; and a second actuator. The first actuator includes: a first link having a variable length and four rotational degrees of freedom or five rotational degrees of freedom, a second-member first attaching unit provided in the second member and having a fixed positional relationship with respect to the joint, one end of the first link being attached rotatably to the second-member first attaching unit with at least two rotational degrees of freedom; a first-member first attaching unit provided in the first member and having a fixed positional relationship with respect to the joint, the other end of the first link being attached rotatably to the first-member first attaching unit with at least two rotational degrees of freedom; and a first power source to generate force changing a length of the first link. The second actuator includes: a second link having a variable length and three rotational degrees of freedom, four rotational degrees of freedom, or five rotational degrees of freedom; a first-link second attaching unit provided on the first link having a fixed positional relationship with respect to the second-member first attaching unit, one end of the second link being attached rotatably to the first-link second attaching unit with at least one rotational degree of freedom; a first-member second attaching unit provided in the first member and having a fixed positional relationship with respect to the joint, the other end of the second link being attached rotatably to the first-member second attaching unit with at least two rotational degrees of freedom; and a second power source to generate force changing a length of the second link. 
     According to another aspect of the present disclosure, a rotation connecting mechanism includes: a joint to connect a second member rotatably to a first member with at least two rotational degrees of freedom; a first actuator; and a second actuator. The first actuator includes: a first link having a fixed length and five rotational degrees of freedom; a second-member first attaching unit provided in the second member and having a fixed positional relationship with respect to the joint, one end of the first link being attached rotatably to the second-member first attaching unit with at least two rotational degrees of freedom; a first-member first attaching unit to which the other end of the first link is attached rotatably with at least two rotational degrees of freedom; a first moving member in which the first-member first attaching unit is provided; a first guide including a first moving shaft, and to guide the first moving member such that the first moving member is moved along the first moving shaft, the first guide being provided in the first member and having a fixed positional relationship with respect to the joint; and a first power source to generate force changing a position of the first moving member with respect to the first guide. The second actuator includes: a second link having a fixed length and five rotational degrees of freedom; a first-link second attaching unit provided on the first link having a fixed positional relationship with respect to the second-member first attaching unit, one end of the second link being attached rotatably to the first-link second attaching unit with at least two rotational degrees of freedom; a first-member second attaching unit to which the other end of the second link is attached rotatably with at least two rotational degrees of freedom; a second moving member in which the first-member second attaching unit is provided; a second guide including a second moving shaft, and to guide the second moving member such that the second moving member is moved along the second moving shaft, the second guide being provided in the first member and having a fixed positional relationship with respect to the joint; and a second power source to generate force changing a position of the second moving member with respect to the second guide 
     According to yet another aspect of the present disclosure, a robot hand includes: a base; and at least three fingers, each of the at least three fingers includes a first dactylus, a second dactylus, and a third dactylus, the first dactylus, the second dactylus, and the third dactylus being connected in series from the base, and three finger joints connecting a tip-side member being one of the first dactylus, the second dactylus, and the third dactylus rotatably to a base-side member provided on a side on which the base exists. In each of a first finger joint being the finger joint connecting the first dactylus rotatably to the base and a second finger joint being the finger joint connecting the second dactylus rotatably to the first dactylus, the tip-side member is rotated with respect to the base-side member by a worm gear mechanism, the worm gear mechanism including a motor disposed in the base-side member, a worm rotated by the motor, and a worm wheel meshing with the worm to be rotated around a rotation shaft of the finger joint together with the tip-side member. 
     Advantageous Effects of Invention 
     According to the present disclosure, it is possible to obtain a rotation connecting mechanism that is lower in cost than conventional one. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a perspective view illustrating a humanoid robot according to a first embodiment of the present disclosure. 
         FIG. 2  is a front view illustrating the humanoid robot of the first embodiment. 
         FIG. 3  is a left side view illustrating the humanoid robot of the first embodiment. 
         FIG. 4  is a rear view illustrating the humanoid robot of the first embodiment. 
         FIG. 5  is a plan view illustrating the humanoid robot of the first embodiment viewing from above. 
         FIG. 6  is a perspective view illustrating a skeleton structure of the humanoid robot of the first embodiment. 
         FIG. 7  is a front view illustrating the skeleton structure of the humanoid robot of the first embodiment. 
         FIG. 8  is a left side view illustrating the skeleton structure of the humanoid robot of the first embodiment. 
         FIG. 9  is a rear view illustrating the skeleton structure of the humanoid robot of the first embodiment. 
         FIG. 10  is a plan view illustrating the skeleton structure of the humanoid robot of the first embodiment. 
         FIG. 11  is a perspective view illustrating an upper half body in the skeletal structure of the humanoid robot of the first embodiment viewing from an oblique front on a left hand side. 
         FIG. 12  is a perspective view illustrating the upper half body in the skeletal structure of the humanoid robot of the first embodiment viewing up from an oblique rear on the right hand side. 
         FIG. 13  is a perspective view illustrating the upper half body in the skeletal structure of the humanoid robot of the first embodiment viewing down from the oblique rear on the right hand side. 
         FIG. 14  is an enlarged front view illustrating a trunk in the skeletal structure of the humanoid robot of the first embodiment. 
         FIG. 15  is an enlarged rear view of the trunk in the skeletal structure of the humanoid robot of the first embodiment. 
         FIG. 16  is a front view illustrating a chest upper portion included in the humanoid robot of the first embodiment. 
         FIG. 17  is a left side view illustrating the chest upper portion included in the humanoid robot of the first embodiment. 
         FIG. 18  is a rear view illustrating the chest upper portion included in the humanoid robot of the first embodiment. 
         FIG. 19  is a plan view illustrating the chest upper portion included in the humanoid robot of the first embodiment viewing from above. 
         FIG. 20  is a plan view illustrating the chest upper portion included in the humanoid robot of the first embodiment viewing from below. 
         FIG. 21  is a plan view illustrating a portion below a waist in the skeleton structure of the humanoid robot of the first embodiment viewing from above. 
         FIG. 22  is a perspective view illustrating the trunk included in the humanoid robot of the first embodiment viewing from an oblique front on the left hand side. 
         FIG. 23  is a perspective view illustrating the trunk included in the humanoid robot of the first embodiment viewing from the oblique rear on the left hand side. 
         FIG. 24  is a left side view illustrating the trunk when an upper limb of the humanoid robot of the first embodiment does not exist. 
         FIG. 25  is a cross-sectional view illustrating a structure of a variable length link included in an actuator used in the humanoid robot of the first embodiment. 
         FIG. 26  is a schematic diagram illustrating a division between the chest upper portion and a chest lower portion and arrangement of the variable length links that drive a chest in the humanoid robot of the first embodiment viewing from a side. 
         FIG. 27  is a schematic diagram illustrating the division between the chest upper portion and the chest lower portion and the arrangement of the variable length links that drive the chest in the humanoid robot of the first embodiment viewing from a front. 
         FIG. 28  is a perspective view illustrating the arrangement of the variable length links in a body bending unit included in the humanoid robot of the first embodiment viewing from the oblique rear on the left hand side. 
         FIG. 29  is a view illustrating the arrangement of the variable length links in a reference state of the body bending unit included in the humanoid robot of the first embodiment viewing from the direction in which a backbone extends. 
         FIG. 30  is a view illustrating whether a torque rotating around a torsion axis is generated by expansion and contraction of the variable length link depending on a positional relationship between the torsion axis and the variable length link in the three-rotational-degree-of-freedom connection mechanism included in the humanoid robot of the first embodiment. 
         FIG. 31  is a view illustrating the arrangement of the variable length links when the chest of the body bending unit included in the humanoid robot of the first embodiment is rotated and tilted forward viewing from the direction in which the backbone extends. 
         FIG. 32  is an enlarged side view illustrating a head of the humanoid robot of the first embodiment. 
         FIG. 33  is an enlarged perspective view illustrating the head of the humanoid robot of the first embodiment. 
         FIG. 34  is a perspective view illustrating the arrangement of the variable length links at a neck included in the humanoid robot of the first embodiment. 
         FIG. 35  is a view illustrating the arrangement of the variable length links in a reference state of the neck included in the humanoid robot of the first embodiment viewing from a direction in which a neck center rod extends. 
         FIG. 36  is a view illustrating the arrangement of the variable length links when the head of the neck included in the humanoid robot of the first embodiment is rotated and tilted forward viewing from the direction in which the neck center rod extends. 
         FIG. 37  is a perspective view illustrating the upper half body of the humanoid robot according to first embodiment. 
         FIG. 38  is a perspective view illustrating the arrangement of the variable length links at a left shoulder joint included in the humanoid robot of the first embodiment. 
         FIG. 39  is a front view illustrating a left upper limb of the humanoid robot of the first embodiment. 
         FIG. 40  is a side view illustrating the left upper limb of the humanoid robot of the first embodiment. 
         FIG. 41  is an enlarged front view illustrating a portion up to an elbow joint of the left upper limb of the humanoid robot of the first embodiment. 
         FIG. 42  is an enlarged side view illustrating the portion up to the elbow joint of the left upper limb of the humanoid robot of the first embodiment. 
         FIG. 43  is a front view illustrating a state in which right and left elbow joints are bent by 90 degrees in the trunk and upper limb included in the humanoid robot of the first embodiment. 
         FIG. 44  is a plan view illustrating in the state in which the right and left elbow joints are bent by 90 degrees in the trunk and upper limb included in the humanoid robot of the first embodiment viewing from above. 
         FIG. 45  is a perspective view illustrating the arrangement of links of a left elbow joint included in the humanoid robot of the first embodiment. 
         FIG. 46  is an enlarged perspective view illustrating a portion of an arm from the left elbow joint in the skeletal structure of the humanoid robot of the first embodiment. 
         FIG. 47  is an enlarged front view illustrating the portion of the arm from the left elbow joint of the humanoid robot of the first embodiment. 
         FIG. 48  is an enlarged left side view illustrating the portion of the arm from the left elbow joint of the humanoid robot of the first embodiment when an outside actuator is excluded. 
         FIG. 49  is an enlarged rear view illustrating the portion of the arm from the left elbow joint of the humanoid robot of the first embodiment. 
         FIG. 50  is a perspective view illustrating the arrangement of the variable length links in a left wrist included in the humanoid robot of the first embodiment. 
         FIG. 51  is a view illustrating the arrangement of the variable length links in the reference state of the left wrist included in the humanoid robot of the first embodiment viewing from the direction in which a forearm extends. 
         FIG. 52  is a view illustrating the arrangement of the variable length links when the left wrist included in the humanoid robot of the first embodiment is tilted toward a fourth finger side viewing from the direction in which the forearm extends. 
         FIG. 53  is a front view illustrating a portion below a waist in the skeleton structure of the humanoid robot of the first embodiment. 
         FIG. 54  is a left side view illustrating the portion below the waist in the skeleton structure of the humanoid robot of the first embodiment. 
         FIG. 55  is a rear view illustrating the portion below the waist in the skeleton structure of the humanoid robot of the first embodiment. 
         FIG. 56  is a perspective view illustrating the portion below the knee joint in the skeleton structure of the humanoid robot of the first embodiment. 
         FIG. 57  is an enlarged front view illustrating a thigh of the humanoid robot of the first embodiment. 
         FIG. 58  is an enlarged left side view illustrating the thigh of the humanoid robot of the first embodiment. 
         FIG. 59  is an enlarged rear view illustrating the thigh of the humanoid robot of the first embodiment. 
         FIG. 60  is a perspective view illustrating the thigh of the humanoid robot of the first embodiment viewing from a front oblique right. 
         FIG. 61  is a perspective view illustrating the thigh of the humanoid robot of the first embodiment viewing from a rear oblique right. 
         FIG. 62  is a perspective view illustrating the arrangement of the variable length links in a left crotch of the humanoid robot of the first embodiment. 
         FIG. 63  is a view illustrating the arrangement of the variable length links in the reference state of the left crotch of the humanoid robot of the first embodiment viewing from the direction in which a thighbone extends. 
         FIG. 64  is a view illustrating the arrangement of the variable length links when the thigh of the left crotch included in the humanoid robot of the first embodiment is raised to a left front viewing from the direction in which the thighbone extends. 
         FIG. 65  is a view illustrating an effect obtained by attaching the variable length link that moves a hip joint included in the humanoid robot of the first embodiment high on a front side and by attaching the variable length link low on a rear side. 
         FIG. 66  is a perspective view illustrating the arrangement of the variable length links for moving the left knee joint included in the humanoid robot of the first embodiment. 
         FIG. 67  is an enlarged front view illustrating the portion below the knee joint of the humanoid robot of the first embodiment. 
         FIG. 68  is an enlarged left side view illustrating the portion below the knee joint of the humanoid robot of the first embodiment. 
         FIG. 69  is an enlarged rear view illustrating the portion below the knee joint of the humanoid robot of the first embodiment. 
         FIG. 70  is a perspective view illustrating a portion below a lower leg of the humanoid robot of the first embodiment. 
         FIG. 71  is a perspective view illustrating the arrangement of the variable length links for moving a left ankle joint included in the humanoid robot of the first embodiment. 
         FIG. 72  is a perspective view illustrating a left hand included in the humanoid robot of the first embodiment viewing from a palm side. 
         FIG. 73  is a perspective view illustrating the left hand included in the humanoid robot of the first embodiment viewing from the backside of the hand. 
         FIG. 74  is a front view illustrating the left hand included in the humanoid robot of the first embodiment. 
         FIG. 75  is a side view illustrating the left hand included in the humanoid robot of the first embodiment viewing from the side where an opposable finger exists. 
         FIG. 76  is a rear view illustrating the left hand included in the humanoid robot of the first embodiment. 
         FIG. 77  is a side view illustrating the left hand included in the humanoid robot of the first embodiment viewing from the side where the opposable finger does not exist. 
         FIG. 78  is a view illustrating the left hand included in the humanoid robot of the first embodiment viewing from a fingertip side. 
         FIG. 79  is a view illustrating a cross section of a second finger of the left hand included in the humanoid robot of the first embodiment. 
         FIG. 80  is a view illustrating variables expressing distances between the joint and link attaching units in an intrathoracic joint and a thoracolumbar joint included in the humanoid robot of the first embodiment. 
         FIG. 81  is a view illustrating variables expressing distances between the joint and the link attaching units in the shoulder joint included in the humanoid robot of the first embodiment. 
         FIG. 82  is a view illustrating variables expressing the distances between the joint and the link attaching units in the elbow joint included in the humanoid robot of the first embodiment. 
         FIG. 83  is a view illustrating variables expressing the distances between the joint and the link attaching units in the wrist joint included in the humanoid robot of the first embodiment. 
         FIG. 84  is a view illustrating variables expressing the distances between the joint and the link attaching units in the ankle joint included in the humanoid robot according to the first embodiment. 
         FIG. 85  is a view illustrating variables expressing the distances between the joint and the link attaching units in the hip joint included in the humanoid robot of the first embodiment. 
         FIG. 86  is a cross-sectional view illustrating a structure of a variable length link of an actuator included in a humanoid robot according to a second embodiment of the present disclosure. 
         FIG. 87  is a perspective view illustrating a left hand included in a humanoid robot according to a third embodiment of the present disclosure viewing from the backside of the hand. 
         FIG. 88  is a perspective view illustrating the left hand included in the humanoid robot of the third embodiment viewing from a palm side. 
         FIG. 89  is a front view illustrating the left hand included in the humanoid robot of the third embodiment. 
         FIG. 90  is a side view illustrating the left hand included in the humanoid robot of the third embodiment viewing from the side on which a first finger exists. 
         FIG. 91  is a rear view illustrating the left hand included in the humanoid robot of the third embodiment. 
         FIG. 92  is a side view illustrating the left hand included in the humanoid robot of the third embodiment viewing from a fingertip side. 
         FIG. 93  is a side view illustrating the left hand included in the humanoid robot of the third embodiment viewing from a wrist side. 
         FIG. 94  is a side view illustrating the left hand included in the humanoid robot of the third embodiment when an opposed finger of the left hand is bent viewing from the side on which the first finger exists. 
         FIG. 95  is a plan view illustrating a palm plate of the left hand included in the humanoid robot of the third embodiment. 
         FIG. 96  is an enlarged perspective view illustrating a vicinity of a second dactylus of the opposed finger of the left hand included in the humanoid robot of the third embodiment. 
         FIG. 97  is a perspective view illustrating a left hand included in a humanoid robot according to a fourth embodiment of the present disclosure when a hand breadth rotation finger extends viewing from the backside of the hand. 
         FIG. 98  is a perspective view illustrating the left hand included in the humanoid robot of the fourth embodiment when the hand breadth rotation finger is directed in a direction intersecting the palm plate viewing from the backside of the hand. 
         FIG. 99  is a front view illustrating the left hand included in the humanoid robot of the fourth embodiment with the hand breadth rotation finger extending. 
         FIG. 100  is a side view illustrating the left hand included in the humanoid robot of the fourth embodiment when the hand breadth rotation finger extends viewing from the side on which the first finger exists. 
         FIG. 101  is a rear view illustrating the left hand included in the humanoid robot of the fourth embodiment when the hand breadth rotation finger extends. 
         FIG. 102  is a side view illustrating the left hand included in the humanoid robot of the fourth embodiment when the hand breadth rotation finger extends viewing from the side on which the fourth finger exists. 
         FIG. 103  is a side view illustrating the left hand included in the humanoid robot of the fourth embodiment when the hand breadth rotation finger extends viewing from the fingertip side 
         FIG. 104  is a front view illustrating the left hand included in the humanoid robot of the fourth embodiment when the hand breadth rotation finger is directed in the direction intersecting the palm plate. 
         FIG. 105  is a side view illustrating the left hand included in the humanoid robot of the fourth embodiment when the hand breadth rotation finger is directed in the direction intersecting the palm plate viewing from the side on which the first finger exists. 
         FIG. 106  is a rear view illustrating the left hand included in the humanoid robot of the fourth embodiment when the hand breadth rotation finger is directed in the direction intersecting the palm plate. 
         FIG. 107  is a side view illustrating the left hand included in the humanoid robot of the fourth embodiment when the hand breadth rotation finger is directed in the direction intersecting the palm plate viewing from the side on which the fourth finger exists. 
         FIG. 108  is a side view illustrating the left hand included in the humanoid robot of the fourth embodiment when the hand breadth rotation finger is directed in the direction intersecting the palm plate viewing from the fingertip side. 
         FIG. 109  is an enlarged perspective view illustrating the left hand included in the humanoid robot of the fourth embodiment when the hand breadth rotation finger extends viewing from the backside of the hand. 
         FIG. 110  is an enlarged perspective view illustrating the left hand included in the humanoid robot of the fourth embodiment when the hand breadth rotation finger is directed in the direction intersecting the palm plate viewing from the backside of the hand. 
         FIG. 111  is a perspective view illustrating the whole of a humanoid upper half body robot according to a fifth embodiment of the present disclosure. 
         FIG. 112  is a front view illustrating the whole of the humanoid upper half body robot of the fifth embodiment. 
         FIG. 113  is a left side view illustrating the whole of the humanoid upper half body robot of the fifth embodiment. 
         FIG. 114  is a perspective view illustrating the humanoid upper half body robot of the fifth embodiment viewing from the front. 
         FIG. 115  is a perspective view illustrating the humanoid upper half body robot of the fifth embodiment viewing from a left arm side. 
         FIG. 116  is a perspective view illustrating the humanoid upper half body robot of the fifth embodiment viewing from a rear side. 
         FIG. 117  is a front view illustrating the humanoid upper half body robot of the fifth embodiment. 
         FIG. 118  is a plan view illustrating the humanoid upper half body robot of the fifth embodiment. 
         FIG. 119  is a bottom view illustrating the humanoid upper half body robot of the fifth embodiment. 
         FIG. 120  is a perspective view illustrating the body bending unit included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 121  is a front view illustrating the body bending unit included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 122  is a left side view illustrating the body bending unit included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 123  is a right side view illustrating the body bending unit included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 124  is a perspective view illustrating link arrangement of the body bending unit included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 125  is a view illustrating the link arrangement in a reference state of the body bending unit included in the humanoid upper half body robot of the fifth embodiment viewing from the direction in which a backbone extends. 
         FIG. 126  is a view illustrating variables for evaluating the link arrangement in the reference state of the body bending unit included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 127  is a front view illustrating a shoulder included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 128  is a plan view of the shoulder included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 129  is a right side view of the shoulder included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 130  is a view of a left shoulder of the humanoid upper half body robot of the fifth embodiment viewing from below. 
         FIG. 131  is a perspective view illustrating the left shoulder of the humanoid robot of fifth embodiment. 
         FIG. 132  is another perspective view illustrating the left shoulder of the humanoid upper half body robot of the fifth embodiment. 
         FIG. 133  is a perspective view illustrating the link arrangement of the shoulder included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 134  is a perspective view illustrating an elbow included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 135  is a front view illustrating the elbow included in the humanoid robot of the fifth embodiment. 
         FIG. 136  is a left side view illustrating the elbow included in the humanoid robot of the fifth embodiment. 
         FIG. 137  is a perspective view illustrating the link arrangement of the elbow included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 138  is a perspective view illustrating a wrist included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 139  is another perspective view illustrating the wrist included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 140  is a front view illustrating the wrist included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 141  is a right side view illustrating the wrist included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 142  is a perspective view illustrating the link arrangement of the elbow included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 143  is a view illustrating the link arrangement in the reference state of the wrist included in the humanoid upper half body robot of the fifth embodiment viewing from the direction in which a forearm extends. 
         FIG. 144  is a view illustrating variables for evaluating the link arrangement in the reference state of the wrist included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 145  is a view illustrating a hand with a wrist included in the humanoid upper half body robot of the fifth embodiment viewing from the backside of the hand. 
         FIG. 146  is a view illustrating the hand with the wrist included in the humanoid upper half body robot of the fifth embodiment viewing from a side. 
         FIG. 147  is a view illustrating the hand included in the humanoid upper half body robot of the fifth embodiment viewing from the backside of the hand. 
         FIG. 148  is a view illustrating the hand included in the humanoid upper half body robot of the fifth embodiment viewing from a palm side. 
         FIG. 149  is a view illustrating the hand included in the humanoid upper half body robot of the fifth embodiment viewing from a side. 
         FIG. 150  is a perspective view illustrating a finger base that rotates a two-way rotation finger around a finger base axis, the finger base being included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 151  is another perspective view illustrating the finger base that rotates the two-way rotation finger around the finger base axis, the finger base being included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 152  is a view illustrating a link arrangement of a thumb of the hand included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 153  is a view illustrating variables for expressing positions of the joint and the link attaching unit in the body bending unit included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 154  is a view illustrating a point where the position is fixed by determining the link length in the body bending unit included in the humanoid upper half body robot of the fifth embodiment. 
         FIG. 155  is a view illustrating a point where the position is fixed by determining the link length in the body bending unit included in the humanoid robot of the first embodiment as a comparative example. 
         FIG. 156  is a front view illustrating a humanoid upper half body robot according to a sixth embodiment of the present disclosure. 
         FIG. 157  is a perspective view illustrating a link arrangement of a body bending unit included in the humanoid upper half body robot of the sixth embodiment. 
         FIG. 158  is a view illustrating a point where the position is fixed by determining the link length in the body bending unit included in the humanoid upper half body robot of the sixth embodiment. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     First Embodiment 
       FIG. 1  is a perspective view of a humanoid robot  100  according to a first embodiment of the present disclosure.  FIGS. 2, 3, 4, and 5  are a front view, a left side view, a rear view, and a plan view of humanoid robot  100 , respectively.  FIG. 6  is a perspective view explaining a skeleton structure of humanoid robot  100 .  FIGS. 7, 8, 9 , and  10  are a front view, a left side view, a rear view, and a plan view of humanoid robot  100  having only a skeleton, respectively. An axis of a right and left direction of humanoid robot  100  is defined as an X-axis, an axis of a front-back direction is defined as a Y-axis, and an axis in a height direction is defined as a Z-axis. A direction from the right to the left is defined as a positive direction of the X-axis, a direction from the front to the rear is defined as a positive direction of the Y-axis, and a direction from a bottom to a top is defined as a positive direction of the Z-axis. 
     A posture in which humanoid robot  100  stands upright and lowers both arms as illustrated in  FIGS. 1 to 5  is referred to as a reference state. The reference state is a posture often taken when humanoid robot  100  is used. The reference state is not necessary to be upright. Desirably the posture used as a starting point for various motions is determined to be the reference state. 
     Humanoid robot  100  has a structure similar to a human body. Humanoid robot  100  includes a trunk  1 , a head  2  connected to an upper center of trunk  1 , a pair of upper limbs  3  protruding from the right and left of an upper part of trunk  1 , and a pair of right and left lower limbs  4  protruding from a lower part of trunk  1 . Trunk  1  is divided into a chest  5  on an upper side and a waist  6  on a lower side. In upper limb  3 , an upper arm  7 , a forearm  8 , and a hand  9  are connected in series. In lower limb  4 , a thigh  10 , a lower leg  11 , and a foot  12  are sequentially connected in series from waist  6 . The pair of right and left upper limbs  3  has a structure in which right upper limb  3  and left upper limb  3  become a mirror image relationship. Similarly, the mirror image relationship also holds for the pair of right and left lower limbs  4 . Right and left upper limbs  3  may have a portion in which the mirror image relationship does not hold. Right and left lower limbs  4  may also have the portion in which the mirror image relationship does not hold. 
     In humanoid robot  100 , each joint connecting rotatably a skeleton is moved by changing a length of a link (variable length link) having a variable length included in an actuator corresponding to a muscle. The number of variable length links that move the joints is the same as a degree of a rotational degree of freedom required at the joint. The length of the variable length link can be changed within a movable range of the variable length link, and any length within the movable range can be maintained. The actuator also includes a motor as a power source that generates force changing the length of the variable length link. A reference sign XXL denotes the link included in an actuator XX, and a reference sign XXM denotes a motor. The variable length link XXL and the motor XXM are illustrated in the drawings. Generally, a reference sign XX of the actuator is not illustrated in the drawings. 
     In this description, the term “link” is used to express a member that has one end and the other end and connects the point where one end is attached and the point where the other end is attached. A freedom degree of rotation of the link is a sum of the rotational degree of freedom at the point where one end is attached, at the point where the other end is attached, and the rotational degree of freedom of the link itself. With respect to the rotational degree of freedom of the link itself, the link has one rotational degree of freedom when the link can twist. When the link cannot twist, the link has no rotational degree of freedom, that is, zero rotational degree of freedom. When a link A is attached to a link B, the rotational degree of freedom of a link attaching unit is included in the rotational degree of freedom of link A and not included in the rotational degree of freedom of link B. 
     The term “actuator” is used to express an object that has the link and moves a second member connected to one end of the link with respect to a first member connected to the other end. The first member is a fixed-side member. The second member is a member that is moved with respect to the first member. There are the following two methods for moving the second member. 
     (Method 1) the link length is changed. 
     (Method 2) the other end of the fixed length link is moved. 
     The actuator includes the link, the link attaching unit to which each of one end and the other end of the link is attached, and a power source. For the actuator that moves the other end of the link, the actuator also includes a member to move the other end of the link. 
     In many conventional humanoid robots, the motor and the gear are disposed in each joint, and joint intersection is disposed on the axis of the gear. For this reason, a space necessary for the joint becomes large, the compact joint is hardly made. On the other hand, in humanoid robot  100 , it is unnecessary to dispose a gear near the joint, so that the joint can be made compact. Additionally, the link exists in parallel with the skeleton connected by the joint, so that the joint can withstand force larger than that of the case of only the joint. Each joint has the rotational degree of freedom of the necessary degree, so that humanoid robot  100  can make motion close to that of a human. For example, being able to make the motion similar to that of a human is a necessary condition as a robot that work on behalf of a human in an area where a human cannot enter. 
     In the neck, the wrist, the crotch, and a connection between chest  5  and waist  6 , each joint of humanoid robot  100  has three rotational degrees of freedom, at which the joint can be moved back and forth and right and left and be twisted. In the shoulder, the elbow, and the ankle, the joint has two rotational degrees of freedom, at which the joint can be moved back and forth and right and left. In the knee, the joint has one rotational degree of freedom, at which the joint can be moved back and forth. In the shoulder, the ankle, and the elbow, the joint may have three rotational degrees of freedom. 
     Chest  5  is divided into a chest upper portion  5 U and a chest lower portion  5 D. Upper arm  7  and head  1  are connected to chest upper portion  5 U. Chest lower portion  5 D is connected to waist  6 . An angle of chest upper portion  5 U can be changed vertically with respect to chest lower portion  5 D with one rotational degree of freedom. Chest  5  includes a chest bending unit C 1  (illustrated in  FIG. 26 ) connecting chest upper portion  5 U rotatably to chest lower portion  5 D with one rotational degree of freedom. 
     Referring to  FIGS. 10 to 24 , a structure of the trunk  1  is described.  FIG. 11  is a perspective view illustrating an upper half body in a skeleton structure viewing from an oblique front on a left hand side.  FIG. 12  is a perspective view illustrating the upper half body in the skeleton structure viewing up from an oblique rear on the right hand side.  FIG. 13  is a perspective view illustrating the upper half body in the skeletal structure viewing down from the oblique rear on the right hand side.  FIG. 14  is an enlarged front view illustrating trunk  1  in the skeleton structure.  FIG. 15  is an enlarged rear view illustrating trunk  1  in the skeleton structure.  FIGS. 16 to 18  are a front view, a left side view, and a rear view of chest upper portion  5 U.  FIG. 19  is a plan view illustrating chest upper portion  5 U viewing from above.  FIG. 20  is a plan view illustrating chest upper portion  5 U viewing from below.  FIG. 21  is a plan view illustrating a portion below waist  6  in the skeleton structure.  FIG. 22  is a perspective view illustrating trunk  1  viewing from an oblique front on the left hand side.  FIG. 23  is a perspective view illustrating trunk  1  viewing from an oblique rear on the left hand side.  FIG. 24  is a left side view illustrating trunk  1  without upper limb  3 . 
     Referring mainly to  FIGS. 10 to 21 , the skeleton constituting trunk  1  and a place to which the variable length link of the actuator, corresponding to a muscle, is attached is described. Chest  5  includes a shoulder frame  51 , a thorax frame  52 , a thorax front-back coupling frame  53 , a chest center coupling frame  54 , an intrathoracic joint frame  55 , a backbone  56 , and a link attaching frame  57 . Chest upper portion  5 U is configured to include shoulder frame  51 , thorax frame  52 , thorax front-back coupling frame  53 , chest center coupling frame  54 , and intrathoracic joint frame  55 . Chest lower portion  5 D is configured to include backbone  56  and link attaching frame  57 . Intrathoracic joint  16  connects chest upper portion  5 U and chest lower portion  5 D with one rotational degree of freedom at which chest upper portion  5 U and chest lower portion  5 D can be rotated vertically. 
     Shoulder frame  51  is a frame connecting positions corresponding to both shoulders. Thorax frame  52  is a bent frame provided on the right and left on a lower side of shoulder frame  51 . The variable length link that moves upper arm  7  is attached to thorax frame  52 . Thorax front-back coupling frame  53  is a frame connecting thorax frames  52  in a front-back direction. Chest center coupling frame  54  is a frame connecting right and left thorax front-back coupling frames  53 . Intrathoracic joint frame  55  is a plate-shaped frame provided on the lower side of each of right and left thorax front-back coupling frames  53 . Intrathoracic joint frame  55  constitutes intrathoracic joint  16  together with backbone  56 . 
     Backbone  56  is a T-shaped rod viewing from the front. A horizontal cylindrical portion on an upper side of backbone  56  is referred to as an intrathoracic rotation shaft  56 T. Intrathoracic rotation shaft  56 T is sandwiched rotatably between two intrathoracic joint frames  55  to form intrathoracic joint  16 . 
     A vertically extending portion of backbone  56  has a columnar shape. Backbone  56  is a coupling rod coupling chest  5  and waist  6 . A thoracolumbar joint  18  connecting backbone  56  rotatably to waist  6  with three rotational degrees of freedom is provided at a lower end of backbone  56 . A spherical bearing is used for thoracolumbar joint  18 . Link attaching frame  57  is connected to the upper side of intrathoracic rotation shaft  56 T. The variable length link that rotates chest  5  with respect to waist  6  is attached to link attaching frame  57 . In  FIGS. 16 to 20 , not only members included in chest upper portion  5 U but also link attaching frame  57  provided in chest lower portion  5 D are illustrated in order to identify an attaching position of the variable length link that rotates chest  5  with respect to waist  6 . 
     As illustrated in  FIG. 5 , portions near right and left ends of shoulder frame  51  are bent backward by an angle ξ 1  with respect to the X-axis. Shoulder joint  13  connecting upper arm  7  rotatably to chest  5  with two rotational degrees of freedom is connected to each of two ends of shoulder frame  51 . Shoulder joint  13  is a biaxial gimbal having two rotation axes orthogonal to each other. A biaxial gimbal of shoulder joint  13  has a shape, in which a member (referred to as a rotation member) that is rotated around a rotation axis Rx 1  existing in a direction of shoulder frame  51  is sandwiched by a yoke provided in upper arm  7  such that an angle formed by upper arm  7  and the rotation member can be changed (rotatably). The yoke has members opposed to each other, and holes or protrusions for holding another member rotatably are provided in the yoke. A member, which is held in holes provided in the yoke and enable to rotate another member, is referred to as a shaft member. In the biaxial gimbal, the rotation axis of the rotation member and the shaft member are orthogonal to each other. In shoulder joint  13 , two protrusions existing on a straight line orthogonal to the rotation axis of the rotation member are inserted in holes provided in the yoke. This enables the yoke to hold the rotation member rotatably. Shoulder joint  13  has the structure described above, so that upper arm  7  can be rotated around the rotation axis existing in the direction in which shoulder frame  51  extends. The angle formed by upper arm  7  and shoulder frame  51  can also be changed. 
     Thorax frame  52  is connected to the lower side of shoulder frame  51  at a place slightly closer to the center side than the places where portions near the right and left ends of shoulder frame  51  are bent backward. Thorax frame  52  has an L-shape viewing from the front-back direction, and has a shape like a rectangle without lower side in which both upper corners of the rectangle are cut viewing from the side. Thorax frame  52  extending downward in the front-back direction from shoulder frame  51  is bent into an L-shape and extends horizontally toward the center side. Portions extending horizontally at the front side and the rear side of thorax frame  52  are coupled together on the center side by thorax front-back coupling frame  53 . Right and left thorax front-back coupling frames  53  are coupled together by chest center coupling frame  54 . 
     A chest-side main link attaching unit J 1  is provided at the L-shaped corner portion on the front side of thorax frame  52 . An upper arm drive main link  14 L (illustrated in  FIG. 37 ), which is a variable length link of an upper arm drive main actuator  14  that moves upper arm  7 , is attached rotatably to a chest-side main link attaching unit J 1  with two rotational degrees of freedom. A chest-side auxiliary link attaching unit J 2  is provided at the L-shaped corner portion on a rear side. Chest-side auxiliary link attaching unit J 2  is a biaxial gimbal to which an upper arm drive auxiliary link  15 L is attached rotatably with two rotational degrees of freedom. There exists a space where upper arm drive main actuator  14  and upper arm drive auxiliary actuator  15  can move freely between thorax frames  52  on the lower side of shoulder frame  51 . 
     Chest-side main link attaching unit J 1  has a structure in which a yoke provided on a rotation member sandwiches and holds a columnar protrusion (shaft member) provided on upper arm drive main link  14 L rotatably. The rotation member is a member that is rotated around the rotation axis (Y-axis) perpendicular to thorax frames  52 . The protrusions (shaft members) protrude vertically from both side surfaces opposite to each other in the rectangular tubular portion of upper arm drive main link  14 L. Chest-side auxiliary link attaching unit J 2  has the same structure. That is, chest-side main link attaching unit J 1  and chest-side auxiliary link attaching unit J 2  are biaxial gimbals each including the rotation member and the yoke provided on thorax frame  52 . The rotation axis around which the rotation member of chest-side main link attaching unit J 1  is rotated and the rotation axis around which the rotation member of chest-side auxiliary link attaching unit J 2  is rotated exist on the same straight line. 
     Plate-shaped intrathoracic joint frame  55  parallel to a YZ-plane is connected to the lower side in the central of thorax front-back coupling frame  53 . A mechanism that holds rotatably the intrathoracic rotation shaft  56 T is provided in intrathoracic joint frame  55 . Intrathoracic rotation shaft  56 T is a horizontal cylindrical portion provided in an upper portion of backbone  56 . Intrathoracic rotation shaft  56 T is sandwiched rotatably between two intrathoracic joint frames  55  to form intrathoracic joint  16 . Intrathoracic joint  16  connects chest upper portion  5 U and chest lower portion  5 D with one rotational degree of freedom at which chest upper portion  5 U and chest lower portion  5 D are rotatable in the front-back direction. A connection angle between chest upper portion  5 U and chest lower portion  5 D is determined by a length of an intrathoracic link  17 L (illustrated in  FIG. 22 ) in which one end is connected to chest upper portion  5 U while the other end is connected to chest lower portion  5 D. Intrathoracic actuator  17  is provided in the center on the front side of chest  5 . 
     One end of intrathoracic link  17 L is attached rotatably to backbone  56  through a lower intrathoracic link attaching unit J 3 . The yoke of lower intrathoracic link attaching unit J 3  protrudes forward from backbone  56 , and intrathoracic link  17 L is sandwiched rotatably by the yoke. The other end of intrathoracic link  17 L is attached rotatably to chest center coupling frame  54  through an upper intrathoracic link attaching unit J 4 . The yoke of upper intrathoracic link attaching unit J 4  is provided in chest center coupling frame  54 . A chest bending unit C 1  is configured to include intrathoracic joint  16 , intrathoracic actuator  17 , upper intrathoracic link attaching unit J 4 , and lower intrathoracic link attaching unit J 3 . 
     As illustrated in  FIGS. 22, 23, and 24 , a thoracolumbar center actuator  19 , a thoracolumbar right actuator  20 , and a thoracolumbar left actuator  21  exist between chest  5  and waist  6 . A thoracolumbar center link  19 L connects a center point existing on the rear side in the lower portion of chest  5  and a center point existing on the rear side in thoracolumbar joint  18  of the waist  6 . A thoracolumbar right link  20 L connects a tight point existing on the front side in the lower portion of chest  5  and a right point existing on the rear side of waist  6 . A thoracolumbar left link  21 L connects a left point existing on the front side in the lower portion of chest  5  and a left point existing on the rear side of waist  6 . Viewing from above, thoracolumbar right link  20 L and thoracolumbar left link  21 L exist so that they sandwich backbone  56 . Thoracolumbar right link  20 L and thoracolumbar left link  21 L are directed from the front-side position in chest  5  to the rear-side position in waist  6 . 
     In link attaching frame  57 , a chest center link attaching unit J 5  is provided in the center on the rear side, a chest right link attaching unit J 6  is provided on the right of the front side, and a chest left link attaching unit J 7  is provided on the left of the front side. Chest center link attaching unit J 5 , chest right link attaching unit J 6 , and chest left link attaching unit J 7  are provided so that they are located at the same height as intrathoracic joint  16  in the reference state. One ends of thoracolumbar center link  19 L, thoracolumbar right link  20 L, and thoracolumbar left link  21 L are attached rotatably to chest center link attaching unit J 5 , chest right link attaching unit J 6 , and chest left link attaching unit J 7  with two rotational degrees of freedom, respectively. 
     Chest center link attaching unit J 5  has the structure in which thoracolumbar center link  19 L is sandwiched rotatably by the yoke, which protrudes from the link attaching frame  57  to the rear side and is rotated around the rotation axis parallel to the Y-axis. Chest right link attaching unit J 6  has the structure in which thoracolumbar right link  20 L is sandwiched rotatably by the yoke, which protrudes from link attaching frame  57  to the front oblique right and is rotated around the rotation axis. Chest left link attaching unit J 7  has the structure in which thoracolumbar left link  21 L is sandwiched rotatably by the yoke, which protrudes from link attaching frame  57  to the front oblique left and is rotated around the rotation axis. 
     The structure of the variable length link is described with thoracolumbar center link  19 L being the variable length link included in thoracolumbar center actuator  19  as an example.  FIG. 25  is a cross-sectional view illustrating the structure of the variable length link included in the actuator.  FIG. 25  also illustrates a motor  19 M not illustrated in cross-sectional view. A positional relationship between motor  19 M and cylinder  19 C is fixed. Thoracolumbar center link  19 L includes a screw rod  19 A, a nut  19 B, a cylinder  19 C, a nut position fixer  19 D, a nut rotation holder  19 E, and a nut gear  19 F. Screw rod  19 A is a rod having a circular shape in cross section, and male threads are provided on a side surface of screw rod  19 A. Nut  19 B is a female screw member including a through-hole in which female threads meshing with screw rod  19 A is provided on the inner surface. Cylinder  19 C accommodates a part of screw rod  19 A and nut  19 B therein. Nut position fixer  19 D fixes the axial position of nut  19 B with respect to cylinder  19 C. Nut rotation holder  19 E holds rotatably nut  19 B with respect to cylinder  19 C. Nut gear  19 F is a gear that is rotated together with nut  19 B. 
     Nut position fixer  19 D is protrusions circumferentially provided in cylinder  19 C to prevent nut  19 B from moving. The protrusions being nut position fixer  19 D are provided so that they sandwich the circumferentially-provided protrusion included in nut  19 B. Nut position fixer  19 D is provided at three places. The three places are the connecting portion between nut gear  19 F and nut  19 B and both sides of nut rotation holder  19 E. Any nut position fixer  19 D may be used as long as nut position fixer  19 D fixes the relative position in the axial direction of nut  19 B with respect to cylinder  19 C. The axial direction of screw rod  19 A is also the length direction of cylinder  19 C. 
     Nut gear  19 F is disposed outside cylinder  19 C. Nut gear  19 F meshes with a drive gear  19 G provided on the rotation shaft of motor  19 M. Nut gear  19 F and nut  19 B are rotated when drive gear  19 G is rotated. Nut  19 B is moved with respect to screw rod  19 A when nut  19 B is rotated. Because the position of nut  19 B is fixed with respect to the length direction of cylinder  19 C, screw rod  19 A is moved with respect to nut  19 B and cylinder  19 C when nut  19 B is rotated. Screw rod  19 A is moved by force generated by motor  19 M. 
     One end of screw rod  19 A is attached rotatably to link attaching frame  57  through chest center link attaching unit J 5 . One end of cylinder  19 C is attached rotatably to a waist main frame  61  through a waist center link attaching unit J 10 . A distance between chest center link attaching unit J 5  and waist center link attaching unit J 10  increases when screw rod  19 A is moved in the direction protruding from cylinder  19 C. The distance between chest center link attaching unit J 5  and waist center link attaching unit J 10  is shorten when screw rod  19 A is moved in the direction entering into cylinder  19 C. In this way, the length of thoracolumbar center link  19 L can be changed, and the distance between two points being attached with both ends of thoracolumbar center link  19 L can be changed. 
     The end of thoracolumbar center link  19 L on the side where screw rod  19 A exists may be attached to waist  6  instead of chest  5 . In this case, cylinder  19 C is attached to chest  5 . One end of screw rod  19 A in which the male threads are provided is attached to one of the link attaching units on both sides of thoracolumbar center link  19 L. One end of cylinder  19 C is attached to the link attaching unit not being attached with screw rod  19 A among the link attaching units at both ends of thoracolumbar center link  19 L. 
     Nut  19 B includes a through-hole in which female threads meshing with male threads provided on screw rod  19 A is provided on an inner surface. Nut  19 B is rotated by transmitting the force from motor  19 M. Nut  19 B is referred to as a perforated member because nut  19 B has a through-hole. Cylinder  19 C is a tube that accommodates screw rod  19 A and nut  19 B. Nut position fixer  19 D is a perforated member position fixer that fixes a position of nut  19 B with respect to cylinder  19 C in the axial direction of screw rod  19 A. Nut rotation holder  19 E is a perforated member holder, which is provided between nut  19 B and cylinder  19 C and holds nut  19 B rotatably with respect to cylinder  19 C. Because thoracolumbar center link  19 L includes the perforated member holder, thoracolumbar center link  19 L being a variable length link has one rotational degree of freedom, that is, thoracolumbar center link  19 L can be rotated around the axis. The rotation around the axis means that both ends of the link differ from each other in the rotation angle around the axis. The variable length link has one rotational degree of freedom, so that the link attaching units being attached with both ends of the variable length link may have two rotational degrees of freedom. In the case that the variable length link does not have one rotational degree of freedom, the link attaching unit being attached with either end of the variable length link has three rotational degrees of freedom. Here, the case where the variable length link has one rotational degree of freedom around the axis and includes both ends attached to the link attaching units with two rotational degrees of freedom, and the case where one end of the variable length link is attached to the link attaching unit with three rotational degrees of freedom and the other end is attached to the link attaching unit with two rotational degrees of freedom are defined as the variable length link having five rotational degrees of freedom. 
     The variable length links included in thoracolumbar right link  20 L, thoracolumbar left link  21 L, and other actuators also have the same structure. 
     A screw, such as a ball screw and a bench screw, which has a small friction coefficient while rotating, is used as a screw between the screw rod and the nut. When a screw pitch is the same, the force necessary to change the length of the variable length link is decreased with decreasing friction coefficient. For this reason, the maximum output of the motor may be smaller than that of the case that the friction coefficient is large. Power consumption required for operation of the actuator is also decreased. Frictional force in a still state is set to such magnitude that the nut is not rotated when the motor does not generate drive force. This enables the angle before interruption of electric power supply to be maintained at each joint of the humanoid robot can be maintained when the electric power supply is interrupted. When the humanoid robot is in a still state, its posture can be maintained. When the humanoid robot holds an object, the state in which the humanoid robot holds the object can be maintained. 
     It is assumed that the magnitude of the frictional force is set such the magnitude that the angle of each joint can be changed by the force of one or a plurality of persons when the electric power supply is interrupted. In a disaster in which the electric power supply is interrupted, there is a possibility that the humanoid robot may interfere with rescue of injured person. When the posture of the humanoid robot can be changed, for example, the humanoid robot can be changed to the posture so as not to interfere with the rescue, or the humanoid robot can be moved. Whether the nut is rotated by the force trying to change the length of the variable length link depends on not only the friction coefficient of the screw but also the pitch. When the friction coefficient is the same, the minimum value of the force with which the nut is rotated can be increased when the pitch is decreased. A screw pitch and a friction coefficient are determined such that the minimum value of the force that can change the length of the variable length link by rotating the nut becomes a proper value. 
     The tube accommodating the screw rod and the nut may be a square tube, or have a side surface in which a flat surface and a curved surface are combined with each other. A diameter of the tube may be changed in a length direction. The variable length link may have any structure as long as one end of the screw rod is attached to the link attaching unit with at least two rotational degrees of freedom and the other end on the side where the tube or motor exists is attached to the link attaching unit with at least two rotational degrees of freedom. The end on the tube or motor side may be attached to the link attaching unit with an attachment interposed therebetween. A portion that is not the end of the tube may be attached to the link attaching unit. In this case, the variable length link is up to the place of the tube attached to the link attaching unit, and one end of the variable length link is attached to the link attaching unit. 
     Waist  6  includes a waist main frame  61  in which thoracolumbar joint  18  is provided, a lower limb connecting frame  62  to which lower limb  4  is connected, and a waist cover  63  covering a lower portion on the rear side of waist main frame  61 . Lower limb connecting frame  62  is provided on each of the right and left. In a space between waist cover  63  and waist main frame  61 , a power supply device is disposed, and wiring and the like are routed. 
     When viewed from above, waist main frame  61  has a shape in which a rectangle and a circle are combined such that a part of the circle overlaps with the front side of the rectangle. Waist main frame  61  includes two thick plate-shaped portions protruding rearward from the rectangular portion at symmetrical positions on the rear side. When viewed from above, the circular portion is a cylinder in which thoracolumbar joint  18  exists. Thoracolumbar joint  18  includes a spherical bearing that holds a spherical surface provided at one end of backbone  56  with three rotational degrees of freedom. As illustrated in  FIG. 12 , waist right link attaching unit J 8  and waist left link attaching unit J 9 , to which the other ends of thoracolumbar right link  20 L and thoracolumbar left link  21 L are attached rotatably with two rotational degrees of freedom, respectively, are provided on the upper side of the two thick plate-shaped portions protruding rearward. Waist center link attaching unit J 10  to which thoracolumbar center link  19 L is attached rotatably with two rotational degrees of freedom is provided in the center on the rear side in the upper portion of waist main frame  61 . 
     Each of waist right link attaching unit J 8 , waist left link attaching unit J 9 , and waist center link attaching unit J 10  is a biaxial gimbal. A yoke including a through-hole is provided rotatably and facing upward, in waist right link attaching unit J 8  and waist left link attaching unit J 9 . The shaft member provided on the variable length link is inserted into the through-hole. In waist center link attaching unit J 10 , the yoke having the through-hole is provided rotatably so that it is directed toward the rear side. 
       FIG. 26  is a schematic diagram illustrating a division between chest upper portion  5 U and chest lower portion  5 D and arrangement of the variable length links that drive chest  5 . In  FIG. 26 , for the purpose of easy understanding of the link arrangement, intrathoracic link  17 L is illustrated on the front side than an actual position.  FIG. 27  is a schematic view illustrating the division and the arrangement viewing from the front. Chest lower portion  5 D is illustrated with hatching. Chest lower portion  5 D can be rotated around thoracolumbar joint  18  around the X-axis, the Y-axis, and the Z-axis by three variable length links. Chest upper portion  5 U can be rotated around the X-axis by one variable length link with respect to chest lower portion  5 D. 
     A body bending unit C 2  is a three-rotational-degree-of-freedom connection mechanism that connects chest  5  rotatably to waist  6  with three rotational degrees of freedom. Body bending unit C 2  includes thoracolumbar joint  18 , thoracolumbar center actuator  19 , thoracolumbar right actuator  20 , thoracolumbar left actuator  21 , chest center link attaching unit J 5 , chest right link attaching unit J 6 , chest left link attaching unit J 7 , waist center link attaching unit J 10 , waist right link attaching unit J 8 , and waist left link attaching unit J 9 . The three rotational degrees of freedom means that the rotation can be performed with a total of three degrees of freedom including one degree of freedom by tilting chest  5  to the front-back direction (the rotation around the X-axis) with respect to waist  6 , one degree of freedom by tilting chest  5  in the right and left direction (the rotation around the Y-axis), and one degree of freedom by turning chest  5  around backbone  56  (Z-axis) with respect to waist  6 . The three-rotational-degree-of-freedom connection mechanism according to the present disclosure has a simple structure including a three-rotational-degree-of-freedom joint and three actuators. When considered more broadly, the three-rotational-degree-of-freedom connection mechanism is a rotation connecting mechanism that connects a second member rotatably to a first member. The rotation connecting mechanisms in which the joint has three rotational degrees of freedom is the three-rotational-degree-of-freedom connection mechanism. 
     When body bending unit C 2  is generally considered as the three-rotational-degree-of-freedom connection mechanism, body bending unit C 2  connects chest  5  being the second member on the connecting side rotatably to waist  6  being the first member on the connected side with three rotational degrees of freedom. Thoracolumbar joint  18  is a joint part that connects chest  5  rotatably to waist  6  with three rotational degrees of freedom. Backbone  56  is a torsion axis in which the direction is fixed with respect to chest  5 . Chest  5  is rotatable around backbone  56  with respect to waist  6 . In the three-rotational-degree-of-freedom connection mechanism, a member provided on the side closer to waist  6  is defined as the first member. A member provided on the side far from waist  6  is defined as the second member. Thoracolumbar joint  18  allows chest  5  being the second member to be rotated around the torsion axis with respect to the waist  6  being the first member, and connects the second member rotatably to the first member with three rotational degrees of freedom. 
     Thoracolumbar center actuator  19 , thoracolumbar right actuator  20 , and thoracolumbar left actuator  21  are three actuators each including the variable length link having the variable length and the motor that generates force changing the length of the variable length link. Waist center link attaching unit J 10 , waist right link attaching unit J 8 , and waist left link attaching unit J 9  are three first-member-side link attaching units provided in waist  6  (first member). One end of each of the three actuators is attached rotatably to each of the three first-member-side link attaching units with at least two rotational degrees of freedom. The positional relationships among waist center link attaching unit J 10 , waist right link attaching unit J 8 , and waist left link attaching unit J 9  are fixed with respect to thoracolumbar joint  18 . Chest center link attaching unit J 5 , chest right link attaching unit J 6 , and chest left link attaching unit J 7  are three second-member-side link attaching units provided in chest  5  (second member). The other end of each of the three actuators is attached rotatably to each of the three second-member-side link attaching units with at least two rotational degrees of freedom. The positional relationships among chest center link attaching unit J 5 , chest right link attaching unit J 6 , and chest left link attaching unit J 7  are fixed with respect to thoracolumbar joint  18 . 
     In the reference state in which humanoid robot  100  stands upright, in body bending unit C 2 , the torsion axis (the backbone, the Z-axis) and other two rotation axes (the X-axis and the Y-axis) in three rotatable axes can be rotated in both directions. Chest center link attaching unit J 5 , chest right link attaching unit J 6 , chest left link attaching unit J 7 , waist center link attaching unit J 10 , waist right link attaching unit J 8 , and waist left link attaching unit J 9  are arranged such that the maximum value of three angles formed by three links and the torsion axis is greater than or equal to an angle δ 0  (for example, about 3 degrees). 
     In all three-rotational-degree-of-freedom connection mechanisms included in humanoid robot  100 , at least one axis of the torsion axis and the other two rotation axes is determined to be rotatable in both directions in the reference state. That is, in the reference state of each three-rotational-degree-of-freedom connection mechanism, rotation can be performed in both directions on at least two rotation axes including the torsion axis. 
     In body bending unit C 2 , for example, the upper half body above thoracolumbar joint  18  can be tilted forward by about 20 degrees, tilted backward by about 20 degrees, and tilted in the right and left direction by about 20 degrees. Chest  5  can be rotated (twisted) with respect to waist  6  around backbone  56  by about 20 degrees in both directions. For example, chest upper portion  5 U can be tilted forward by about 15 degrees with respect to chest lower portion  5 D, and tilted backward by about 20 degrees with respect to chest lower portion  5 D by the intrathoracic joint  16 . For this reason, for example, when chest lower portion  5 D is tilted in the front-back direction, chest upper portion  5 U can be kept vertical. The posture that makes both hands easy to work can be taken. The movable range is an example, and the movable range can be widened or narrowed. 
       FIG. 28  is a perspective view illustrating the arrangement of the variable length links in body bending unit C 2  in the reference state in which humanoid robot  100  stands upright viewing from the oblique rear on the left hand side. Body bending unit C 2  includes three variable length links  19 L,  20 L,  21 L, which connect three second-member-side link attaching units J 5 , J 6 , J 7  provided in chest lower portion  5 D to three first-member-side link attaching unit J 10 , J 8 , J 9  provided in waist  6 , respectively. The positions of three second-member-side link attaching units J 5 , J 6 , J 7  provided in chest lower portion  5 D are fixed with respect to thoracolumbar joint  18 . The positions of three first-member-side link attaching units J 10 , J 8 , J 9  provided in waist  6  are fixed with respect to thoracolumbar joint  18 . A connection angle of chest lower portion  5 D with respect to waist  6  can be changed with three rotational degrees of freedom by changing the lengths of three variable length links  19 L,  20 L,  21 L. It is assumed that as is the rotation angle around the X-axis of thoracolumbar joint  18 , that βs is the rotation angle around the Y-axis, and that γs is the rotation angle around the Z-axis. Chest upper portion  5 U can be rotated around the X-axis with respect to the chest lower portion  5 D by intrathoracic joint  16 . It is assumed that ψ is the rotation angle around the X axis at intrathoracic joint  16 . 
     A range of the direction, in which the torsion axis is directed and is changed by the rotation of the joint such as thoracolumbar joint  18 , is referred to as a movable range of the joint. The example illustrated above as the angle range rotatable around the front-back direction and the right and left direction of thoracolumbar joint  18  and backbone  56  indicates the maximum angle range that can be taken on the rotation axis. The angle range that can be taken by a rotation axis is influenced by the angle taken by another rotation axis. For this reason, all the regions obtained by arbitrarily combining the angular ranges of the rotation axes do not become the movable range. The same holds true for other joints. 
       FIG. 29  is a view illustrating the arrangement of the variable length links in body bending unit C 2  viewing from the direction in which the backbone extends. In  FIG. 29 , backbone  56  being the torsion axis is represented by a double circle. Chest center link attaching unit J 5 , chest right link attaching unit J 6 , and chest left link attaching unit J 7 , being the second-member-side link attaching unit, are represented by a white circle. Waist center link attaching unit J 10 , waist right link attaching unit J 8 , and waist left link attaching unit J 9 , being the first-member-side link attaching unit, are represented by a black circle. Thoracolumbar center link  19 L, thoracolumbar right link  20 L, and thoracolumbar left link  21 L, being the variable length links, are represented by a bold line. The similar expression is made in other similar drawings. A triangle formed by connecting three second-member-side link attaching units is referred to as a second-member-side triangle T 1 . 
     The following facts can be understood from  FIGS. 28 and 29 . Variable length links  20 L,  21 L are long, are located at a twisted position with respect to torsion axis  56 , and are largely inclined with respect to the horizontal plane. Viewing from the direction of torsion axis  56 , variable length links  20 L,  21 L are substantially parallel to each other such that torsion axis  56  is sandwiched therebetween. The rotation direction around torsion axis  56  for shortening the variable length link  20 L and the rotation direction around torsion axis  56  for shortening the variable length link  21 L are opposite to each other. For this reason, when second member  6  is rotated, one of variable length links  20 L,  21 L is lengthened, and the other is shortened. Consequently, in the rotation around torsion axis  56 , both the force pushed by the extending link and the force drawn by the shortening link are generated, the rotation is performed around torsion axis  56  easily. In body bending unit C 2 , in each state within the movable range, the rotation around the torsion axis causes both of lengthening and shortening of the variable length links. 
     Torsion axis  56  represented by a double circle is located inside of second-member-side triangle T 1 , and exists on a bisector of a base side of second-member-side triangle T 1 . The bisector of the base side of the second-member-side triangle is referred to as a symmetrical axis line, and the base side is referred to as a symmetrical axis perpendicular line. When variable length links  20 L,  21 L are similarly expanded while variable length link  19 L is contracted, the tilt of second member  6  can be changed in the direction of the symmetrical axis line. When variable length links  20 L,  21 L are similarly contracted while variable length link  19 L is expanded, the tilt of second member  6  can be changed to the opposite direction in the direction of the symmetrical axis line. While the length of variable length link  19 L is kept unchanged, when variable length link  20 L is lengthened, and variable length link  21 L is shortened, or when variable length link  20 L is shortened, and variable length link  21 L is lengthened, the tilt of second member  6  can be changed in the direction of the symmetrical axis perpendicular line. 
     It is examined about the condition on the arrangement of the links that allows the second member to be rotated around the torsion axis by the expansion and contraction of the variable length link.  FIG. 30  is a view illustrating whether a torque rotating around the torsion axis is generated by the expansion and contraction of the variable length link depending on the positional relationship between the torsion axis and the variable length link. In  FIG. 30 , it is assumed that the lower end (indicated by the white circle) of variable length link L 3  has the fixed positional relationship with the torsion axis.  FIG. 30( a )  illustrates the case that a torsion axis G 1  and variable length link L 1  are parallel with each other.  FIG. 30( b )  illustrates the case that a torsion axis G 2  and variable length link L 2  are located on the same plane and are not parallel with each other.  FIG. 30( c )  illustrates the case that a torsion axis G 3  and variable length link L 3  have a twisted relationship. In each of  FIGS. 30( a ) to 30( c ) , the view viewed from the direction of the torsion axis is illustrated on the upper side, and the view viewed from the direction perpendicular to the torsion axis is illustrated on the lower side.  FIG. 30( c )  also illustrates the view viewed from the direction being perpendicular to the torsion axis and being able to view a lower end P 3  of variable length link L 3  on torsion axis G 3  (illustrated by an arrow A). 
     In the case that torsion axis G 1  and variable length link L 1  are parallel with each other, as illustrated in  FIG. 30( a ) , torsion axis G 1  and variable length link L 1  are points viewing from the direction of torsion axis G 1 . Thus, a component of the force in the direction perpendicular to torsion axis G 1  and the torque rotating around torsion axis G 1  are not generated by the expansion and contraction of variable length link L 1 . In the case that torsion axis G 2  and variable length link L 2  are located on the same plane and are not parallel with each other, as illustrated in  FIG. 30( b ) , variable length link L 2  is directed in the direction of torsion axis G 2 . For this reason, although the component of the force applying in the direction perpendicular to torsion axis G 2  is generated by the expansion and contraction of variable length link L 2 , the torque rotating around torsion axis G 1  is zero because the component is directed in the direction of torsion axis G 2 . In the case that torsion axis G 3  and variable length link L 3  have the twisted relationship, as illustrated in  FIG. 30( c ) , the torque around torsion axis G 3  is generated in proportion to an area of a triangle U 3  by the expansion and contraction of variable length link L 3 . 
     Because a distance K between one end P 3  of variable length link L 3  and torsion axis G 3  is fixed, the torque is determined by a distance D between the other end Q 3  of variable length link L 3  and a plane (referred to as a link reference plane) determined by torsion axis G 3  and one end P 3 . A ratio (D/W) of distance D to a length (represented by W) of the variable length link L 3  represents a change amount of distance D in the case that the length of variable length link L 3  is changed by a unit amount. Assuming that θ is an angle (referred to as the tilt angle) formed by the link reference plane and variable length link L 3 , the following equation holds. 
       sin θ= D/W  
 
     In  FIGS. 30( a ) and 30( b ) , the tilt angle θ is determined to be θ=0. In order to generate the necessary torque around the torsion axis by the expansion and contraction of the variable length link, tilt angle θ is required to be greater than or equal to a predetermined angle δ 0  (for example, about 3 degrees). Here, the case of one variable length link is examined. However, in the case of at least two variable length links, the maximum value among the tilt angles of the variable length links may be greater than or equal to δ 0 . The link reference plane is a plane that is determined in each variable length link. Specifically, when the direction of the torsion axis is fixed with respect to the first member, the link reference plane is a plane including the torsion axis and the first-member-side link attaching unit of the variable length link. When the direction of the torsion axis is fixed with respect to the second member, the link reference plane is a plane including the torsion axis and the second-member-side link attaching unit of the variable length link. 
     In the case of tilt angle θ, a torque TA by the variable length link L 3  is given as follows. 
         TA∝K*W* sinθ= K*D= 2*area of triangle  U 3
 
     The torque required to rotate the second member around the torsion axis also relates to inertia moment of the second member. The threshold value δ 0  with respect to tilt angle θ may be set to the same value in all three-rotational-degree-of-freedom connection mechanisms, or set in each three-rotational-degree-of-freedom connection mechanism. In determining tilt angle θ, the change amount of the length of the variable length link may be not the unit amount but a change amount in consideration of a width of the variable range of the length of the variable length link. 
     In the reference state, variable length link  19 L and torsion axis  56  are located on the same plane, and a tilt angle θs 1  formed by variable length link  19 L and the link reference plane is 0 degree. Variable length link  20 L and variable length link  21 L have the twisted relationship with torsion axis  56 . Tilt angles θs 2  and θs 3  of variable length link  20 L and variable length link  21 L are about 41 degrees. A maximum value θsmax of the tilt angles between three variable length links  19 L,  20 L,  21 L and the link reference plane is greater than or equal to δ 0 . Thus, the torque around torsion axis  56  can be generated when any one of variable length links  20 L,  21 L expands or contracts. 
     Because tilt angles θs 2  and θs 3  are about 41 degrees, at least one of tilt angles θs 2  and θs 3  is greater than or equal to δ 0  when chest  5  is tilted largely. That is, in each state within the movable range of thoracolumbar joint  18 , at least one of three variable length links  19 L,  20 L,  21 L has a twisted relationship with torsion axis  56 . Furthermore, the tilt angle formed by the link reference plane and variable length link  20 L is greater than or equal to δ 0 . Because the direction of torsion axis  56  is fixed to second member  5 , the link reference plane is a plane including chest right link attaching unit J 6  or chest left link attaching unit J 7 , which is the second-member-side link attaching unit, and torsion axis  56 . 
       FIG. 31  is a view illustrating the arrangement of the variable length links in body bending unit C 2  when chest  5  is rotated and tilted forward viewing from the direction in which the backbone extends. In  FIG. 31 , chest  5  (second member) is twisted to the left by 15 degrees, and tilted forward by 30 degrees in the direction of 15 degrees to the left. Because the direction of torsion axis  56  is fixed with respect to chest  5 , when torsion axis  56  is tilted, waist  6  (first member) is viewed to be expanded or contracted in the direction in which waist  6  is tilted when viewed from the direction of torsion axis  56  depending on the tilted angle. In  FIG. 31 , waist  6  is contracted to cos(30 degrees)=about 0.87 times. Because of the rotation around torsion axis  56 , variable length link  20 L is lengthened and variable length link  21 L is shortened. In the case other than the rotation around torsion axis  56 , the following result is obtained. In the case that torsion axis  56  is tilted forward, both tilt angles θs 2 , θs 3  of variable length links  20 L,  21 L are decreased. In the case that torsion axis  56  is tilted to the right, tilt angle θs 2  of variable length link  20 L is increased and tilt angle θs 3  of variable length link  21 L is decreased. In body bending unit C 2 , maximum value θsmax of the tilt angle is greater than or equal to about 30 degrees even if body bending unit C 2  is tilted in what way within the movable range. In the case that the movable range of the joint is determined such that rotation around the torsion axis is not required in the vicinity of the boundary within the movable range, maximum value θsmax of the tilt angle may not be greater than or equal to determined angle δ 0  in the vicinity of the boundary within the movable range. 
     The description is returned to the structure of waist  6 . Lower limb connecting frame  62  has a substantially rectangular plate member. Lower limb connecting frame  62  is fixed to the right and left in the lower portion of waist main frame  61  such that the front side of lower limb connecting frame  62  is higher than the rear side. A protrusion  64  protrudes inside (the side closer to the center of the body) perpendicularly from lower limb connecting frame  62 . At a tip of protrusion  64 , a hip joint  22  is provided to connect thigh  10  to waist  6  outward and obliquely upward. Hip joint  22  includes a spherical bearing in which a spherical surface provided on waist  6  is surrounded by a recess provided on thigh  10 . Hip joint  22  includes a spherical member and a spherical receiving member provided at the end of thigh  10  that holds the spherical surface of the spherical member rotatably with three rotational degrees of freedom. The spherical member includes a spherical surface protruding obliquely outward and upward from protrusion  64  that is a part of waist  6 . Consequently, the movable range of thigh  10  can be widened. 
     Protrusion  65  protrudes from the front side of lower limb connecting frame  62 , and a crotch front link attaching unit J 11  is provided on the front side at the tip of protrusion  65 . A thigh front link  23 L (illustrated in  FIG. 57 ) that rotates hip joint  22  is attached to crotch front link attaching unit J 11 . Protrusion  65  is bent, and has the surface of the portion on which crotch front link attaching unit J 11  is provided and that is substantially vertical in the reference state. In crotch front link attaching unit J 11 , the rotation member and the cylinder rotated by the rotation member are provided on protrusion  65 , and the yoke and the shaft member are provided at one end of thigh front link  23 L. Crotch front link attaching unit J 11  is a biaxial gimbal having a structure in which the shaft member provided rotatably at one end of thigh front link  23 L is inserted into the cylinder provided on protrusion  65 . 
     Protrusion  66  protrudes from the vicinity of the corner on the rear side outside lower limb connecting frame  62 , and a crotch outside link attaching unit J 12  is provided on an outside surface of the tip of protrusion  66 . A thigh outside link  24 L is attached to crotch outside link attaching unit J 12 . Protrusion  67  protrudes vertically from the vicinity of the corner existing on the rear side and inside of lower limb connecting frame  62 , and a crotch inside link attaching unit J 13  is provided on an inside surface of the tip of protrusion  67 . A thigh inside link  25 L is attached to crotch inside link attaching unit J 13 . Protrusion  67  is bent, and crotch inside link attaching unit J 13  is provided obliquely below on the inside. Crotch outside link attaching unit J 12  and crotch inside link attaching unit J 13  are a biaxial gimbal having the same structure as that of crotch front link attaching unit J 11 . 
     Referring to  FIGS. 5, 10, 12, 13, 32, and 33 , the structure of head  2  is described.  FIG. 32  is an enlarged side view of head  2 .  FIG. 33  is an enlarged perspective view of head  2 . A neck center rod  26  extends upward from the center of the upper surface of shoulder frame  51 . Head  2  is connected to a neck joint  27  provided at the tip of neck center rod  26 . A spherical bearing in which a spherical surface is provided at the tip of neck center rod  26  is used in neck joint  27 . Neck joint  27  connects head  2  and chest  5  rotatably with three rotational degrees of freedom. Head  2  includes an octagonal plate-shaped head base plate  2 A in which four corners of a square are cut. A device that implements functions such as an eye, an ear, and a mouth is attached to head base plate  2 A. 
     Head  2  can be rotated around neck joint  27  with three rotational degrees of freedom by a neck rear actuator  28 , a neck right-side actuator  29 , and a neck left-side actuator  30 . That is, head  2  can be tilted by, for example, about 20 degrees in the front-back direction and the right and left direction. Head  2  can be rotated around neck center rod  26  in both directions by, for example, about 60 degrees. 
     A neck lower frame  58  is provided on the upper surface of the shoulder frame  51 . One ends of the variable length links included in the three actuators that move head  2  are attached to neck lower frame  58 . Neck lower frame  58  includes three plate-like portions extending from the center at intervals of 120 degrees on a horizontal plane. Tips of the three plate-shaped portions are bent by 90 degrees, and a neck rear link attaching unit J 14 , a neck right-side link attaching unit J 15 , and a neck left-side link attaching unit J 16  are provided on the bent portion. Neck rear link attaching unit J 14  is located at the center of the rear side of shoulder frame  51 . Neck right-side link attaching unit J 15  is located to the slight right of the front center of shoulder frame  51 . Neck left-side link attaching unit J 16  is located to the slight left of the front center of shoulder frame  51 . 
     Neck rear link attaching unit J 14  is a biaxial gimbal in which the shaft member provided at the other end of a neck rear link  28 L is held rotatably by the yoke that is rotated by the rotation member protruding rearward from neck lower frame  58 . Neck right-side link attaching unit J 15  and neck left-side link attaching unit J 16  are also a biaxial gimbal having the same structure. 
     A head rear link attaching unit J 17  is provided in the center on the rear side in the lower portion of head  2 . A head right-side link attaching unit J 18  is provided on the right side in the lower portion of head  2 . A head left-side link attaching unit J 19  is provided on the left side in the lower portion of head  2 . 
     One ends of neck rear link  28 L, a neck right-side link  29 L, and a neck left-side link  30 L are attached rotatably to head rear link attaching unit J 17 , head right-side link attaching unit J 18 , and head left-side link attaching unit J 19  with two rotational degrees of freedom, respectively. The other ends of neck rear link  28 L, neck right-side link  29 L, and neck left-side link  30 L are attached to neck rear link attaching unit J 14 , neck right-side link attaching unit J 15 , and neck right-side link attaching unit J 16  with two rotational degrees of freedom, respectively. 
     Neck rear link  28 L is attached to head rear link attaching unit J 17  with a link attachment  28 N interposed therebetween. The length of neck rear link  28 L is shorter than a distance between head rear link attaching unit J 17  and neck rear link attaching unit J 14 . Link attachment  28 N extends along motor  28 M from between the cylinder of neck rear link  28 L and motor  28 M. Link attachment  28 N is a member that is bent in an L-shape when viewed from the side. The tip of L-shaped link attachment  28 N is attached to head rear link attaching unit  17  at the position where neck rear link  28 L is extended. The lower end of motor  28 M exists below an attachment position of link attachment  28 N. A neck right-side link  29 L and a neck left-side link  30 L have the same structure. This allows use of a motor that is longer than the length of the variable length link included in the actuator. 
     A neck C 3  is a three-rotational-degree-of-freedom connection mechanism that connects head  2  being the second member rotatably to chest  5  being the first member with three rotational degrees of freedom. Neck C 3  includes neck joint  27  being the joint, neck rear links  28 L, neck right-side link  29 L, and neck left-side link  30 L, being the three variable length links, neck rear link attaching unit J 14 , neck right-side link attaching unit J 15 , and neck left-side link attaching unit J 16 , being the three first-member-side link attaching units, and head rear link attaching unit J 17 , head right-side link attaching unit J 18 , and head left-side link attaching unit J 19 , being the three second-member-side link attaching units. 
     The direction of neck center rod  26 , being the torsion axis, is fixed with respect to chest  5 . The angle of neck center rod  26  can be changed with respect to head  2 . Each of relative positional relations with respect to neck center rod  26  and neck joint  27  is fixed in each of neck rear link attaching unit J 14 , neck right-side link attaching unit J 15 , and neck left-side link attaching unit J 16 . Each of the relative positional relationships with neck joint  27  is also fixed in each of head rear link attaching unit J 17 , head right-side link attaching unit J 18 , and head left-side link attaching unit J 19 . 
     The arrangement of the variable length links in neck C 3  is described.  FIG. 34  is a perspective view illustrating the arrangement of the variable length links in neck C 3 . Neck C 3  includes three variable length links  28 L,  29 L,  30 L that connect three second-member-side link attaching units J 17 , J 18 , J 19  and three first-member-side link attaching units J 14 , J 15 , J 16 , respectively. For this reason, the connection angle of head  2  with respect to chest  5  can be changed with three rotational degrees of freedom by changing the lengths of three variable length links  28 L,  29 L,  30 L. It is assumed that αp is the rotation angle around the X-axis of neck joint  27 , that βp is the rotation angle around the Y-axis, and that γp is the rotation angle around the Z axis. 
     Neck joint  27  exists on a line segment connecting the second-member-side link attaching units J 18 , J 19 . A second-member-side triangle T 2  is an isosceles triangle, and neck joint  27  is located at a midpoint of the base side. For this reason, in the case that second member  2  is tilted in the front-rear direction, it is only necessary to change the length of variable length link  28 L. In the case that second member  2  is tilted in the right and left direction, one of variable length links  29 L,  30 L is lengthened while the other is shortened. 
     The similar effect is also obtained in the case that the first-member-side link attaching units are arranged in other joints such that the joint exists on the line segment connecting the two first-member-side link attaching units provided in the first member having a changeable angle with respect to the torsion axis. Alternatively, the similar effect is also obtained in the case that the second-member-side link attaching units are arranged such that the joint exists on the line segment connecting the two second-member-side link attaching units provided in the second member having a changeable angle with respect to the torsion axis. 
       FIG. 35  is a view illustrating the arrangement of the variable length links of neck C 3  in the reference state viewing from the direction in which neck center rod  26  extends. In the reference state, variable length links  29 L,  30 L and torsion axis  26  have the twisted relationship. A tilt angle θp 1  formed between variable length link  28 L and the link reference plane including first-member-side link attaching unit J 14  of variable length link  28 L and torsion axis  26  is zero degree. Tilt angles θp 2 , θp 3  of variable length links  29 L,  30 L are about 16 degrees. A maximum value θpmax of the angle formed between each of three variable length links  28 L,  29 L,  30 L and torsion axis  26  is about 16 degrees, and is greater than or equal to δ 0  (for example, about 3 degrees). The torque rotating around torsion axis  26  is generated in the case that the lengths of variable length links  28 L,  29 L,  30 L are changed. 
     When head  2  is tilted, maximum value θpmax of the three tilt angles is greater than or equal to δ 0 .  FIG. 36  is a view illustrating the arrangement of the variable length links in neck C 3  while head  2  is rotated and tilted forward viewing from the direction in which neck center rod  26  extends.  FIG. 36  illustrates the arrangement of the variable length links while head  2  is twisted to the left by 15 degrees and tilted forward by 30 degrees in the direction of 15 degrees to the left. Tilt angles θp 1 , θp 3  of variable length links  28 L,  30 L are increased, and tilt angle θp 2  of variable length link  29 L is decreased. In the case that the rotation around torsion axis  26  is not performed, tilt angles θp 2 , θp 3  of variable length links  29 L,  30 L are kept unchanged at about 16 degrees when second member (head)  2  is tilted back and forth. When second member  2  is tilted in the right and left direction, one of tilt angles θp 2 , θp 3  of variable length links  29 L,  30 L is increased while the other is decreased. Thus, in each case that the length of each of variable length links  28 L,  29 L,  30 L varies within a possible range, any one of the variable length links has the twisted relationship with respect to torsion axis  26 , and maximum value θpmax in the tilt angles of the three variable length links is greater than or equal to about 16 degrees. 
     A plane determined by three first-member-side link attaching units, or a plane determined by three second-member-side link attaching units is referred to as a link attaching plane. The intersection point of neck center rod  26  being the torsion axis and the link attaching plane is referred to as a torsion center. First-member-side link attaching units J 14 , J 15 , J 16  existing on chest  5  being the first member are arranged at three points where a center angle becomes 120 degrees on a circumference of a circle having a predetermined distance from the torsion center on the link attaching plane. Second-member-side link attaching units J 17 , J 18 , J 19  existing on head  2  being the second member are arranged at positions, being equidistant from neck joint  27  and has center angles of 90 degrees, 90 degrees, and 180 degrees with respect to the neck joint  27 , on the link attaching plane. Consequently, all of variable length links  28 L,  29 L,  30 L cannot be located on the same plane including torsion axis  26  at the same time even if neck joint  27  is rotated in what way. That is, at least one of variable length links  28 L,  29 L,  30 L has the twisted relationship with torsion axis  26 . 
     In other three-rotational-degree-of-freedom connection mechanisms, three center angles formed by the three first-member-side link attaching units and the torsion center in the link attaching plane on the first member side are different from three central angles formed by the three second-member-side link attaching units and the torsion center in the link attaching plane on the second member side. For this reason, the situation in that the plane including each one of the three variable length links also includes the torsion axis is not simultaneously generated in all the three variable length links. Maintaining a situation in that one variable length link (referred to as a link A) is disposed on the same plane as the torsion axis, the joint is rotated within the movable range around a rotation axis that is perpendicular to the plane. In the rotation of the joint within the movable range, one of the following states occurs. (A) At least one of the remaining two variable length links is not disposed on the same plane as the torsion axis. (B) The remaining two variable length links are disposed on the same plane as the torsion axis at different rotation angles. Consequently, even if the joint is rotated in what way, the fact that the plane including the variable length link includes the torsion axis is not simultaneously generated in all the three variable length links. That is, at least one of the three variable length links has the twisted relationship with the torsion axis. 
     In the rotation around neck center rod  26  (torsion axis), one of neck right-side link  29 L and neck left-side link  30 L is lengthened and the other is shortened. Consequently, in the rotation around the torsion axis, both the force pushed by the extending link and the force drawn by the shortening link are generated, the rotation is performed around torsion axis easily. 
     Referring to  FIGS. 10 to 16 and 37 , a structure of a shoulder C 4  is described below.  FIG. 37  is a perspective view illustrating the upper half body of humanoid robot  100 . Upper arm  7  is connected rotatably to chest  5  by shoulder joint  13  with two rotational degrees of freedom. Upper arm  7  and forearm  8  have a straight rod shape. The rod-shaped portion of upper arm  7  is referred to as a humerus  7 B. The rod-shaped portion of forearm  8  is referred to as a forearm bone  8 B. An upper arm main link attaching unit J 20  to which upper arm drive main link  14 L is attached rotatably with two rotational degrees of freedom is provided in the humerus  7 B at a position having a predetermined distance from shoulder joint  13 . Upper arm main link attaching unit J 20  is a biaxial gimbal having a structure in which a rotation member provided in humerus  7 B is sandwiched by a semicircular yoke provided at one end of upper arm drive main link  14 L. The rotation member is provided in humerus  7 B to be rotated around the axis in a direction in which humerus  7 B extends. The rotation member is sandwiched by the yoke such that the angle formed with humerus  7 B can be changed. The protrusions protruding from both sides of the rotation member are sandwiched rotatably by the yoke provided on upper arm drive main link  14 L. The protrusion has a cylindrical shape. The two protrusions exist on the same straight line perpendicular to the rotation member. Upper arm main link attaching unit J 20  has two rotational degrees of freedom including one rotational degree of freedom around the axis of humerus  7 B. 
     An upper arm drive main-link-side auxiliary link attaching unit J 21  is provided on upper arm drive main link  14 L at the position having the predetermined distance from upper arm main link attaching unit J 20 . One end of upper arm drive auxiliary link  15 L is attached rotatably to upper arm drive main-link-side auxiliary link attaching unit J 21  with one rotational degree of freedom. The center lines of upper arm drive main link  14 L and upper arm drive auxiliary link  15 L exist on the same plane. The plane on which the center lines of upper arm drive main link  14 L and upper arm drive auxiliary link  15 L exist is referred to as a link moving plane. In upper arm drive main-link-side auxiliary link attaching unit J 21 , upper arm drive auxiliary link  15 L is attached rotatably to upper arm drive main link  14 L with one rotational degree of freedom at which the angle formed by upper arm drive main link  14 L and upper arm drive auxiliary link  15 L can be changed on the link moving plane. Upper arm drive main-link-side auxiliary link attaching unit J 21  has the structure in which the protrusion (shaft member) provided on upper arm drive main link  14 L is sandwiched by the yoke provided at one end of upper arm drive auxiliary link  15 L. The protrusion provided on upper arm drive main link  14 L is provided perpendicular to the link moving plane. 
     The link moving plane is a plane determined by chest-side main link attaching unit J 1 , chest-side auxiliary link attaching unit J 2 , and upper arm drive main-link-side auxiliary link attaching unit J 21 . When the lengths of upper arm drive main link  14 L and upper arm drive auxiliary link  15 L change, upper arm drive main link  14 L and upper arm drive auxiliary link  15 L are moved on the link moving plane. Furthermore, the link moving plane is rotated around a straight line (referred to as a link moving plane rotation axis) passing chest-side main link attaching unit J 1  and chest-side auxiliary link attaching unit J 2 . In a case where the lengths of upper arm drive main link  14 L and upper arm drive auxiliary link  15 L are changed while a certain condition is satisfied, the link moving plane does not rotate. In another case where the lengths of upper arm drive main link  14 L and upper arm drive auxiliary link  15 L are changed while another condition is satisfied, only the link moving plane is rotated and upper arm drive main link  14 L and upper arm drive auxiliary link  15 L are not moved within the link moving plane. The link moving plane rotation axis is also a rotation axis around which the rotation member of chest-side main link attaching unit J 1  is rotated and a rotating axis around which the rotation member of chest-side auxiliary link attaching unit J 2  is rotated. 
     Upper arm drive main link  14 L and upper arm drive auxiliary link  15 L exist on the link moving plane. In the link moving plane, only the angle formed by upper arm drive main link  14 L and upper arm drive auxiliary link  15 L is changed at upper arm drive main-link-side auxiliary link attaching unit J 21  in a relative positional relationship between upper arm drive main link  14 L and upper arm drive auxiliary link  15 L. Thus, upper arm drive main-link-side auxiliary link attaching unit J 21  may have one rotational degree of freedom at which only the rotation can be performed in the link moving plane. Upper arm drive main-link-side auxiliary link attaching unit J 21  may have two rotational degrees of freedom. 
       FIG. 38  is a perspective view illustrating the arrangement of the variable length links in left shoulder joint  13 . Shoulder joint  13 , chest-side main link attaching unit J 1 , and chest-side auxiliary link attaching unit J 2  are fixed to chest  5 , and the relative positional relationships among shoulder joint  13 , chest-side main link attaching unit J 1 , and chest-side auxiliary link attaching unit J 2  are fixed. In upper arm main link attaching unit J 20 , the distance from shoulder joint  13  is predetermined. Upper arm drive main-link-side auxiliary link attaching unit J 21  exists on upper arm drive main link  14 L at the position having the predetermined distance from upper arm main link attaching unit J 20 . When the position of upper arm main link attaching unit J 20  is determined in a three-dimensional space, humerus  7 B is directed in the direction from shoulder joint  13  toward upper arm main link attaching unit J 20 . Upper arm  7  including humerus  7 B can be moved with respect to chest  5  by changing the position of upper arm main link attaching unit J 20 . Upper arm drive main link  14 L and upper arm drive auxiliary link  15 L constitute a truss structure. 
     When the lengths of upper arm drive main link  14 L and upper arm drive auxiliary link  15 L are determined, the distance to upper arm main link attaching unit J 20  from each of shoulder joint  13 , chest-side main link attaching unit J 1 , and chest-side auxiliary link attaching unit J 2  is determined. Because the distance from the three points to upper arm main link attaching unit J 20  is determined, the position of upper arm main link attaching unit J 20  is determined. 
     Humerus  7 B is raised by lengthening upper arm drive main link  14 L, and humerus  7 B is lowered by shortening upper arm drive main link  14 L. Humerus  7 B is moved forward by lengthening upper arm drive auxiliary link  15 L, and humerus  7 B is moved rearward by shortening upper arm drive auxiliary link  15 L. Humerus  7 B can be moved freely within a determined movable range in which shoulder joint  13  is set to the center of the rotation. For example, regarding the vertical direction and the front-back direction, when the downward direction is set to 0 degrees and the forward direction is set to 90 degrees, humerus  7 B can be rotated from about −30 degrees to about 95 degrees. In the right and left direction, humerus  7 B can be rotated outward by about 95 degrees, and rotated inward by about 5 degrees (−5 degrees) beyond the front direction. 
     In the biaxial gimbal of the type used in shoulder joint  13 , in the case where humerus  7 B is directed in the direction of a rotation axis Rx 1  (illustrated in  FIG. 5 ) of the rotation member of the biaxial gimbal (referred to as a singular point), humerus  7 B cannot be tilted in the direction orthogonal to the yoke of the biaxial gimbal. The direction of rotation axis Rx 1  is set to a direction forming an angle of ξ 1  on the rear side with respect to the right and left direction (X-axis direction) of humanoid robot  100  in the horizontal plane. Consequently, the singular point exists behind shoulder joint  13 . This enables humerus  7 B to be moved freely within the movable range on the front side with respect to the right and left direction. In the conventional humanoid robot, sometimes the humanoid robot performs unnatural motion caused by avoiding the singular point of the biaxial gimbal of the shoulder joint. In humanoid robot  100 , it is not necessary to perform the unnatural motion within the movable range in order to avoid the singular point. That is, the motion of humanoid robot  100  can be brought closer to the natural motion of a person than before. 
     Shoulder joint  13  exists at an end of shoulder frame  51 , which exists on the upper portion of chest  5  and extends in the right and left direction. Shoulder joint  13  allows the rotation around rotation axis Rx 1  extending in a direction being directed to the side far from the center of chest  5  and onto the rear side. The rotation in which the angle formed by rotation axis Rx 1  and humerus  7 B is changed can be performed. Shoulder joint  13  connects humerus  7 B rotatably to chest  5  with two rotational degrees of freedom. Chest-side main link attaching unit J 1  is provided in chest  5  at the position lower than shoulder joint  13  and on the front side. Chest-side auxiliary link attaching unit J 2  is provided in chest  5  at the position lower than shoulder joint  13  and on the rear side. Chest-side main link attaching unit J 1  may be provided on the rear side of shoulder joint  13 , and chest-side auxiliary link attaching unit J 2  may be provided on the front side. Chest-side main link attaching unit J 1  and chest-side auxiliary link attaching unit J 2  may be provided at positions where shoulder joint  13  is sandwiched therebetween in the front-back direction. 
     Shoulder C 4  is a rotation connecting mechanism that connects upper arm  7  being the second member rotatably to chest  5  being the first member by shoulder joint  13 . Shoulder joint  13  is a joint that connects the upper arm  7  including humerus  7 B rotatably to chest  5  with two rotational degrees of freedom. Shoulder C 4  changes the angle of shoulder joint  13  to move upper arm  7  with respect to chest  5 . 
     Upper arm drive main link  14 L is a first link having four rotational degrees of freedom or five rotational degrees of freedom. Upper arm main link attaching unit J 20  is a second-member first attaching unit that is provided in the upper arm  7  so that it has a fixed positional relationship with respect to shoulder joint  13 . One end of upper arm drive main link  14 L is attached rotatably to upper arm main link attaching unit J 20  with at least two rotational degrees of freedom. Chest-side main link attaching unit J 1  is a first-member first attaching unit to which the other end of upper arm drive main link  14 L is attached rotatably with at least two rotational degrees of freedom. Chest-side main link attaching unit J 1  is also a first reference point that is provided in chest  5  having a fixed relative positional relationship with respect to the shoulder joint  13 . Upper arm drive main link  14 L itself has one rotational degree of freedom. Upper arm drive main link  14 L itself is not required to have one rotational degree of freedom. Motor  14 M is a first power source that generates force changing the length of upper arm drive main link  14 L. The length of upper arm drive main link  14 L is a distance between upper arm main link attaching unit J 20  and chest-side main link attaching unit J 1 . Upper arm drive main actuator  14  including upper arm drive main link  14 L, upper arm main link attaching unit J 20 , chest-side main link attaching unit J 1 , and motor  14 M is a first actuator. 
     Upper arm drive auxiliary link  15 L is a second link having three rotational degrees of freedom, four rotational degrees of freedom, or five rotational degrees of freedom. Upper arm drive main-link-side auxiliary link attaching unit J 21  is a first-link second attaching unit that is provided on upper arm driving main link  14 L so that it has a fixed positional relationship with respect to upper arm main link attaching unit J 20 . One end of upper arm drive auxiliary link  15 L is attached rotatably to upper arm drive main-link-side auxiliary link attaching unit J 21  with at least one rotational degree of freedom. Chest-side auxiliary link attaching unit J 2  is a second reference point that is provided in chest  5  so that it has a fixed position with respect to shoulder joint  13 . Upper arm drive auxiliary link  15 L itself has one rotational degree of freedom. Upper arm drive auxiliary link  15 L itself is not required to have one rotational degree of freedom. Chest-side auxiliary link attaching unit J 2  is a first-member second attaching unit to which the other end of the upper arm drive auxiliary link  15 L is attached rotatably with at least two rotational degrees of freedom. Motor  15 M is a second power source that generates the force changing the length of upper arm drive auxiliary link  15 L. The length of upper arm drive auxiliary link  15 L is a distance between upper arm drive main-link-side auxiliary link attaching unit J 21  and chest-side auxiliary link attaching unit J 2 . Upper arm driving auxiliary actuator  15  including upper arm drive auxiliary link  15 L, upper arm drive main-link-side auxiliary link attaching unit J 21 , chest-side auxiliary link attaching unit J 2 , and motor  15 M is a second actuator. 
     When upper arm drive main link  14 L and upper arm drive auxiliary link  15 L expand or contract, upper arm drive main-link-side auxiliary link attaching unit J 21  always exists on the link moving plane. Thus, upper arm drive main-link-side auxiliary link attaching unit J 21  has one rotational degree of freedom around the rotation axis perpendicular to the link moving plane (referred to as a vertical rotation axis). 
     Chest-side main link attaching unit J 1  and chest-side auxiliary link attaching unit J 2  have two rotational degrees of freedom by the link moving plane rotation axis and the vertical rotation axis. Thus, no matter how upper arm drive main link  14 L and upper arm drive auxiliary link  15 L expand or contract, upper arm drive main link  14 L and chest-side auxiliary link attaching unit J 2  are not twisted. For this reason, upper arm drive main link  14 L and upper arm drive auxiliary link  15 L are not required to have one rotational degree of freedom around the axis. Upper arm drive main link  14 L has four rotational degrees of freedom, and upper arm drive auxiliary link  15 L has three rotational degrees of freedom. When upper arm drive main link  14 L is rotated around the link moving plane rotation axis at chest-side main link attaching unit J 1 , the vertical rotation axis is also rotated around the link moving plane rotation axis. When upper arm drive auxiliary link  15 L rotates around the link moving surface rotation axis at chest-side auxiliary link attaching unit J 2 , the vertical rotation axis is also rotated around the link moving surface rotation axis. 
     Upper arm main link attaching unit J 20  has two rotational degrees of freedom including one rotational degree of freedom around the axis of humerus  7 B. Consequently, upper arm main link attaching unit J 20  can be used in cases in which the angle around the axis of humerus  7 B is changed in upper arm main link attaching unit J 20  or the angle between humerus  7 B and upper arm drive main link  14 L is changed. 
     Upper arm drive main link  14 L twists when chest-side main link attaching unit J 1  has two rotational degrees of freedom including the rotation axis in the direction from the link moving plane rotation axis and the vertical rotation axis. In order to absorb the twist, upper arm drive main link  14 L has one rotational degree of freedom around the axis. Alternatively, upper arm drive main-link-side auxiliary link attaching unit J 21  may have two rotational degrees of freedom. One rotational degree of freedom added to upper arm drive main-link-side auxiliary link attaching unit J 21  is one rotational degree of freedom around the axis of upper arm drive main link  14 L. When chest-side main link attaching unit J 1  has three rotational degrees of freedom, the upper arm drive main link  14 L is not required to have one rotational degree of freedom around the axis, and the rotational degree of freedom is not required to be added to upper arm drive main-link-side auxiliary link attaching unit J 21 . 
     Upper arm drive auxiliary link  15 L twists when chest-side auxiliary link attaching unit J 2  has two rotational degrees of freedom including the rotation axis in the direction different from the link moving plane rotation axis and the vertical rotation axis. In order to absorb the twist, upper arm drive auxiliary link  15 L has one rotational degree of freedom around the axis. Alternatively, upper arm drive main-link-side auxiliary link attaching unit J 21  may have two rotational degrees of freedom. One rotational degree of freedom added to upper arm drive main-link-side auxiliary link attaching unit J 21  is one rotational degree of freedom around the axis of upper arm drive auxiliary link  15 L. Upper arm drive main-link-side auxiliary link attaching unit J 21  has three rotational degrees of freedom when upper arm drive main-link-side auxiliary link attaching unit J 21  has two rotational degrees of freedom to prevent upper arm drive main link  14 L from twisting. When chest-side auxiliary link attaching unit J 2  has three rotational degrees of freedom, the upper arm drive auxiliary link  15 L is not required to have one rotational degree of freedom around the axis, and the rotational degree of freedom is not required to be added to upper arm drive main-link-side auxiliary link attaching unit J 21 . 
     When one of chest-side main link attaching unit J 1  and chest-side auxiliary link attaching unit J 2  has two rotational degrees of freedom around the link moving plane rotation axis and the vertical rotation axis while the other has two rotational degrees of freedom including the rotation axis in the direction different from the link moving plane rotation axis and the vertical rotation axis, the total of the rotational degrees of freedom of chest-side main link attaching unit J 1  and the rotational degrees of freedom of chest-side auxiliary link attaching unit J 2  may be set to eight rotational degrees of freedom. That is, upper arm drive main link  14 L or upper arm drive auxiliary link  15 L may have one rotational degree of freedom around the axis, or upper arm drive main-link-side auxiliary link attaching unit J 21  may have two rotational degrees of freedom. Chest-side main link attaching unit J 1  or chest-side auxiliary link attaching unit J 2  may have three rotational degrees of freedom. 
     When both chest-side main link attaching unit J 1  and chest-side auxiliary link attaching unit J 2  have two rotational degrees of freedom including the rotation axis in the direction different from the link moving plane rotation axis and the vertical rotation axis, the total of the rotational degree of freedom of chest-side main link attaching unit J 1  and the rotational degree of freedom of chest-side auxiliary link attaching unit J 2  may be set to nine rotational degrees of freedom. 
     Although the positions of chest-side main link attaching unit J 1  and chest-side auxiliary link attaching unit J 2  are fixed, the link moving plane is not always rotated around the link moving plane rotation axis when at least one of chest-side main link attaching unit J 1  and chest-side auxiliary link attaching unit J 2  is movable. For this reason, upper arm drive main-link-side auxiliary link attaching unit J 21  is required to have at least two rotational degrees of freedom. 
     When the joint has three rotational degrees of freedom, the first link and the second link have five rotational degrees of freedom, and a third link having five rotational degrees of freedom is added between the second and first members. The same holds true for the rotation connecting mechanism that connects the second member rotatably to the first member with two rotational degrees of freedom or three rotational degrees of freedom. 
     Referring to  FIGS. 11 to 15 and 39 to 44 , the structure of an elbow C 5  is described.  FIGS. 39 and 40  are a front view and a side view of left upper limb  3 .  FIGS. 41 and 42  are an enlarged front view and an enlarged side view illustrating a portion up to elbow joint  31  of left upper limb  3 .  FIG. 43  is a front view illustrating humanoid robot  100  when right and left elbow joints  31  are bent by 90 degrees.  FIG. 44  is a plan view illustrating humanoid robot  100  when right and left elbow joints  31  are bent by 90 degrees viewing from above. Only trunk  1  and right and left upper limbs  3  are illustrated in  FIGS. 43 and 44 . In  FIGS. 43 and 44 , right upper arm  7  has moved to be far from trunk  1 , left upper arm  7  has moved to come close to trunk  1 , and right and left elbow joints  31  are bent by 90 degrees. As can be seen from  FIG. 44 , each of right and left forearm bones  8 B is directed in the direction open outward with respect to the front direction of trunk  1 . That is, a main bending direction of elbow joint  31  is a direction forming an angle ξ 2  with the front direction (Y-axis) of trunk  1 . 
     The front direction of upper limb  3  is a direction in which forearm bone  8 B is directed when elbow joint  31  is bent by 90 degrees only in the main bending direction. When humanoid robot  100  stands upright and upper limbs  3  are directed vertically downward, the front direction of upper limb  3  is directed outward by 2 from the front direction of humanoid robot  100 . For this reason, the upper limb  3  is viewed obliquely in  FIG. 2  that is the front view of humanoid robot  100 . In the description of upper limb  3 , the front direction of upper limb  3  is set to the Y-axis direction and the direction orthogonal to the front direction of upper limb  3  is set to the X-axis direction. 
     Forearm  8  is connected rotatably to upper arm  7  by elbow joint  31  with two rotational degrees of freedom. Elbow joint  31  is a biaxial gimbal having a rotation axis Rz 2  in the same direction as upper arm  7 . In the biaxial gimbal, forearm  8  is rotated around rotation axis Rz 2 . Furthermore, the angle of forearm  8  with respect to upper arm  7  can be changed. In elbow joint  31 , the rotation member is provided in upper arm  7 , and the yoke is provided in forearm bone  8 B. An elbow drive outside link  32  and an elbow drive inside link  33  are attached to upper arm  7  and forearm  8 . Elbow drive outside link  32  and elbow drive inside link  33  are links having a fixed length, and are two elbow drive links. Elbow drive outside link  32  and elbow drive inside link  33  have one rotational degree of freedom at which the link can be twisted. 
     The attachment positions of elbow drive outside link  32  and elbow drive inside link  33  to upper arm  7  are movable. For this reason, an upper arm outside linear guide  34 G and an upper arm inside linear guide  35 G, which are two linear guides, are provided on both sides of humerus  7 B and are parallel to humerus  7 B. As illustrated in  FIG. 11  and the like, a motor holder  7 A holding a motor  34 M of upper arm outside linear guide  34 G and a motor  35 M of upper arm inside linear guide  35 G is provided near shoulder joint  13  of upper arm  7 . 
     An upper arm outside link attaching unit J 22 , being the attachment position of elbow drive outside link  32  to upper arm  7 , is moved by upper arm outside actuator  34 . An upper arm inside link attaching unit J 23 , being the attachment position of elbow drive inside link  33  to upper arm  7 , is moved by upper arm inside actuator  35 . Elbow drive outside link  32  and elbow drive inside link  33  are attached to upper arm outside link attaching unit J 22  and upper arm inside link attaching unit J 23  with two rotational degrees of freedom, respectively. Elbow drive outside link  32  and elbow drive inside link  33  constitute a truss structure. 
     Referring to  FIG. 41 , the structure of an upper arm outside actuator  34  is described. Upper arm outside actuator  34  includes upper arm outside linear guide  34 G, elbow drive outside link  32 , an elbow drive outside link attaching unit J 25 , upper arm outside link attaching unit J 22 , and motor  34 M. Upper arm outside linear guide  34 G includes a screw rod  34 A, a nut  34 B, a rail  34 C, and a gripper  34 D in an upper arm outside frame  34 F that is a frame body. 
     Motor  34 M is disposed behind upper arm outside linear guide  34 G. Consequently, upper arm outside linear guide  34 G and motor  34 M can be made compact. Motor  34 M transmits the force to screw rod  34 A by the timing belt on the side closer to shoulder joint  13 , which rotates screw rod  34 A. The use of the timing belt can reduce weight as compared with the case where the force is transmitted using a gear. A nut  34 B including a through-hole provided with female threads engaged with male threads of screw rod  34 A is movable in the length direction of screw rod  34 A. A mechanism that prevents nut  34 B from being rotated around screw rod  34 A is provided. For this reason, nut  34 B is moved along screw rod  34 A when screw rod  34 A is rotated. Upper arm outside link attaching unit J 22  is attached to nut  34 B, and upper arm outside link attaching unit J 22  is also moved when nut  34 B moves. Nut  34 B is a moving member that is moved by upper arm outside actuator  34 . 
     The mechanism that prevents nut  34 B from being rotated around screw rod  34 A includes a rail  34 C provided in parallel with screw rod  34 A and a gripper  34 D being connected to nut  34 B and sandwiching rail  34 C. Gripper  34 D is provided so that it has low friction with rail  34 C. Because gripper  34 D sandwiches rail  34 C, gripper  34 D and nut  34 B are not rotated around screw rod  34 A. Another mechanism that prevents nut  34 B from being rotated around screw rod  34 A may be used. 
     Upper arm inside actuator  35  also has the same structure as upper arm outside actuator  34 . Upper arm inside actuator  35  includes upper arm inside linear guide  35 G, elbow drive inside link  33 , an elbow drive inside link attaching unit J 24 , upper arm inside link attaching unit J 23 , and motor  35 M. Upper arm inside linear guide  35 G includes a screw rod  35 A, a nut  35 B, a rail  35 C, and a gripper  35 D in an upper arm inside frame  35 F being a frame body. Upper arm inside link attaching unit J 23  is attached to nut  35 B. Nut  35 B is a moving member that is moved by upper arm inside actuator  35 . 
     Upper arm outside frame  34 F and upper arm inside frame  35 F are manufactured integrally. Upper arm outside frame  34 F and upper arm inside frame  35 F can be made compact and high in strength by manufacturing upper arm outside frame  34 F and upper arm inside frame  35 F integrally. Upper arm outside frame  34 F and upper arm inside frame  35 F may be manufactured separately. 
     Rail  34 C and rail  35 C are both sides of the rectangular plate material. Rail  34 C, rail  35 C, screw rod  34 A, and rail  35 C are required to be arranged in parallel with one another. Upper arm outside linear guide  34 G and upper arm inside linear guide  35 G are required to be disposed with predetermined accuracy. It takes a lot of time to perform that work. 
     Gripper  35 D is provided in nut  35 B. Gripper  35 D engages with rail  35 C. Gripper  35 D and rail  35 C are a first rotation preventing unit to prevent nut  35 B, which is the first moving member, from rotating around screw rod  35 A. 
     Gripper  34 D is provided in nut  34 B. Gripper  34 D engages with rail  34 C. Gripper  34 D and rail  34 C are a second rotation preventing unit to prevent nut  34 B, which is the second moving member, from rotating around screw rod  34 A. 
     Upper arm outside link attaching unit J 22  is the biaxial gimbal having the following structure. The rotation member, the yoke rotated by the rotation member, and the shaft member sandwiched rotatably by the yoke are provided in nut  34 B being the moving member moved by upper arm outside actuator  34 . The through-hole in which the shaft member is inserted is made at the end of elbow drive outside link  32 . Upper arm inside link attaching unit J 23  is also the biaxial gimbal having the same structure. 
     Elbow drive inside link attaching unit J 24  is provided at a position having a predetermined distance from elbow joint  31  of forearm bone  8 B. One end of elbow drive inside link  33  is attached rotatably to elbow drive inside link attaching unit J 24  with two rotational degrees of freedom. Elbow drive inside link attaching unit J 24  is the biaxial gimbal having the same structure as upper arm outside link attaching unit J 22 . Elbow drive outside link attaching unit J 25  is provided at a position having a predetermined distance from elbow drive inside link attaching unit J 24  of elbow drive inside link  33 . The other end of elbow drive outside link  32  is attached rotatably to elbow drive outside link attaching unit J 25  with two rotational degrees of freedom. Elbow drive outside link attaching unit J 25  has a structure in which the protrusion provided on elbow drive inside link  33  are sandwiched by the yoke extending from one end of elbow drive outside link  32 . The yoke of elbow drive outside link attaching unit J 25  has a length enough to sandwich the protrusions when the angle formed by elbow drive outside link  32  and elbow drive inside link  33  is small. The portion in which the protrusions of elbow drive inside link  33  are provided can be rotated around elbow drive inside link  33 . The yoke extending from one end of elbow drive outside link  32  sandwiches the protrusions such that the angle formed by elbow drive inside link  33  and the yoke can be changed. Elbow drive outside link attaching unit J 25  has two rotational degrees of freedom including one rotational degree of freedom around the axis of elbow drive inside link  33 . 
     At least one of upper arm outside link attaching unit J 22  and elbow drive outside link attaching unit J 25  may have three rotational degrees of freedom. At least one of upper arm inside link attaching unit J 23  and elbow drive inside link attaching unit J 24  may have three rotational degrees of freedom. 
       FIG. 45  is a perspective view illustrating the arrangement of the links in left elbow C 5 . Elbow joint  31 , upper arm outside actuator  34 , and upper arm inside actuator  35  are fixed to upper arm  7 . Upper arm outside link attaching unit J 22  is moved along humerus  7 B by upper arm outside actuator  34 . Upper arm inside link attaching unit J 23  is moved along upper arm inside actuator  35 . Elbow drive inside link attaching unit J 24  provided in forearm  8  exists at a position having a predetermined distance K 1u  from elbow joint  31 . Elbow drive outside link attaching unit J 25  provided on elbow drive inside link  33  exists at a position having a predetermined distance K 2u  from elbow drive inside link attaching unit J 24  (strictly, its rotation center). Forearm  8  is directed in the direction of elbow drive inside link attaching unit J 24  located at distance K 1u  from elbow joint  31  (strictly, its rotation center). Forearm  8  can be moved with respect to upper arm  7  by changing the position of elbow drive inside link attaching unit J 24 . 
     The lengths of elbow drive inside link  33  and elbow drive outside link  32  are fixed. Upper arm outside link attaching unit J 22  and upper arm inside link attaching unit J 23  are moved along humerus  7 B, thus the position of elbow drive inside link attaching unit J 24  is moved. 
     Elbow C 5  includes elbow joint  31 , elbow drive inside link  33 , elbow drive outside link  32 , elbow drive inside link attaching unit J 24  being the forearm-side main link attaching unit, elbow drive outside link attaching unit J 25  being the elbow drive main-link-side auxiliary link attaching unit provided on elbow drive inside link  33 , upper arm inside link attaching unit J 23  and upper arm outside link attaching unit J 22  that are two upper-arm-side link attaching units, and upper arm outside linear guide  34 G and upper arm inside linear guide  35 G that are two linear guides. 
     When both upper arm outside link attaching unit J 22  and upper arm inside link attaching unit J 23  are moved to come close to shoulder joint  13 , elbow joint  31  is bent and the forearm  8  comes close to upper arm  7 . When upper arm outside link attaching unit J 22  and upper arm inside link attaching unit J 23  are moved to be far from shoulder joint  13 , elbow joint  31  extends and forearm  8  is moved to be far from upper arm  7 . When upper arm outside link attaching unit J 22  is moved to come close to shoulder joint  13 , and upper arm inside link attaching unit J 23  is moved to be far from shoulder joint  13 , forearm  8  is directed outside. When upper arm inside link attaching unit J 23  is moved to come close to shoulder joint  13 , and upper arm outside link attaching unit J 22  is moved to be far from shoulder joint  13 , forearm  8  is directed inside. 
     In elbow joint  31 , the angle in the plane (elbow main drive plane) including the front direction of upper limb  3  and humerus  7 B can be changed from a state in which humerus  7 B and forearm bone  8 B become one straight line to a state in which the angle formed by humerus  7 B and forearm bone  8 B becomes, for example, about 70 degrees. In the plane (elbow auxiliary drive plane) perpendicular to humerus  7 B, elbow joint  31  can be rotated inside and outside by, for example, about 70 degrees when elbow joint  31  is bent at right angles. When the rotation angle of elbow joint  31  in the elbow main drive plane is not the right angles (90 degrees), the rotation angle in the elbow auxiliary drive plane becomes smaller than the case of the right angles. When the rotation angle of elbow joint  31  is 180 degrees, that is, when the elbow joint  31  extends, forearm  8  cannot be rotated in the elbow auxiliary drive plane. 
     The mechanism that drives elbow joint  31  can be made compact by adopting a system, in which the position of the link attaching unit is moved in the upper arm while the two links having a fixed length drive elbow joint  31 . When the elbow joint is driven by two variable length links, in order to rotate the elbow joint in the elbow auxiliary drive plane, the angle formed by the two links at the attaching position of the forearm is required to be greater than or equal to a predetermined angle. In order to do that, an interval between the attaching positions of the two variable length links is required to be wider than an interval between the two linear guides used in the first embodiment. 
     Elbow drive inside link  33  is the elbow drive main link having the fixed length. Elbow drive outside link  32  is the elbow drive auxiliary link having the fixed length. Elbow drive inside link attaching unit J 24  is the forearm-side main link attaching unit being attached rotatably with one end of elbow drive inside link  33  with at least two rotational degrees of freedom. Elbow drive outside link attaching unit J 25  is an elbow drive main-link-side auxiliary link attaching unit to which one end of elbow drive outside link  32  is attached rotatably with at least two rotational degrees of freedom. Upper arm inside link attaching unit J 23  and upper arm outside link attaching unit J 22  are two upper-arm-side link attaching units, the other ends of elbow drive inside link  33  and elbow drive outside link  32  being attached rotatably to the two upper-arm-side link attaching units with at least two rotational degrees of freedom, the two upper-arm-side link attaching units being provided in upper arm  7  to be movable along humerus  7 B. 
     One end of elbow driving outside link  32  on the side where forearm  8  exists may be attached to forearm  8  instead of elbow drive inside link  33 . In this case, two forearm-side link attaching units are provided on forearm  8 . One ends of elbow drive outside link  32  and elbow drive inside link  33 , which are the two elbow drive links, are attached rotatably to the two forearm-side link attaching units with at least two rotational degrees of freedom. 
     Nut  34 B included in upper arm outside actuator  34  is a moving member that moves elbow drive outside link  32 . Nut  35 B included in upper arm inside actuator  35  is a moving member that moves elbow drive inside link  33 . Screw rod  34 A and screw rod  35 A are guides that guide nut  34 B and nut  35 B to be moved along humerus  7 B, respectively. Motor  34 M is a power source that generates force changing the position of nut  34 B with respect to screw rod  34 A. Motor  35 M is a power source that generates force changing the position of nut  35 B with respect to screw rod  35 A. Upper arm outside linear guide  34 G is a linear guide including nut  34 B, screw rod  34 A, and motor  34 M. Upper arm inside linear guide  35 G is a linear guide including nut  35 B, screw rod  35 A, and motor  35 M. 
     Elbow C 5  is a rotation connecting mechanism that connects forearm  8  being the second member rotatably to upper arm  7  being the first member by the elbow joint  31 . Elbow joint  31  is a joint that connects forearm  8  rotatably to upper arm  7  with two rotational degrees of freedom. Elbow C 5  changes the angle of elbow joint  31  to move forearm  8  with respect to upper arm  7 . 
     Elbow drive inside link  33  is a first link having a fixed length with five rotational degrees of freedom. Elbow drive inside link attaching unit J 24  is the second-member first attaching unit provided in forearm  8  so that it has a fixed positional relationship with respect to elbow joint  31 . One end of elbow drive inside link  33  is attached rotatably to elbow drive inside link attaching unit J 24  with at least two rotational degrees of freedom. Upper arm inside link attaching unit J 23  is the first-member first attaching unit to which the other end of elbow drive inside link  33  is attached rotatably with at least two rotational degrees of freedom. Nut  35 B is the first moving member in which upper arm inside link attaching unit J 23  is provided. Screw rod  35 A is a first moving shaft along which nut  35 B is moved. Upper arm inside linear guide  35 G includes screw rod  35 A of which both ends are fixed by upper arm inside frame  35 F. Upper arm inside linear guide  35 G constitutes a first guide that guides nut  35 B to be moved along screw rod  35 A. 
     Motor  35 M is a power source that generates force changing the position of nut  35 B with respect to screw rod  35 A. A point P 1N  (illustrated in  FIG. 82 ) is a point where a straight line passing through the center of screw rod  35 A intersects with an upper end of upper arm inside frame  35 F. Point P 1N  is a first reference point provided in upper arm  7  so that it has a fixed positional relationship with respect to elbow joint  31 . Motor  35 M rotates and screw rod  35 A is rotated, which moves nut  35 B along screw rod  35 A. The distance between point P 1N  and elbow drive inside link attaching unit J 24  is changed when nut  35 B is moved. Motor  35 M is a power source that generates force changing the distance between point P 1N  and elbow drive inside link attaching unit J 24 . Upper arm inside actuator  35  including elbow drive inside link  33 , upper arm inside linear guide  35 G, elbow drive inside link attaching unit J 24 , upper arm inside link attaching unit J 23 , and motor  35 M is the first actuator. 
     Elbow drive outside link  32  is the second link having a fixed length with five rotational degrees of freedom. Elbow drive outside link attaching unit J 25  is a first-link second attaching unit provided on elbow drive inside link  33  so that it has a fixed positional relationship with respect to elbow drive inside link attaching unit J 24 . One end of elbow drive outside link  32  is attached rotatably to elbow drive outside link attaching unit J 25  with at least two rotational degrees of freedom. The rotational degree of freedom of elbow drive outside link attaching unit J 25  includes one rotational degree of freedom around the axis of elbow drive inside link  33 . Upper arm outside link attaching unit J 22  is the first-member second attaching unit to which the other end of elbow drive outside link  32  is attached rotatably with at least two rotational degrees of freedom. Nut  34 B is the second moving member in which upper arm outside link attaching unit J 22  is provided. Screw rod  34 A is a second moving shaft along which nut  34 B is moved. Upper arm inside linear guide  34 G includes screw rod  35 A of which both ends are fixed by upper arm inside frame  34 F. Upper arm inside linear guide  34 G constitutes a second guide that guides nut  34 B to be moved along screw rod  34 A. 
     Motor  34 M is a power source that generates force changing the position of nut  4  with respect to screw rod  34 A. A point P 2N  (illustrated in  FIG. 82 ) is a point where a straight line passing through the center of screw rod  34 A intersects with the upper end of upper arm outside frame  34 F. Point P 2N  is a second reference point provided in upper arm  7  having a fixed positional relationship with respect to elbow joint  31 . Motor  34 M rotates to rotate screw rod  34 A, which moves nut  34 B along screw rod  35 A. The distance between point P 2N  and elbow drive outside link attaching unit J 25  is changed when nut  34 B is moved. Motor  34 M is a power source that generates force changing the distance between point P 2N  and elbow drive outside link attaching unit J 25 . Upper arm outside actuator  34  including elbow drive outside link  32 , upper arm outside linear guide  35 G, elbow drive outside link attaching unit J 25 , upper arm outside link attaching unit J 22 , and motor  34 M is the second actuator. 
     Referring to  FIGS. 46 to 49 , the structure of a wrist C 6  is described.  FIGS. 46, 47, 48, and 49  are an enlarged perspective view, an enlarged front view, an enlarged left side view, and an enlarged rear view illustrating a portion of the arm from left elbow joint  31  in the skeleton structure. 
     Hand  9  similar to a human hand is connected rotatably to forearm  8  by a wrist joint  36  with three rotational degrees of freedom. A spherical bearing holding a spherical surface provided at one end of rod-shaped forearm bone  8 B rotatably is used as wrist joint  36 . A member that holds the spherical surface is provided in wrist plate  91 . Hand  9  can be rotated around wrist joint  36  with three rotational degrees of freedom. The angle between hand  9  and forearm bone  8 B is changed when the lengths of the three actuators, namely, a forearm front actuator  37 , a forearm outside actuator  38 , and a forearm inside actuator  39  change. For example, hand  9  can be tilted with respect to forearm bone  8 B by about 20 degrees in the direction (front direction) on the palm side of the hand, tilted by about 20 degrees in the direction (rear direction) on the back side of the hand, and tilted by about 20 degrees onto both the sides in the direction of forearm bone  8 B and the direction perpendicular to the direction directed from the front toward the rear. Hand  9  can be rotated by about 70 degrees in both directions around forearm bone  8 B. 
     Although the angle of the movable range of wrist C 6  in the front direction and the rear direction is small, wrist C 6  can be bent by 90 degrees together with elbow C 5 . In pushing the palm against a wall or the like, for example, wrist C 6  is bent by 20 degrees toward the backside of the hand, and elbow C 5  is bent by about 70 degrees. As a result, the palm being parallel to a vertical axis of the body is formed, and the palm being parallel to a chest surface is pushed out. 
     A forearm front link attaching unit J 26 , a forearm outside link attaching unit J 27 , and a forearm inside link attaching unit J 28  are provided at positions having distances predetermined from wrist joint  36  of forearm  8  in order to attach one ends of a forearm front link  37 L, a forearm outside link  38 L, and a forearm inside link  39 L to forearm  8 . Forearm front link attaching unit J 26  is provided on the front side of forearm  8 . Forearm outside link attaching unit J 27  is provided at the position forming the angle of 90 degrees with respect to forearm front link attaching unit J 26  in the plane perpendicular to forearm  8 . Forearm inside link attaching unit J 28  is provided at the position where the angle between forearm inside link attaching unit J 27  and forearm outside link attaching unit J 27  becomes 180 degrees. A middle point of the line segment connecting forearm outside link attaching unit J 27  and forearm inside link attaching unit J 28  is matched with the center of the cross section of forearm  8 . 
     Hand  9  includes a wrist plate  91 , a plate-shaped palm plate  92 , a hand  98  that connects palm plate  92  vertically to wrist plate  91 , a first finger  93 , a second finger  94 , a third finger  95 , and a fourth finger  96 , which are four ordinary fingers, and an opposable finger  97 . The wrist plate  91  has a hexagonal plate shape in which a long side and a short side are alternately arranged. The four ordinary fingers are connected to an opposite side to wrist plate  91  of palm plate  92 . Opposable finger  97  is connected to palm plate  92  in the direction different from that of the four ordinary fingers, and can be moved to the position opposed to the ordinary fingers. Wrist plate  91  is connected to forearm bone  8 B with wrist joint  36  interposed therebetween. The four ordinary fingers are aligned in almost the same direction. 
     Hand  9  resembles a human hand. Opposable finger  97  corresponds to a thumb, and first finger  93 , second finger  94 , third finger  95 , and fourth finger  96  correspond to an index finger, a middle finger, a ring finger, and a little finger, respectively. 
     In palm plate  92 , the surface existing on the side where the finger is bent is referred to as the palm side, and the opposite surface is referred to as the backside of the hand. In the hand, the palm side is referred to as the front, the backside of the hand is referred to as the rear. In the plane parallel to palm plate  92 , the direction in which the ordinary finger extends is referred to as a fingertip direction. The fingertip direction is a direction from the wrist toward a fingertip. The direction orthogonal to the fingertip direction is referred to as a hand breadth direction. 
     Forearm front link attaching unit J 26  is the biaxial gimbal in which the shaft member provided at one end of forearm front link  37 L is held rotatably by the yoke that is rotated by the rotation member protruding on the front side of forearm  8 . Forearm outside link attaching unit J 27  and forearm inside link attaching unit J 28  are also the biaxial gimbal having the same structure. The direction from the front to the rear of forearm  8  is substantially parallel to the direction in which first finger  93  to fourth finger  96  are arranged in hand  9 . 
     In forearm front link  37 L, the force generated by a motor  37 M is transmitted to a nut  37 B by a timing belt provided on the side where hand  9  exists. Forearm front link  37 L is attached to forearm front link attachment J 26  using a link attachment  37 N extending in L-shape from between the cylinder of the variable length link and the motor. One end of the motor exists at a position closer to elbow joint  31  than the attachment position on one side. Forearm outside link  38 L and forearm inside link  39 L have the same structure. 
     The state in which wrist plate  91  is perpendicular to forearm bone  8 B while opposable finger  97  exists in the front direction of upper limb  3  is the reference state of hand  9 . A hand-side front link attaching unit J 29 , a hand-side outside link attaching unit J 30 , and a hand-side inside link attaching unit J 31  are provided on the surface on the side where forearm  8  of wrist plate  91  exists in order to attach the other ends of forearm front link  37 L, forearm outside link  38 L, and forearm inside link  39 L to wrist plate  91 . 
     Hand-side front link attaching unit J 29 , hand-side outside link attaching unit J 30 , hand-side inside link attaching unit J 31 , and wrist joint  36  exist on a same plane. Hand-side front link attaching unit J 29 , hand-side outside link attaching unit J 30 , and hand-side inside link attaching unit J 31  are arranged at positions constituting an equilateral triangle. Wrist joint  36  is located at a center of gravity of the equilateral triangle. Consequently, wrist joint  36  exists on a bisector of the line segment connecting the hand-side outside link attaching unit J 30  and the hand-side inside link attaching unit J 31 . Hand-side front link attaching unit J 29  exists in the reference state on the plane determined by forearm bone  8 B and forearm front link attaching unit J 26 . 
     Hand-side front link attaching unit J 29  is the biaxial gimbal in which the shaft member provided at one end of forearm front link  37 L is held rotatably by the yoke that is rotated by the rotation member protruding in the direction of the wrist joint  36  from the protrusion provided on the surface of the wrist plate  91  on the side of forearm  8 . Hand-side outside link attaching unit J 30  and hand-side inside link attaching unit J 31  are also the biaxial gimbal having the same structure. 
     One ends of forearm front link  37 L, forearm outside link  38 L, and forearm inside link  39 L are attached rotatably to hand-side front link attaching unit J 29 , hand-side outside link attaching unit J 30 , and hand-side inside link attaching unit J 31  with two rotational degrees of freedom, respectively. The other ends of forearm front link  37 L, forearm outside link  38 L, and forearm inside link  39 L are attached rotatably to forearm-side front link attaching unit J 26 , forearm-side outside link attaching unit J 27 , and forearm-side inside link attaching unit J 28  with two rotational degrees of freedom, respectively. 
     Wrist C 6  is a three-rotational-degree-of-freedom connection mechanism that connects hand  9  being the second member rotatably to forearm  8  being the first member with three rotational degrees of freedom. Wrist C 6  includes wrist joint portion  36  being the joint, forearm front link  37 L, forearm outside link  38 L, and forearm inside link  39 L, being three variable length links, forearm front link attaching unit J 26 , forearm outside link attaching unit J 27 , and forearm inside link attaching unit J 28 , being three first-member-side link attaching units, and hand-side front link attaching units J 29 , hand-side outside link attaching unit J 30 , and hand-side inside link attaching unit J 31 , being three second-member-side link attaching units. 
     Forearm bone  8 B is a torsion axis in which the direction is fixed with respect to forearm  8  being the first member. In forearm bone  8 B, the angle with respect to hand  9  can be changed. The relative positional relationships with wrist joint  36  are fixed in forearm front link attaching unit J 26 , forearm outside link attaching unit J 27 , and forearm inside link attaching unit J 28 . The relative positional relationships with wrist joint  36  are also fixed by wrist plate  91  in hand-side front link attaching unit J 29 , hand-side outside link attaching unit J 30 , and hand-side inside link attaching unit J 31 , being the link attaching units provided in hand  9  being the second member. 
     The arrangement of the variable length links in wrist C 6  is described.  FIG. 50  is a perspective view illustrating the arrangement of the variable length links in left wrist C 6 . Wrist C 6  includes three variable length links  37 L,  38 L,  39 L connecting three first-member-side link attaching units J 26 , J 27 , J 28  and three second-member-side link attaching units J 29 , J 30 , J 31 , respectively. Consequently, the connection angle of hand  9  to forearm bone  8 B can be changed with three rotational degrees of freedom by changing the lengths of three variable length links  37 L,  38 L,  39 L. It is assumed that αv is the rotation angle of wrist joint  36  around the X-axis, that βv is the rotation angle around the Y-axis, and that γv is the rotation angle around the Z-axis. 
     Wrist joint  36  is located on the link attaching plane determined by second-member-side link attaching units J 29 , J 30 , and J 31 . Consequently, wrist joint  36  is also the torsion center being the intersection point of the link attachment plane and torsion axis  8 . A second-member triangle T 3  is an equilateral triangle. Wrist joint  36  exists at the position of the center of gravity of second-member triangle T 3 . Second-member-side link attaching units J 30 , J 31  are symmetrically arranged with respect to the straight line passing second-member-side link attaching unit J 29  and the torsion center. 
       FIG. 51  is a view illustrating the arrangement of the variable length links in left wrist C 6  in the reference state viewing from the direction in which the forearm extends. In the reference state, variable length links  38 L,  39 L have the twisted relationship with torsion axis  8 . A tilt angle θv 1  formed between the link reference plane including first-member-side link attaching unit J 26  of variable length link  37 L and torsion axis  8  and variable length link  37 L is zero degree. Tilt angles θv 2 , θv 3  of variable length links  38 L,  39 L are about 8.1 degrees. In the reference state, a maximum value θvmax of the tilt angles of three variable length links  37 L,  38 L,  39 L is about 8.1 degrees, and is greater than or equal to δ 0  (for example, about 3 degrees). The torque rotating around torsion axis  8  is generated in the case that the lengths of variable length links  38 L,  39 L are changed. 
     When hand  9  is tilted or twisted within the movable range with respect to forearm bone  8 B, at least one of three variable length links  37 L,  38 L,  39 L has the twisted relationship with torsion axis  8 , and maximum value θvmax of the tilt angle is greater than or equal to δ 0 . In the reference state, variable length link  37 L is located on the same plane as torsion axis  8 , and variable length links  38 L,  39 L has the twisted relationship with torsion axis  8 . To decrease both tilt angles θv 2 , θv 3  of variable-length links  38 L,  39 L, hand  9  is tilted toward the side of fourth finger  96 . When hand  9  is tilted toward the side of fourth finger  96 , variable length link  37 L exists on the same plane as torsion axis  8 .  FIG. 52  is a view illustrating the arrangement of the variable length links with left wrist C 6  tilted toward the side of fourth finger  96  when the arrangement of the variable length links is viewed from the direction in which forearm bone  8 B extends. In  FIG. 52 , hand  9  is tilted by 20 degrees toward the side of fourth finger  96 . Tilt angles θv 2 , θv 3  of variable length links  38 L,  39 L are about 7.4 degrees. In the case in that wrist C 6  is tilted in the direction to the palm or the backside of the hand, and in the case in that wrist C 6  is rotated around torsion axis  8 , one of tilt angles θv 2 , θv 3  of variable length links  38 L,  39 L is increased, and the other is decreased. 
     Referring to  FIGS. 11, 21, 22, and 53 to 61 , the structure of a crotch C 7  that moves thigh  10  with respect to waist  6  is described.  FIGS. 53, 54, and 55  are a front view, a left side view, and a rear view of a portion below the waist in the skeleton structure.  FIG. 56  is a perspective view illustrating a portion below a knee joint  40  in the skeleton structure.  FIGS. 57, 58, and 59  are an enlarged front view, an enlarged left side view, and an enlarged rear view of the thigh.  FIG. 60  is a perspective view illustrating the thigh viewing from the front oblique right.  FIG. 61  is a perspective view illustrating the thigh viewing from the rear oblique right. 
     As illustrated in  FIG. 53 , in the reference state, crotch front link attaching unit J 11  exists on the straight line being viewed from the front, passing through thigh  10 , and being extended to the upper side than hip joint  22 . Crotch outside link attaching unit J 12  protrudes horizontally outward. Crotch inside link attaching unit J 13  protrudes obliquely forward and downward on the inside. In the reference state, hip joint  22 , knee joint  40 , and an ankle joint  41  exist on the same straight line viewed from the front. As illustrated in  FIG. 58 , lower limb connecting frame  62  on the flat plate is tilted at an angle ξ 3  (about 45 degrees) with respect to the horizontal plane (XY-plane), and the front side is high. For this reason, the plane determined by crotch front link attaching unit J 11 , crotch outside link attaching unit J 12 , and crotch inside link attaching unit J 13  faces obliquely forward and downward. 
     Thigh  10  includes a rod-shaped thighbone  10 A, a knee-side link attaching plate  10 B provided perpendicular to thighbone  10 A, and a knee connecting frame  10 C being two frames connecting knee-side link attaching plate  10 B and knee joint  40 . Knee connecting frame  10 C is tilted with respect to thighbone  10 A and connected to knee-side link attaching plate  10 B such that knee joint  40  is located behind thighbone  10 A. One ends of the three variable length links that rotate hip joint  22  with three rotational degrees of freedom are attached to the three link attaching units provided on knee-side link attaching plate  10 B. Knee joint  40  exists behind thighbone  10 A, which allows hip joint  22 , knee joint  40 , and ankle joint  41  to exist easily on the vertical line viewing from the front. 
     Thigh front link  23 L, thigh outside link  24 L, and thigh inside link  25 L are attached to a knee front link attaching unit J 32 , a knee outside link attaching unit J 33 , and a knee inside link attaching unit J 34 , being provided on knee-side link attaching plate  10 B that is perpendicular to thigh  10 . Knee-side link attaching plate  10 B has a shape in which three rectangles connected on the center side extend in the directions each of which has an angle of 120 degrees. The rectangle provided with the knee front link attaching unit J 32  exists on the front side of thigh  10 . 
     Knee front link attaching unit J 32  has a structure that allows rotation with two rotational degrees of freedom using a cross member in which two cylinders are joined into a cross shape. The yoke that holds rotatably one of the cylinders of the cross member is provided on knee-side link attaching plate  10 B. The yoke that holds rotatably the other cylinder of the cross member is provided at one end of thigh front link  23 L. 
     Knee outside link attaching unit J 33  and knee inside link attaching unit J 34  have the same structure as knee front link attaching unit J 32 . 
     Crotch C 7  is a three-degree-of-freedom connection mechanism that connects thigh  10  being the second member rotatably to waist  6  being the first member with three rotational degrees of freedom. Crotch C 7  includes hip joint  22  being the joint, thigh front links  23 L, thigh outside link  24 L, and thigh inside link  25 L that are three variable length links, crotch front link attaching unit J 11 , crotch outside link attaching unit J 12 , and crotch inside link attaching unit J 13  that are three first-member-side link attaching unit, and knee front link attaching units J 32 , knee outside link attaching unit J 33 , and knee inside link attaching unit J 34  that are three second-member-side link attaching units. 
     The direction of thighbone  10 A being the torsion axis is fixed with respect to thigh  10 . The angle between thighbone  10 A and waist  6  can be changed. In crotch front link attaching unit J 11 , crotch outside link attaching unit J 12 , and crotch inside link attaching unit J 13 , the positional relationships with respect to hip joint  22  are fixed by lower limb connecting frame  62 . The relative positional relationships with hip joint  22  are also fixed by thighbone  10 A and knee-side link attaching plate  10 B in knee front link attaching unit J 32 , knee outside link attaching unit J 33 , and knee inside link attaching unit J 34 . 
     The arrangement of the variable length links that move hip joint  22  is described.  FIG. 62  is a perspective view illustrating the arrangement of the variable length links in crotch C 7 . Crotch C 7  includes three variable length links  23 L,  24 L,  25 L connecting three first-member-side link attaching units J 11 , J 12 , J 13  and three second-member-side link attaching units J 32 , J 33 , J 34 , respectively. For this reason, the connection angle of thigh  10  to waist  6  can be changed with three rotational degrees of freedom by changing the lengths of three variable length links  23 L,  24 L,  25 L. It is assumed that αq is the rotation angle around the X-axis of hip joint  22 , that βq is the rotation angle around the Y-axis, and that γq is the rotation angle around the Z axis. 
     In crotch C 7 , thigh  10  can be raised forward by, for example, about 90 degrees, and raised rearward by, for example, 10 degrees. In the right and left direction, thigh  10  can be moved inside by, for example, about 10 degrees, and moved outside by, for example, about 30 degrees. Further, around thighbone  10 A, thigh  10  can be twisted and rotated outside (crotch opening direction) by, for example, about 20 degrees, and twisted and rotated inside by, for example, about 10 degrees. 
       FIG. 63  is a view illustrating the arrangement of the variable length links in left crotch C 7  viewing from the direction in which the thighbone extends. In the reference state, variable length links  24 L,  25 L and torsion axis  10 A have the twisted relationship. A tilt angle θq 1  formed between the link reference plane including second-member-side link attaching unit J 32  of variable length link  23 L and torsion axis  10 A and variable length link  23 L is zero degree. A tilt angle θq 2  of variable length link  24 L is about 1.9 degrees. A tilt angle θq 3  of variable length link  25 L is about 3.9 degrees. A maximum value θqmax of the tilt angles of three variable length links  23 L,  24 L,  25 L is greater than or equal to δ 0  (for example, about 3 degrees). The torque rotating around torsion axis  10 A is generated in the case that the lengths of variable length links  24 L,  25 L are changed. 
       FIG. 64  is a view illustrating the arrangement of the variable length links when thigh  10  of left crotch C 7  is raised to the left front viewing from the direction in which thighbone  10 A extends.  FIG. 64  illustrates the state in which thigh  10  is raised by 30 degrees in the direction of the left front of 15 degrees. As can be seen from  FIG. 64 , when thigh  10  is raised, lower limb connecting frame  62  is lengthened in the vertical direction of the drawing, and tilt angle θq 3  of variable length link  25 L is larger than that in the case of  FIG. 63 . Tilt angle θq 1  of variable length link  23 L is also increased. In moving thigh  10  within the movable range, namely, in each state within the movable range of hip joint  22 , at least one of variable length links  23 L,  24 L,  25 L has the twisted relationship with torsion axis  10 A. In each state within the movable range of hip joint  22 , maximum value θqmax of the tilt angles of three variable length links  23 L,  24 L,  25 L is greater than or equal to δ 0  (for example, about 3 degrees). 
     The fact that hip joint  22  is rotatable around thighbone  10 A is necessary when humanoid robot  100  changes the direction and walks. In the case that hip joint  22  cannot be rotated around thighbone  10 A, humanoid robot  100  walks in the oblique direction while facing the front. In changing the orientation of the entire body by moving lower limb  3 , it is necessary to be able to change a direction in which a leg is opened at hip joint  22 . 
     Referring to  FIG. 65 , the effect obtained by attaching the variable length link that moves hip joint  22  high on the front side and attaching the variable length link low on the rear side is described. In  FIG. 65 , only variable length links  23 L,  24 L are illustrated for convenience. The left side in  FIG. 65  is a side view illustrating the case that variable length links  23 L,  24 L,  25 L that move hip joint  22  are attached high on the front side and attached low in the rear side as in the first embodiment. The right side in  FIG. 65  is a side view illustrating the case that variable length links  23 L,  24 L,  25 L that move hip joint  22  are attached at the same height. The upright state is indicated by a solid line, and the state in which the thigh is raised forward by 45 degrees and to a limit of the movable range is indicated by a broken line. 
     When variable length links  23 L,  24 L,  25 L that move hip joint  22  are attached at the same height, the movable range on the front side of the hip joint  22  becomes smaller than that of the case that variable length links  23 L,  24 L,  25 L are attached high on the front side. This is because variable length link  23 L and lower limb connecting frame  62  interfere with each other when hip joint  22  is rotated in the direction in which thigh  10  and knee joint  40  are located forward. When variable length link  23 L on the front side is set to the higher position, the interference between variable length link  23 L and lower limb connecting frame  62  is hardly generated, hip joint  22  can largely be rotated forward, and thigh  10  can further be raised. 
     In the case that all variable length links  23 L,  24 L,  25 L are attached at the same height, despite the movable range is narrow, it is necessary to lengthen variable length link  24 L longer in moving hip joint  22  to the limit of the movable range as compared with the case that the front side is set higher. On the other hand, it is necessary to shorten variable length link  23 L shorter. 
     Referring to  FIGS. 53 to 62 , the structure of a knee C 8  that moves lower leg  11  with respect to thigh  10  is described. As illustrated in  FIG. 56 , knee joint  40  has the structure in which plate-shaped lower leg  11  is sandwiched between two knee connecting frames  10 C and the rotation axis is passed through lower leg  11  and two knee connecting frames  10 C. In the reference state, the rotation axis is parallel to the X-axis. Two knee connecting frames  10 C are coupled together on the front side by a coupling plate  10 D in order to increase strength. Coupling plate  10 D also has a function of preventing knee joint  40  from being bent in the reverse direction. As illustrated in  FIG. 58  and other figures, the angle of knee joint  40  can be changed by changing the length of a knee drive link  42 L included in one knee drive actuator  42  provided on the rear side of thigh  10 . Lower leg  11  is a plate-shaped member, which is bent near knee joint  40  and bent at the position predetermined from ankle joint  41 . Lower leg  11  is located on the front side of the straight line connecting knee joint  40  and ankle joint  41 . 
     Knee drive actuator  42  has the structure in which force from a motor  42 M being the power source is transmitted to knee drive link  42 L by a gear provided on the side where knee joint  40  exists. 
     A knee drive link attaching unit J 35  to which one end of knee drive link  42 L is attached rotatably with one rotational degree of freedom is provided on the back side of thighbone  10 A close to hip joint  22 . 
     Knee drive link attaching unit J 35  has the structure in which the yoke is provided on thighbone  10 A and the columnar shaft member is provided at one end of knee drive link  42 L. 
     Knee drive link  42 L is connected to both thigh  10  and the lower leg  11  using two auxiliary tools on the side where knee joint  40  exists. The two auxiliary tools are a thigh-side auxiliary tool  43  and a lower leg-side auxiliary tool  44 . One end of thigh-side auxiliary tool  43  is attached rotatably to one end of knee drive link  42 L. A place to which one end of thigh-side auxiliary tool  43  and one end of knee drive link  42 L are attached is referred to as a knee drive link auxiliary tool connecting unit J 37 . The other end of thigh-side auxiliary tool  43  is attached rotatably to a thigh-side auxiliary tool attaching unit J 36  provided on the rear side of thigh  10 . One end of lower leg-side auxiliary tool  44  is also attached rotatably to knee drive link auxiliary tool connecting unit J 37 . The other end of lower leg-side auxiliary tool  44  is attached rotatably to a lower leg-side auxiliary tool attaching unit J 38  provided on the rear side of lower leg  11 . 
     A rod-shaped thigh-side auxiliary tool attaching unit  10 D extends backward from the position slightly upper than a knee-side link attaching plate  10 B of thighbone  10 A. Thigh-side auxiliary tool attaching unit J 36  is provided at the tip of thigh-side auxiliary tool attaching unit  10 D. Thigh-side auxiliary tool attaching unit J 36  exists near knee-side link attaching plate  10 B. Thigh-side auxiliary tool  43  has a structure in which the side faces of the two frames are connected to each other. The through-hole is made at the tip of thigh-side auxiliary tool attaching unit  10 D. The through-holes are also made at both ends of thigh-side auxiliary tool  43 . Thigh-side auxiliary tool attaching unit J 36  has the structure, in which thigh-side auxiliary tool attaching unit  10 D is sandwiched by thigh-side auxiliary tool  43  such that the positions of the through-holes are aligned with each other and the rotation shaft passes through the through-holes. 
     The end on the opposite side to thigh-side auxiliary tool  43  is connected to lower leg-side auxiliary tool  44  and knee drive link  42 L with one rotational degree of freedom by knee drive link auxiliary tool connecting unit J 37 . Lower leg-side auxiliary tool  44  has a structure in which the side faces of the two frames are connected to each other. In knee drive link auxiliary tool connecting unit J 37 , thigh-side auxiliary tool  43  sandwiches knee drive link  42 L. Lower leg-side auxiliary tool  44  sandwiches thigh-side auxiliary tool  43  and knee drive link  42 E At the place where lower leg-side auxiliary tool  44  sandwiches thigh-side auxiliary tool  43  and knee drive link  42 L, the through-holes are made in lower leg-side auxiliary tool  44 , thigh-side auxiliary tool  43 , and knee drive link  42 L. Each of thigh-side auxiliary tool  43 , lower-leg-side auxiliary tool  44 , and knee drive link  42 L can be rotated with one rotational degree of freedom by the shaft member passing through these through-holes. 
     Lower leg-side auxiliary tool attaching unit J 38  is provided near the place where lower leg  11  is bent on the side where knee joint  40  exists. One end of lower-leg-side auxiliary tool  44  is attached rotatably to lower-leg-side auxiliary tool attaching unit J 38  with one rotational degree of freedom. Lower leg-side auxiliary tool attaching unit J 38  has the structure in which the rotation shaft is inserted in the through-holes provided in lower leg  11  and lower leg-side auxiliary tool  44 . Lower-leg-side auxiliary tool  44  is attached rotatably to lower leg  11  with one rotational degree of freedom by lower-leg-side auxiliary tool attaching unit J 38 . 
       FIG. 66  is a perspective view illustrating the arrangement of the variable length link that moves left knee joint  40 . Knee joint  40 , knee drive link attaching unit J 35 , and thigh-side auxiliary tool attaching unit J 36  are fixed to thigh  10 , and the relative positional relationships among knee joint  40 , knee drive link attaching unit J 35 , and thigh-side auxiliary tool attaching unit J 36  are fixed. Lower leg-side auxiliary tool attaching unit J 38  is fixed to lower leg  11 . Lower leg-side auxiliary tool attaching unit J 38  has a predetermined distance from knee joint  40 . Knee drive link auxiliary tool connecting unit J 37  has predetermined distances from thigh-side auxiliary tool attaching unit J 36  and lower leg-side auxiliary tool attaching unit J 38 . Therefore, when the rotation angle of knee joint  40  is determined, thigh-side auxiliary tool  43  and lower leg-side auxiliary tool  44  are moved like a pantograph, and the position of knee drive link auxiliary tool connecting unit J 37  is determined. On the other hand, when the position of knee drive link auxiliary tool connecting unit J 37  is determined, the rotation angle of knee joint  40  is determined. 
     The length of knee drive link  42 L is the distance between knee drive link attaching unit J 35  and knee drive link auxiliary tool connecting unit J 37 . Thus, the rotation angle of knee joint  40  can be changed by changing the length of knee drive link  42 L. 
     Knee C 8  includes knee joint  40 , knee drive actuator  42 , knee drive link attaching unit J 35  provided on the rear side of thigh  10 , thigh-side auxiliary tool  43 , thigh-side auxiliary tool attaching unit J 36  provided on the rear side of thigh  10 , lower leg-side auxiliary tool  44 , and lower leg-side auxiliary tool attaching unit J 38  provided on the rear side of the lower leg. Knee joint  40  connects thigh  10  and lower leg  11  rotatably with one rotational degree of freedom. Knee drive actuator  42  includes knee drive link  42 L having a variable length and motor  42 M. One end of knee drive link  42  is attached rotatably to knee drive link attaching unit J 35 . One end of thigh-side auxiliary tool  43  is attached rotatably to the other end of knee drive link  42 L. The other end of thigh-side auxiliary tool  43  is attached rotatably to thigh-side auxiliary tool attaching unit J 36 . One end of lower leg-side auxiliary tool  44  is attached rotatably to the other end of knee drive link  42 L. The other end of lower leg-side auxiliary tool  44  is attached rotatably to lower leg-side auxiliary tool attaching unit J 38 . 
     Knee C 8  can be bent from the state in which hip joint  22 , knee joint  40 , and ankle joint  41  are arranged on the same straight line to the state in which the angle between thigh  10  and lower leg  11  is about 40 degrees. 
     Knee C 8  includes thigh-side auxiliary tool  43  and lower leg-side auxiliary tool  44 , so that the force caused by the expansion and contraction of knee drive link  42 L can be transmitted to thigh-side auxiliary tool attaching unit J 36  and lower leg-side auxiliary tool attaching unit J 38  like the pantograph. Consequently, the force rotating knee joint  40  is transmitted easily even in the case that knee joint  40  is largely bent as thigh  10  and lower leg  11  become closer to a parallel position. As a result, with small force generated by knee drive actuator  42 , the bending and stretching motion of knee joint  40  can be performed more smoothly. 
     Referring to  FIGS. 53 to 56, and 67 to 70 , the structure of an ankle C 9  that moves foot  12  with respect to lower leg  11  is described.  FIGS. 67, 68, 69, and 70  are a front view, a left side view, a rear view, and a perspective view of a portion below lower leg  11 . 
     Ankle joint  41  is the biaxial gimbal that rotatably connects foot  12  to lower leg  11  with two rotational degrees of freedom in the front-back direction and in the right and left direction. A columnar portion in the right and left direction is provided at a lower end of lower leg  11  such that lower leg  11  can be rotated in the front-back direction. The columnar portion of lower leg  11  is held and sandwiched rotatably by a front-back rotation yoke  41 A, and lower leg  11  can be rotated in the front-back direction with respect to front-back rotation yoke  41 A. Columnar portions (shaft member) are provided on the surfaces in the front-rear direction of front-back rotation yoke  41 A. A right and left rotation yoke  41 B provided on foot  10  holds rotatably the shaft member of front-back rotation yoke  41 A by sandwiching the shaft member from the front-back direction, and lower leg  11  and front-back rotation yoke  41 A are moved in the right and left direction with respect to foot  12 . 
     Foot  12  can be rotated around ankle joint  41  with two rotational degrees of freedom in the front-back direction and the right and left direction by a lower leg outside actuator  45  and a lower leg inside actuator  46 . A lower leg outside link attaching unit J 39  and a lower leg inside link attaching unit J 40 , which attach one ends of a lower leg outside link  45 L and a lower leg inside link  46 L rotatably with two rotational degrees of freedom, are provided on the right and left surfaces of plate-shaped lower leg  11 . Lower leg outside link attaching unit J 39  has the structure, in which the rotation member, the yoke, and the shaft member are provided on lower leg  11  and the shaft member is inserted into the cylinder provided at one end of lower leg outside link  45 L. Lower leg inside link attaching unit J 40  also has the same structure. 
     Lower leg outside actuator  45  has the structure in which the force from a motor  45 M is transmitted to lower leg outside link  45 L by the gear provided on the side where foot  12  exists. Lower leg inside actuator  46  also has the same structure. 
     A foot outside link attaching unit J 41  and a foot inside link attaching unit J 42 , which are attached rotatably to the other ends of lower leg outside link  45 L and lower leg inside link  46 L with two rotational degrees of freedom, are provided at the right and left positions in the back of foot  12 . Foot outside link attaching unit J 41  and foot inside link attaching unit J 42  are the biaxial gimbal having the same structure as lower leg outside link attaching unit J 39  and lower leg inside link attaching unit J 40 . 
     The interval between foot outside link attaching unit J 41  and foot inside link attaching unit J 42  is larger than the interval between lower leg outside link attaching unit J 39  and lower leg inside link attaching unit J 40 . Consequently, ankle joint  41  can be rotated in the right and left direction easily. 
     Foot  12  includes ankle joint  41 , a foot main body  12 A, and a toe  12 B provided on the front side of foot main body  12 A. Foot outside link attaching unit J 41  and foot inside link attaching unit J 42  are provided in foot main body  12 A. A toe joint  12 C is provided between foot main body  12 A and toe  12 B. The vertical angle of toe  12 B with respect to foot main body  12 A is changed by toe joint  12 C. A spring (not illustrated) is provided between toe  12 B and foot main body  12 A, and toe  12 B is appropriately bent according to the force when the force bending toe  12 B is applied. 
     A heel wheel  12 D is provided in the center at the rear end of foot main body  12 A. Heel wheel  12 D is a wheel having proper rolling friction. Foot  12  includes heel wheel  12 D, which allows a heel on the rear side of foot  12  to be landed smoothly when humanoid robot  100  walks. Heel wheel  12 D acts as a touch sensor that reports the landing of the heel while rotating. Foot side-surface wheels  12 E having proper rolling friction are provided on the side where foot  12  exists in the vicinity of toe joint  12 C. Foot side-surface wheel  12 E acts as a touch sensor that reports the landing of not only the heel but also entire foot  12 . When foot  12  is moved, foot side-surface wheel  12 E can detect that toe  12 B is in contact with a floor or a ground while rotating, and then detect that the toe  12 B is separated from the floor or the ground. 
       FIG. 71  is a perspective view illustrating the arrangement of the variable length links that move ankle joint  41 . 
     Ankle joint  41 , foot outside link attaching unit J 41 , and foot inside link attaching unit J 42  are fixed to foot main body  12 A, and the relative positional relationships among ankle joint  41 , foot outside link attaching unit J 41 , and foot inside link attaching unit J 42  are fixed. Lower leg outside link attaching unit J 39  and lower leg inside link attaching unit J 40  are fixed to lower leg  11 . The relative positional relationships among ankle joint  41 , lower leg outside link attaching unit J 39 , and lower leg inside link attaching unit J 40  are fixed. Lower leg outside link  45 L and lower leg inside link  46 L are the variable length link having the variable length. Lower leg outside link  45 L connects lower leg outside link attaching unit J 39  and foot outside link attaching unit J 41 . Lower leg inside link  46 L connects lower leg inside link attaching unit J 40  and foot inside link attaching unit J 42 . By changing the lengths of lower leg outside link  45 L and lower leg inside link  46 L, the connection angle of lower leg  41  to leg main body  12 A can be changed around the X-axis and the Y-axis. It is assumed that am is the rotation angle around the X-axis of ankle joint  41 , and that βm is the rotation angle around the Y-axis. 
     Ankle C 9  includes ankle joint  41 , lower leg outside actuator  45 , and lower leg inside actuator  46 . Ankle joint  41  connects the lower portion of lower leg  11  and foot  12  rotatably with at least two rotational degrees of freedom. Lower leg outside actuator  45  and lower leg inside actuator  46  are two ankle actuators including lower leg outside link  45 L and lower leg inside link  46 L and motor  45 M and a motor  46 M, respectively. 
     Ankle C 9  also includes lower leg outside link attaching unit J 39  and lower leg inside link attaching unit J 40 , foot outside link attaching unit J 41 , and foot inside link attaching unit J 42 . Lower leg outside link attaching unit J 39  and lower leg inside link attaching unit J 40  are two lower leg-side link attaching units that are provided in lower leg  11  being attached rotatably with one ends of lower leg outside link  45 L and lower leg inside link  46 L, respectively. Foot outside link attaching unit J 41  and foot inside link attaching unit J 42  are two foot-side link attaching units being attached rotatably with one ends of lower leg outside link  45 L and lower leg inside link  46 L, respectively. Foot outside link attaching unit J 41  and foot inside link attaching unit J 42  are provided in foot main body  12 A at positions behind ankle joint  41 . 
     In ankle C 9 , ankle joint  41  can be rotated in the range where the straight line connecting ankle joint  41  and knee joint  40  forms the angle from, for example, about 60 degrees forward to, for example, about 30 degrees backward with respect to foot  12 , and ankle joint  41  can be tilted by, for example, about 15 degrees in the right and left direction. 
     When both lower leg outside link  45 L and lower leg inside link  46 L are lengthened, lower leg  41  can be tilted forward. When both lower leg outside link  45 L and lower leg inside link  46 L are shortened, lower leg  41  can be tilted backward. When lower leg outside link  45 L is lengthened while lower leg inside link  46 L is shortened, lower leg  41  can be inclined inside. When lower leg outside link  45 L is shortened while lower leg inside link  46 L is lengthened, lower leg  41  can be inclined outside. 
     Referring to  FIGS. 72 to 79 , the structure of hand  9  is described.  FIG. 72  is a perspective view illustrating left hand  9  viewing from the palm side.  FIG. 73  is a perspective view illustrating left hand  9  viewing from the backside of the hand.  FIGS. 74, 75, 76, and 77  are a front view of left hand  9 , a side view of left hand  9  viewing from the side where opposable finger  97  exists, a rear view of left hand  9 , and a side view of left hand  9  viewing from the side where opposable finger  97  does not exist.  FIG. 78  is a view illustrating left hand  9  viewing from the fingertip side.  FIG. 79  is a view illustrating second finger  94  of left hand  9  in cross section. 
     As can be seen from  FIGS. 74 and 79 , hand attaching tool  98  that attaches palm plate  92  to wrist plate  91  is a member in which an attaching plate  98 A and a palm plate connecting part  98 B are connected into an L-shape in the side view. Attaching plate  98 A is connected to wrist plate  91 . Palm plate  92  is connected to palm plate connecting part  98 B. First finger  93 , second finger  94 , third finger  95 , and fourth finger  96  are connected to the side of palm plate  92  opposed to attaching plate  98 A. In the reference state, first finger  93 , second finger  94 , third finger  95 , and fourth finger  96  extend in the direction substantially parallel to palm plate  92 . Second finger  94  is located at the substantial center of wrist plate  91 . First finger  93 , second finger  94 , third finger  95 , and fourth finger  96  are provided such that the interval on the tip side is wider than the interval on the base side. As can be seen from  FIG. 76 , second finger  94  is perpendicular to attaching plate  98 A, and the center of second finger  94  and the center of attaching plate  98 A are matched with each other. 
     Opposable finger  97  is rotatable in the direction substantially orthogonal to first finger  93  and other fingers, and provided in a portion of palm plate  92 , the portion exists on the side closer to attaching plate  98 A than first finger  93  and other fingers and on the side where first finger  93  exists. Palm plate  92  is a base being connected with the fingers. In the reference state of hand  9 , opposable finger  97  extends side by side with palm plate  92  viewing from the direction perpendicular to palm plate  92 . 
     First finger  93 , second finger  94 , third finger  95 , and fourth finger  96  have the same structure. First finger  93 , second finger  94 , third finger  95 , and fourth finger  96  are referred to as ordinary fingers. The structure of the ordinary finger is described using fourth finger  96  to which the reference sign is added easily in the drawings. 
     In fourth finger  96 , a first dactylus  96 A, second dactylus  96 B, and a third dactylus  96 C are connected in series from the side closer to palm plate  92 . A first finger joint  96 D exists between palm plate  92  and first dactylus  96 A. First finger joint  96 D connects first dactylus  96 A rotatably to palm plate  92 . A second finger joint  96 E exists between first dactylus  96 A and second dactylus  96 B. Second finger joint  96 E connects second dactylus  96 B rotatably to first dactylus  96 A. A third finger joint  96 F exists between second dactylus  96 B and third dactylus  96 C. Third finger joint  96 F connects third dactylus  96 C rotatably to second dactylus  96 B. The rotation axes of first finger joint  96 D, second finger joint  96 E, and third finger joint  96 F are parallel to one another. 
     Regarding adjacent two of palm plate  92 , first dactylus  96 A, second dactylus  96 B, and third dactylus  96 C, a member located on the side closer to palm plate  92  is referred to as a base-side member, and the other member located on the side where the base-side member does not exist is referred to as a tip-side member. First finger joint  96 D, second finger joint  96 E, and third finger joint  96 F are three finger joints that connect the tip-side member being one of first dactylus  96 A, second dactylus  96 B, and third dactylus  96 C rotatably to the base-side member. 
     In the reference state, first finger joint  96 D exists on the rear side of palm plate  92 . As illustrated in  FIG. 77 , when hand  9  in the reference state is viewed from the side, the rotation axes of first finger joint  96 D, second finger joint  96 E, and third finger joint  96 F exist on one plane substantially perpendicular to attaching plate  98 A. In the reference state, a line extending from forearm bone  8 B toward hand  9  passes through or near this plane. In the reference state, forearm  7  is perpendicular to attaching plate  98 A. 
     The rotation shaft of first finger joint  96 D is held by a finger base yoke  96 G provided on the rear side of palm plate  92 . The rotation axis of first finger joint  96 D is disposed at a predetermined position slightly outside from palm plate  92 . A finger first motor  96 H is disposed in finger base yoke  96 G. A first worm  96 J (screw gear) connected directly to the rotation shaft of finger first motor  96 H meshes with a first worm wheel  96 K (helical gear) that is rotated around the rotation axis of first finger joint  96 D. First worm  96 J meshes with first worm wheel  96 K existing on the side of palm plate  92 . Finger first motor  96 H and first worm  96 J are provided obliquely with respect to palm plate  92 . First worm wheel  96 K is attached to first dactylus  96 A. When finger first motor  96 H rotates, first worm  96 J is rotated, and first worm wheel  96 K is rotated together with first dactylus  96 A. 
     In first finger joint  96 D, a worm gear mechanism rotates first dactylus  96 A with respect to palm plate  92 . The worm gear mechanism includes finger first motor  96 H disposed on palm plate  92 , first worm  96 J rotated by finger first motor  96 H, and first worm wheel  96 K that meshes with first worm  96 J to be rotated around the rotation axis of first finger joint  96 D together with first dactylus  96 A. 
     First dactylus  96 A has the structure in which the member rotating together with first worm wheel  96 K and the yoke member holding the rotation axis of second finger joint  96 E are coupled together in the direction toward the fingertip. A finger second motor  96 L is attached to first dactylus  96 A. A second worm  96 M, which is connected directly to the rotation shaft of finger second motor  96 L, meshes with a second worm wheel  96 N that is rotated around the rotation axis of second finger joint  96 E. Finger second motor  96 L and second worm  96 M are provided obliquely with respect to first dactylus  96 A. Second worm wheel  96 N is attached to second dactylus  96 B. When finger second motor  96 L rotates, second worm  96 M is rotated, and second worm wheel  96 N is rotated together with second dactylus  96 B. 
     In second finger joint  96 E, a worm gear mechanism rotates second dactylus  96 B with respect to first dactylus  96 A. The worm gear mechanism includes finger second motor  96 L disposed on first dactylus  96 A, second worm  96 M rotated by finger second motor  96 L, and second worm wheel  96 N that meshes with second worm  96 M to be rotated around the rotation axis of second finger joint  96 E together with second dactylus  96 B. 
     First finger joint  96 D and second finger joint  96 E are driven by different motors, so that the rotation angles of first finger joint  96 D and second finger joint  96 E can independently be determined. 
     In the reference state, the direction in which first finger joint  96 D rotates first dactylus  96 A, the direction in which second finger joint  96 E rotates second dactylus  96 B, the direction in which third finger joint  96 F rotates third dactylus  96 C are the direction toward the palm side. 
     Palm plate  92  can have small size by providing finger first motor  96 H and first worm  96 J obliquely with respect to palm plate  92 . First dactylus  96 A can be shortened by providing finger second motor  96 L and second worm  96 M obliquely with respect to first dactylus  96 A. As a result, hand  9  can be made as large as a human hand. 
     First dactylus  96 A is rotated with respect to palm plate  92  by first finger joint  96 D having the worm gear mechanism, and connected rotatably to second dactylus  96 B by second finger joint  96 E having the worm gear mechanism. As described above, in hand  9 , the worm gear mechanism is applied to the first finger joint and the second finger joint that are the two finger joints from the palm sides of the four ordinary fingers. 
     Referring to  FIG. 79 , the mechanism that rotates third finger joint  94 F is described. A third dactylus drive gear  94 P is provided in third finger joint  94 F. Third dactylus drive gear  94 P is rotated together with third dactylus  94 C. Three idler gears  94 Q,  94 R,  94 S are provided in second dactylus  94 B. Three idler gears  94 Q,  94 R,  94 S transmit the rotation of second worm wheel  94 N to third dactylus drive gear  94 P. Idler gear  94 Q meshes with second worm wheel  94 N, and idler gear  94 Q is rotated in the opposite direction when second worm wheel  94 N is rotated. Idler gear  94 R meshes with idler gear  94 Q, and idler gear  94 R is rotated in the opposite direction when idler gear  94 Q is rotated. Idler gear  94 S meshes with idler gear  94 R, and idler gear  94 S is rotated in the opposite direction when idler gear  94 R is rotated. Third dactylus drive gear  94 P meshes with idler gear  94 S, and third dactylus drive gear  94  is rotated in the opposite direction when idler gear  94 S is rotated. Because three that is the number of idler gears  94 Q,  94 R,  94 S is an odd number, third dactylus drive gear  94 P is rotated in the same direction when second worm wheel  94 N is rotated. 
     Idler gears  94 Q,  94 R,  94 S are the gears that are rotated on the odd number of rotating shafts driven by second worm wheel  94 N included in second finger joint  94 E. Third dactylus drive gear  94 P is the gear provided in third finger joint  94 F driven by idler gears  94 Q,  94 R,  94 S. Second worm wheel  94 N is the gear that is rotated in conjunction with the rotation of second finger joint  94 E. 
     A gear ratio of second worm wheel  94 N, idler gear  94 Q,  94 R,  94 S, and third dactylus drive gear  94 P is determined such that a rotation angle φ 2  of second worm wheel  94 N and a rotation angle φ 3  of third dactylus drive gear  94 P are equal to each other. That is, a value f=φ 3 /φ 2  being a ratio of φ 3  to φ 2  is set to f=1. Value f=φ 3 /φ 2  of the ratio of third dactylus drive gear  94 P, namely, rotation angle φ 3  of third dactylus  94 C to second worm wheel  94 N, namely, rotation angle φ 2  of second dactylus  94 B may be a proper value close to 1. 
     The three dactyli can be rotated by two motors per one finger by rotating the third dactylus in conjunction with the second dactylus. Because there is almost no need to make the motion to bend only the third finger joint without bending the second finger joint, no problem arises in use of hand  9 . The third finger joint may be rotated by the worm gear mechanism similarly to the first finger joint and the second finger joint. The third finger joint may be rotated in conjunction with the second finger joint in some finger, and the third finger joint may be rotated by the worm gear mechanism in another finger. 
     The structure of opposable finger  97  is described. As illustrated in  FIG. 76 , a finger base yoke  97 G that holds the rotation axis of a first finger joint  97 D of opposable finger  97  is provided at the position close to an attaching plate  98 A on the rear side of palm plate  92  in a direction substantially orthogonal to second finger  94 . A finger first motor  97 H is disposed in finger base yoke  97 G. A first worm  97 J connected directly to the rotation shaft of finger first motor  97 H meshes with a first worm wheel  97  that is rotated around the rotation axis of first finger joint  97 D. First worm wheel  97  is attached to second dactylus  97 B. When finger first motor  97 H rotates, first worm wheel  97  is rotated together with first dactylus  97 A. When first dactylus  97 A is rotated, second dactylus  97 B and third dactylus  97 C are moved to positions opposed to first finger  93  and other fingers. 
     First dactylus  97 A of opposable finger  97  includes a first dactylus base  97 T that is rotated together with first worm wheel  97  and a first dactylus tip  97 U that is directed in the direction having the angle of about 70 degrees with respect to the rotation direction of first dactylus base  97 T. The direction in which first dactylus tip  97 U is directed is substantially parallel to the direction in which first dactylus  93 A and the like are directed. The end existing on the side opposite to the side connected to first finger joint  97 D of first dactylus base  97 T has a flat plate shape. First dactylus tip  97 U is coupled to the flat-plate-shaped portion of first dactylus base  97 T. Finger second motor  97 H is disposed in first dactylus tip  97 U, and the yoke member holding the rotation shaft of second finger joint  93 E is provided in first dactylus tip  97 U. 
     In opposable finger  97 , the direction in which first finger joint  97 D rotates first dactylus  97 A is different from the direction in which second finger joint  97 E rotates second dactylus  97 B. The structure on the fingertip side from second finger joint  97 E of opposable finger  97  is the same as first finger  93  and other fingers. 
     All the mechanisms that drive the finger joint are provided within hand  9 . For this reason, maintenance, repair of trouble, and the like can be performed by removing only the hand  9  from humanoid robot  100 . 
     The operation is described. The posture of humanoid robot  100  is determined by angles taken by intrathoracic joint  16 , thoracolumbar joint  18 , shoulder joint  13 , elbow joint  31 , wrist joint  36 , hip joint  22 , knee joint  40 , ankle joint  41 , and neck joint  27 . The angles of these joints are determined by the lengths of the links that drive the joints. The link that drives each joint of humanoid robot  100  is set to a value determined from the designated angle that is the angle of each joint that can take the designated attitude, which allows humanoid robot  100  to take the designated posture. When humanoid robot  100  is moved, time series of the designated angles corresponding to a change in the posture are converted into time series of the link lengths, and the lengths of the links are changed according to the determined time series, which allow humanoid robot  100  to be moved as designated. 
     How to determine the length of the variable length link such that the joint can take a designated angle, and how to determine the position of the link attaching unit in the linear guide are described for each joint. The designated angle is required to be within the movable range of the joint. First, intrathoracic joint  16  and thoracolumbar joint  18  are described. Thoracolumbar joint  18  changes the connection direction of chest lower portion  5 D with respect to waist  6 . Intrathoracic joint  16  changes the connection direction of chest upper portion  5 U with respect to chest lower portion  5 D. 
     The distances between the joint and the link attaching units in intrathoracic joint  16  and thoracolumbar joint  18  are expressed by the following variables.  FIG. 80  is a view illustrating the variables expressing distances between the joint and the link attaching units in the intrathoracic joint and the thoracolumbar joint. 
     The variable expressing the position of each point is defined as follows. 
     P 0s : position of thoracolumbar joint  18 . 
     P 1s : position of waist-side center link attaching unit J 10 . 
     P 2s : position of waist-side right link attaching unit J 8 . 
     P 3s : position of waist-side left link attaching unit J 9 . 
     P 4s : position of chest-side center link attaching unit J 5 . 
     P 4s0 : position of chest-side center link attaching unit J 5  in reference state. 
     P 5s : position of chest-side right link attaching unit J 6 . 
     P 5s0 : position of chest-side right link attaching unit J 6  in reference state. 
     P 6s : position of chest-side left link attaching unit J 7 . 
     P 6s0 : position of chest-side left link attaching unit J 7  in reference state. 
     P 0As : position where position of thoracolumbar joint  18  is projected on plane determined by three points P 4s , P 5s , P 6s . 
     P 7s : position of intrathoracic joint  16 . 
     P 7s0 : position of intrathoracic joint  16  in reference state. 
     P 8s : position of lower intrathoracic link attaching unit J 3 . 
     P 8s0 : position of lower intrathoracic link attaching unit J 3  in reference state. 
     P 9s : position of upper intrathoracic link attaching unit J 4 . 
     P 9s0 : position of upper intrathoracic link attaching unit J 4  in reference state. 
     The intervals between points are expressed by the following variables. 
     Ws1: lengths of line segment P 0s P 1s , and line segment P 0s P 2s  projected on X-axis. 
     Ds1: length of the line segment P 0s P 1s  projected on Y-axis. 
     Ds2: lengths of line segment P 0s P 2s  and line segment P 02 P 3s  projected on Y-axis. 
     Ws2: lengths of line segment P 0As0 P 5s0  and line segment P 0As0 P 6s0  projected on X-axis. 
     Ds3: length of line segment P A0s P 4s0  projected on Y-axis. 
     Ds4: lengths of line segment P A0s P 5s0  and line segment P A0s P 6s0  projected on Y-axis. 
     Ds5: lengths of the line segment P 7s0 P 8s0  and line segment P 7s0 P 9s0  projected on Y-axis. 
     Hs1: length of line segment P 0s P 7s . The distance between plane determined by three points P 4s , P 5s , P 6s  and point P 0s . 
     Hs2: lengths of line segment P 0s P 1s , line segment P 0s P 2s , and line segment P 0s P 3s  projected on Z-axis. 
     Hs3: length of line segment P 7s0 P 8s0  projected on Z-axis. 
     Hs4: length of line segment P 7s0 P 9s0  projected on Z-axis. 
     Using the variables defined above, a coordinate of each point is expressed as follows. Position P 0s  of thoracolumbar joint  18  is set to an origin of the coordinate. 
         P   0s =(0, 0, 0) 
         P   1s =(0,  Ds 1, − Hs 2)
 
         P   2s =( Ws 1,  Ds 2,  −Hs 2) 
         P   3s =(− Ws 1,  Ds 2,  −Hs 2)
 
         P   4s0 =(0,  Ds 3,  Hs 1) 
         P   5s0 =( Ws 2,  −Ds 4,  Hs 1) 
         P   6s0 =(− Ws 2, − Ds 4,  Hs 1)
 
         P   7s0 =(0, 0,  Hs 1) 
         P   8s0 =(0, − Ds 5,  Hs 1− Hs 3)
 
         P   9s0 =(0, − Ds 5,  Hs 1+ Hs 3)
 
     The rotation angles of thoracolumbar joint  18  and intrathoracic joint  16  are expressed by the following variables. 
     α s : rotation angle around X-axis of thoracolumbar joint  18 . α s =0 in reference state 
     β s : rotation angle around Y-axis of thoracolumbar joint  18 . β s =0 in reference state 
     γ s : rotation angle around Z-axis of thoracolumbar joint  18 . γ s =0 in reference state 
     [Rs]: rotation matrix of thoracolumbar joint  18 . 
     ψ: rotation angle around X-axis of intrathoracic joint  16 . ψ=0 in reference state 
     [Rs2]: rotation matrix of intrathoracic joint  16 . 
     The rotation matrix [Rs] of thoracolumbar joint  18  is given as follows. 
     
       
         
           
             
               
                 
                   
                     [ 
                     Rs 
                     ] 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             1 
                           
                           
                             0 
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             
                               cosα 
                                
                               s 
                             
                           
                           
                             
                               sinα 
                                
                               s 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               sinα 
                                
                               s 
                             
                           
                           
                             
                               cosα 
                                
                               s 
                             
                           
                         
                       
                       ) 
                     
                      
                     
                       ( 
                       
                         
                           
                             
                               cosβ 
                                
                               s 
                             
                           
                           
                             0 
                           
                           
                             
                               - 
                               
                                 sinβ 
                                  
                                 s 
                               
                             
                           
                         
                         
                           
                             0 
                           
                           
                             1 
                           
                           
                             0 
                           
                         
                         
                           
                             
                               sinβ 
                                
                               s 
                             
                           
                           
                             0 
                           
                           
                             
                               cosβ 
                                
                               s 
                             
                           
                         
                       
                       ) 
                     
                      
                     
                       ( 
                       
                         
                           
                             
                               cosγ 
                                
                               s 
                             
                           
                           
                             
                               - 
                               
                                 sinγ 
                                  
                                 s 
                               
                             
                           
                           
                             0 
                           
                         
                         
                           
                             
                               sinγ 
                                
                               s 
                             
                           
                           
                             
                               cosγ 
                                
                               s 
                             
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             1 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Mathematical 
                      
                     
                         
                     
                      
                     Formula 
                      
                     
                         
                     
                      
                     1 
                   
                   ] 
                 
               
             
           
         
       
     
     The rotation matrix [Rs2] of intrathoracic joint  16  is given as follows. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       R 
                        
                       s 
                        
                       2 
                     
                     ] 
                   
                   - 
                   
                     ( 
                     
                       
                         
                           1 
                         
                         
                           0 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           
                             c 
                              
                             o 
                              
                             s 
                              
                             ψ 
                           
                         
                         
                           
                             - 
                             sinψ 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           sinψ 
                         
                         
                           
                             c 
                              
                             o 
                              
                             s 
                              
                             ψ 
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   
                     Mathematical 
                      
                     
                         
                     
                      
                     Formula 
                      
                     
                         
                     
                      
                     2 
                   
                   ] 
                 
               
             
           
         
       
     
     Assuming that point P D0  is the position in the reference state of any point P D  existing in chest lower portion  5 D, the position of point P D  after rotation in thoracolumbar joint  18  can be given as follows. 
         P   D =[ Rs ]* P   D0    
     Assuming that a point P U0  is the position in the reference state of any point P U  existing in chest upper portion  5 U, the position of point P U  after rotation in intrathoracic joint  16  and thoracolumbar joint  18  can be given as follows. 
         P   u =[ Rs ]*([ Rs 2]*( P   U0   −P   7s0 )+ P   7s0 ) 
     The lengths of the links are expressed by the following variables. 
     L 1s : length of thoracolumbar center link  19 L. Length of line segment P 1s P 4s . 
     L 2s : length of thoracolumbar right link  20 L. Length of line segment P 2s P 5s . 
     L 3s : length of thoracolumbar left link  21 L. Length of line segment P 3s P 6s . 
     L 1s0 : length of thoracolumbar center link  19 L in reference state. Length of line segment P 1s P 4s0 . 
     L 2s0 : length of thoracolumbar right link  20 L in reference state. Length of line segment P 2s P 5s0 . 
     L 3s0 : length of thoracolumbar left link  21 L in reference state. Length of line segment P 3s P 6s0 . 
     L 4s : length of intrathoracic link  17 L. Length of line segment P 8s P 9s . 
     In the reference state, how to obtain length L 4s  of intrathoracic link  17 L for setting the intrathoracic joint  16  to specified angle ψ is described. Position P 9s  of upper intrathoracic link attaching unit J 4  existing in chest upper portion  5 U is expressed as follows. 
     
       
         
           
             
               
                 
                   
                     P 
                     
                       9 
                        
                       s 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         x 
                          
                         9 
                          
                         s 
                       
                       , 
                       
                         y 
                          
                         9 
                          
                         s 
                       
                       , 
                       
                         z 
                          
                         9 
                          
                         s 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       
                         [ 
                         
                           Rs 
                            
                           2 
                         
                         ] 
                       
                       * 
                       
                         
                           ( 
                           
                             0 
                             , 
                             
                               - 
                               
                                 Ds 
                                  
                                 5 
                               
                             
                             , 
                             
                               Hs 
                                
                               4 
                             
                           
                           ) 
                         
                         t 
                       
                     
                     + 
                     
                       ( 
                       
                         0 
                         , 
                         0 
                         , 
                         
                           Hs 
                            
                           1 
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
     The expression for each variable is obtained as follows. 
       x9s=0 
         y 9 s=−Ds 5*cos ψ− Hs 4*sin ψ
 
         z 9 s=−Ds 5*sin ψ+ Hs 4*cos ψ+ Hs 1
 
     Position P 8s  of lower intrathoracic link attaching unit J 3  existing in chest lower portion  5 D is not changed by the rotation in intrathoracic joint  16 . For this reason, position P 8s  is equal to position P 8s0  in the reference state. Length L 4s  of intrathoracic link  17 L can be calculated as follows. 
         L   4s =√(( Ds 5*(1−cos ψ)− Hs 4*sin ψ) 2 +(− Ds 5*sin ψ+ Hs 4*cos ψ+ Hs 3) 2 )
 
     Positions P 4s , P 5s , P 8s  of the three points existing in chest lower portion  5 D are given by the rotation in thoracolumbar joint  18 . 
     
       
         
           
             
               
                 
                   
                     P 
                     
                       4 
                        
                       s 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         x 
                          
                         4 
                          
                         s 
                       
                       , 
                       
                         y 
                          
                         4 
                          
                         s 
                       
                       , 
                       
                         z 
                          
                         4 
                          
                         s 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       
                         [ 
                         Rs 
                         ] 
                       
                       * 
                       
                         P 
                         
                           4 
                            
                           
                             s 
                              
                             0 
                           
                         
                       
                     
                     = 
                     
                       
                         [ 
                         Rs 
                         ] 
                       
                       * 
                       
                         
                           ( 
                           
                             0 
                             , 
                             
                               Ds 
                                
                               3 
                             
                             , 
                             
                               Hs 
                                
                               1 
                             
                           
                           ) 
                         
                         t 
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     
                       5 
                        
                       s 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         x 
                          
                         5 
                          
                         s 
                       
                       , 
                       
                         y 
                          
                         5 
                          
                         s 
                       
                       , 
                       
                         z 
                          
                         5 
                          
                         s 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       
                         [ 
                         Rs 
                         ] 
                       
                       * 
                       
                         P 
                         
                           5 
                            
                           
                             s 
                              
                             0 
                           
                         
                       
                     
                     = 
                     
                       
                         [ 
                         Rs 
                         ] 
                       
                       * 
                       
                         
                           ( 
                           
                             
                               Ws 
                                
                               2 
                             
                             , 
                             
                               - 
                               
                                 Ds 
                                  
                                 4 
                               
                             
                             , 
                             
                               Hs 
                                
                               1 
                             
                           
                           ) 
                         
                         t 
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     
                       6 
                        
                       s 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         x 
                          
                         6 
                          
                         s 
                       
                       , 
                       
                         y 
                          
                         6 
                          
                         s 
                       
                       , 
                       
                         z 
                          
                         6 
                          
                         s 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       
                         [ 
                         Rs 
                         ] 
                       
                       * 
                       
                         P 
                         
                           6 
                            
                           
                             s 
                              
                             0 
                           
                         
                       
                     
                     = 
                     
                       
                         [ 
                         Rs 
                         ] 
                       
                       * 
                       
                         
                           ( 
                           
                             
                               - 
                               
                                 Ws 
                                  
                                 2 
                               
                             
                             , 
                             
                               - 
                               
                                 Ds 
                                  
                                 4 
                               
                             
                             , 
                             
                               Hs 
                                
                               1 
                             
                           
                           ) 
                         
                         t 
                       
                     
                   
                 
               
             
           
         
       
     
     Because P 4s , P 5s , P 6s  are obtained, lengths L 1s , L 2s , L 3s  of the links can be calculated by the following equations. 
         L   1s =√( x 4 s   2 +( y 4 s−Ds 1) 2 +( z 4 s+Hs 2) 2 )
 
         L   2s =√(( x 5 s−Ws 1) 2 +( y 5 s−Ds 2) 2 +( z 5 s+Hs 2) 2 )
 
         L   3s =√( x 6 s+Ws 1) 2 +( y 6 s−Ds 2) 2 +( z 5 s+Hs 2) 2 )
 
         L   1s0 =√(( Ds 3 −Ds 1) 2 +( Hs 1+ Hs 2) 2 )
 
         L   2s0 =√(( Ws 2 −Ws 1) 2 +( Ds 2+ Ds 4) 2 +( Hs 1+ Hs 2) 2 )
 
         L   3s0 =√(( Ws 2 −Ws 1) 2 +( Ds 2+ Ds 4) 2 +( Hs 1+ Hs 2) 2 )
 
     In the case that the rotation is performed slightly around the Z-axis from the reference state, how the length of each link is changed is examined. P 4s , P 5s , P 6s  are given as follows. Here, assuming that γs is small, approximation is performed using sin γs≈γs and cos γs≈1. 
     
       
         
           
             
               
                 
                   
                     P 
                     
                       4 
                        
                       s 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         x 
                          
                         4 
                          
                         s 
                       
                       , 
                       
                         y 
                          
                         4 
                          
                         s 
                       
                       , 
                       
                         z 
                          
                         4 
                          
                         s 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       ( 
                       
                         
                           
                             - 
                             
                               Ds 
                                
                               3 
                             
                           
                           * 
                           
                             sinγ 
                              
                             s 
                           
                         
                         , 
                         
                           
                             Ds 
                              
                             3 
                           
                           * 
                           
                             cosγ 
                              
                             s 
                           
                         
                         , 
                         
                           Hs 
                            
                           1 
                         
                       
                       ) 
                     
                     ≈ 
                     
                       ( 
                       
                         
                           
                             - 
                             
                               Ds 
                                
                               3 
                             
                           
                           * 
                           
                             γ 
                              
                             s 
                           
                         
                         , 
                         
                           Ds 
                            
                           3 
                         
                         , 
                         
                           Hs 
                            
                           1 
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     
                       5 
                        
                       s 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         x 
                          
                         5 
                          
                         s 
                       
                       , 
                       
                         y 
                          
                         5 
                          
                         s 
                       
                       , 
                       
                         z 
                          
                         5 
                          
                         s 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       
                         
                           ( 
                           
                             
                               
                                 
                                   Ws 
                                    
                                   2 
                                 
                                 * 
                                 
                                   cosγ 
                                    
                                   s 
                                 
                               
                               + 
                               
                                 
                                   Ds 
                                    
                                   4 
                                 
                                 * 
                                 
                                   sinγ 
                                    
                                   s 
                                 
                               
                             
                             , 
                             
                               
                                 
                                   Ws 
                                    
                                   2 
                                 
                                 * 
                                 
                                   sinγ 
                                    
                                   s 
                                 
                               
                               - 
                               
                                 
                                   Ds 
                                    
                                   4 
                                 
                                 * 
                                 
                                   cosγ 
                                    
                                   s 
                                 
                               
                             
                             , 
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               Hs 
                                
                               1 
                             
                             ) 
                           
                           ≈ 
                           
                             ( 
                             
                               
                                 
                                   Ws 
                                    
                                   2 
                                 
                                 + 
                                 
                                   
                                     Ds 
                                      
                                     4 
                                   
                                   * 
                                   
                                     γ 
                                      
                                     s 
                                   
                                 
                               
                               , 
                               
                                 
                                   
                                     Ws 
                                      
                                     2 
                                   
                                   * 
                                   
                                     γ 
                                      
                                     s 
                                   
                                 
                                 - 
                                 
                                   Ds 
                                    
                                   3 
                                 
                               
                               , 
                               
                                 Hs 
                                  
                                 1 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     
                       6 
                        
                       s 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         x 
                          
                         6 
                          
                         s 
                       
                       , 
                       
                         y 
                          
                         6 
                          
                         s 
                       
                       , 
                       
                         z 
                          
                         6 
                          
                         s 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       
                         
                           ( 
                           
                             
                               
                                 
                                   - 
                                   
                                     Ws 
                                      
                                     2 
                                   
                                 
                                 * 
                                 
                                   cosγ 
                                    
                                   s 
                                 
                               
                               + 
                               
                                 
                                   Ds 
                                    
                                   4 
                                 
                                 * 
                                 
                                   sinγ 
                                    
                                   s 
                                 
                               
                             
                             , 
                             
                               
                                 
                                   - 
                                   
                                     Ws 
                                      
                                     2 
                                   
                                 
                                 * 
                                 
                                   sinγ 
                                    
                                   s 
                                 
                               
                               - 
                               
                                 
                                   Ds 
                                    
                                   4 
                                 
                                 * 
                                 
                                   cosγ 
                                    
                                   s 
                                 
                               
                             
                             , 
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               Hs 
                                
                               1 
                             
                             ) 
                           
                           ≈ 
                           
                             ( 
                             
                               
                                 
                                   - 
                                   
                                     Ws 
                                      
                                     2 
                                   
                                 
                                 + 
                                 
                                   
                                     Ds 
                                      
                                     4 
                                   
                                   * 
                                   
                                     γ 
                                      
                                     s 
                                   
                                 
                               
                               , 
                               
                                 
                                   
                                     - 
                                     
                                       Ws 
                                        
                                       2 
                                     
                                   
                                   * 
                                   
                                     γ 
                                      
                                     s 
                                   
                                 
                                 - 
                                 
                                   Ds 
                                    
                                   4 
                                 
                               
                               , 
                               
                                 Hs 
                                  
                                 1 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     The lengths of the links are calculated as follows. 
         L   1s =√(( Ds 3*γ s ) 2 +( Ds 3 −Ds 1) 2 +( Hs 1+ Hs 2) 2 )
 
         L   2s =√(( Ws 2 −Ws 1 −Ds 4*γ s ) 2 +( Ds 2+ Ds 4 −Ws 2*γ s ) 2 +( Hs 1+ Hs 2) 2 )
 
         L   3s =√(( Ws 2− Ws 1 +Ds 4*γ s ) 2 +( Ds 2+ Ds 4+ Ws 2*γ s ) 2 +( Hs 1+ Hs 2) 2 )
 
     Differences from the lengths of the links in the reference state are determined as follows. Here, γs&gt;0 is assumed. 
         L   1s   2   −L   1s0   2 =( Ds 2*γ s ) 2 &gt;0
 
         L   2s   2   −L   2s0   2 =( Ws 2 −Ws 1 −Ds 4*γ s ) 2 −( Ws 2 −Ws 1) 2 +( Ds 2+ Ds 4+ Ws 2*γ s ) 2 −( Ds 2+ Ds 4) 2 &lt;0
 
         L   3s   2   −L   3s0   2 =( Ws 2 −Ws 1+ Ds 4*γ s ) 2 −( Ws 2− Ws 1) 2 +( Ds 2+ Ds 4+ Ws 2*γ s ) 2 −( Ds 2+ Ds 4) 2 &gt;0
 
     In the reference state, it is found that one of length L 2s  of thoracolumbar right link  20 L and length L 3s  of thoracolumbar left link  21 L is lengthened while the other is shortened. Thus, in the rotation around the torsion axis, both the force pushed by the extending link and the force drawn by the shortening link are generated, the rotation is performed around torsion axis easily. 
     How to determine the lengths of the variable length links such that the designated angle can be taken with respect to shoulder joint  13  is described. The distances between the joint and the link attaching units in shoulder joint  13  are defined by the following variables.  FIG. 81  is a view illustrating the variables expressing the distances between the joint and the link attaching units in shoulder joint  13 . Q 1t  and Q 2t  are illustrated in  FIG. 82 . 
     The variable expressing the position of each point is defined as follows. 
     P 0t : position of shoulder joint  13 . 
     P 1t : position of the chest-side main link attaching unit J 1 . 
     P 2t : position of chest-side auxiliary link attaching unit J 2 . 
     Q 1t : position of upper arm main link attaching unit J 20 . Q 1t =(x1t, y1t, z1t) 
     Q 1t0 : position of upper arm main link attaching unit J 20  in reference state. 
     Q 2t : position of upper arm drive main-link-side auxiliary link attaching unit J 21 . Q 2t =(x2t, y2t, z2t) 
     Q 2t0 : position of upper arm drive main-link-side auxiliary link attaching unit J 21  in reference state. 
     The intervals between points are expressed by the following variables. K 1t  and K 2t  are illustrated in  FIG. 82 . 
     Wt1: lengths of line segment P 0t P 1t  and line segment P 0t P 2t  projected on X-axis. 
     Dt1: length of line segment P 0t P 1t  projected on Y-axis. 
     Dt2: length of the line segment P 0t P 2t  projected on Y-axis. 
     Ht1: lengths of line segment P 0t P 1t  and line segment P 0t P 2t  projected on Z-axis. 
     K 1t : length of line segment P 0t Q 1t . 
     K 2t : length of line segment Q 1t Q 2t . 
     Using the variables defined above, a coordinate of each point is expressed as follows. The position P 0t  of shoulder joint  13  is set to the origin of coordinate. 
         P   0t =(0, 0, 0) 
         P   1t =(− Wt 1, − Dt 1,  −Ht 1)
 
         P   2t =(− Wt 1,  Dt 2,  −Ht 1)
 
         Q   1t0 =(0, 0, − K   1t )
 
     The rotation angles of shoulder joint  13  are expressed by the following variables. 
     α t : rotation angle of shoulder joint  13  around X-axis. α t =0 in reference state 
     β t : rotation angle of shoulder joint  13  around Y-axis. β t =0 in reference state 
     [Rt]: rotation matrix of shoulder joint  13 . 
     The rotation matrix [Rt] is given as follows. 
     
       
         
           
             
               
                 
                   
                     [ 
                     Rt 
                     ] 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             1 
                           
                           
                             0 
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             
                               cosα 
                                
                               t 
                             
                           
                           
                             
                               - 
                               
                                 sinα 
                                  
                                 t 
                               
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               sinα 
                                
                               t 
                             
                           
                           
                             
                               cosα 
                                
                               t 
                             
                           
                         
                       
                       ) 
                     
                      
                     
                       ( 
                       
                         
                           
                             
                               cosβ 
                                
                               t 
                             
                           
                           
                             0 
                           
                           
                             
                               
                                 - 
                                 sin 
                               
                                
                               
                                 β 
                                  
                                 t 
                               
                             
                           
                         
                         
                           
                             0 
                           
                           
                             1 
                           
                           
                             0 
                           
                         
                         
                           
                             
                               sinβ 
                                
                               t 
                             
                           
                           
                             0 
                           
                           
                             
                               cosβ 
                                
                               t 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Mathematical 
                      
                     
                         
                     
                      
                     Formula 
                      
                     
                         
                     
                      
                     3 
                   
                   ] 
                 
               
             
           
         
       
     
     The lengths of the links are expressed by the following variables. 
     L 1t : length of upper arm drive main link  14 L. Length of line segment P 1t Q 1t . 
     L 2t : length of upper arm drive auxiliary link  15 L. Length of line segment P 2t Q 2t . 
     In shoulder joint  13 , because upper arm drive main-link-side auxiliary link attaching unit J 21  is located on upper arm drive main link  14 L, a position Q 2t  of upper arm drive main-link-side auxiliary link attaching unit J 21  is required to satisfy the following condition. 
         Q   2t =( K   2t   /L   1t )* P   1t +(1− K   2t   /L   1t )* Q   1t  
 
     The following constraint condition is required to hold with respect to an interval of the link attaching unit. 
       √( x 1 t   2   +y 1 t   2   +z 1 t   2 )= K   1t  
 
     Using the angle matrix [Rt] of the shoulder joint  13 , position Q 1t  of the upper-arm-side main link attaching unit J 20  is determined as follows. 
         Q   1t =[ Rt ]* Q   1t0    
     The expression for each variable is obtained as follows. 
         x 1 t=K   1t *cos α t *sin β t  
 
         y 1 t=K   1t *sin α t  
 
         z 1 t=−K   1t *cos α t *cos β t  
 
     When position Q 1t  is determined, L 1t  can be calculated by the following equation. 
         L   1t =√(( x 1 t+Wt 1) 2 +( y 1 t+Dt 1) 2 +( z 1 t+Ht 1) 2 )
 
     The following constraint equation relating to position Q 2t  is expressed for each variable. 
         x 2 t=x 1 t −( x 1 t+Wt 1)*( K   1t   /L   1t )
 
         y 2 t=y 1 t −( y 1 t+Dt 1)*( K   1t   /L   1t )
 
         z 2 t=z 1 t −( z 1 t+Ht 1)*( K   1t   /L   1t )
 
     When position Q 2t  is determined, L 2t  can be calculated by the following equation. 
         L 2 t =√(( x 2 t+Wt 1) 2 +( y 2 t−Dt 2) 2 +( z 2 t+Ht 1) 2 )
 
     How to determine the link attaching unit in the upper arm such that the designated angle can be taken with respect to elbow joint  31  is described. The distances between the joint and the link attaching units in elbow joint  31  are defined by the following variables.  FIG. 82  is a view illustrating the variables expressing the distances between the joint and the link attaching units in elbow joint  31 . 
     The variable expressing the position of each point is defined as follows. 
     P 0u : position of elbow joint  31 . 
     P 1u : position of upper arm outside link attaching unit J 22 . 
     P 1u0 : position of upper arm outside link attaching unit J 22  in reference state. 
     P 2u : position of upper arm inside link attaching unit J 23 . 
     P 2u0 : position of upper arm inside link attaching unit J 23  in reference state. 
     P 3u : position of elbow drive outside link attaching unit J 25 . P 3u =(x3u, y3u, z3u) 
     P 3u0 : position of elbow drive outside link attaching unit J 25  in reference state. 
     P 4u : position of elbow drive inside link attaching unit J 24 . P 4u =(x4u, y4u, z4u) 
     P 4u0 : position of elbow drive inside link attaching unit J 24  in reference state. 
     The intervals between points are expressed by the following variables. 
     Wu1: length of the line segment P 0u P 1u  projected on X-axis. 
     Wu2: length of line segment P 0u P 2u  projected on X-axis. 
     Du1: lengths of line segment P 0u P 1u  and line segment P 0u P 2u  projected on Y-axis. 
     Hu1: lengths of line segment P 0u P 1u0  and line segment P 0u P 2u0  projected on Z-axis. 
     K 1u : length of line segment P 0u P 4u0  projected on Z-axis. 
     L 1u0 : length of line segment P 1u P 3u . Length of the elbow drive outside link  32 . 
     L 2u0 : length of line segment P 2u P 4u . Length of elbow drive inside link  33 . 
     K 2u : length of line segment P 3u P 4u . 
     Using the variables defined above, a coordinate of each point is expressed as follows. Position P 0u  of elbow joint  31  is set to the origin of the coordinate. 
         P   0u =(0, 0, 0) 
         P   1u0 =( Wu 1,  Du 1,  Hu 1) 
         P   2u0 =(− Wu 2,  Du 1,  Hu 1)
 
         P   4u0 =(0,  Du 1,  −K   1u ) 
     Upper arm outside actuator  34  and upper arm inside actuator  35  are provided in parallel with upper arm  9  (Z-axis). Positions P 1u , P 2u  of upper arm outside link attaching unit J 22  and upper arm inside link attaching unit J 23 , which are moved by upper arm outside actuator  34  and upper arm inside actuator  35 , are moved in the direction parallel to Z-axis. That is, P 1u  and P 2u  can be expressed as follows. 
         P   1u =( Wu 1,  Du 1,  z 1 u ) 
         P   2u =(− Wu 2,  Du 1,  z 2 u )
 
     Because elbow drive outside link  32  is attached to elbow drive inside link  33 , P 2u , P 3u , P 4u  exist on the same straight line. Thus, the following equation holds. 
         P   3u =( K   2u   /L   2u0 )* P   2u +(1− K   2u   /L   2u0 )*P 4u  
 
     By applying this equation in the reference state, P 3u0  is determined as follows. 
         P   3u0 =(−( K   2u   /L   2u0 )* Wu 1,  Du 1, −( K   2u   /L   2u0 )*( Hu 1+ K   1u )− K   1u )
 
     The lengths, which are constant, of elbow drive outside link  32  and elbow drive inside link  33  are given as follows. 
         L   2u0 =√( Wu 2 2 +( Hu 1+ K   1u ) 2 )
 
         L   1u0 =√( Wu 1 2 +( Hu 1+ K   1u ) 2 + K   2u *( K   2u   −Hu 1− K   1u   +Wu 1)/( Wu 1 2 +( Hu 1+ K   1u ) 2 ))
 
     The rotation angles of elbow joint  31  are expressed by the following variables. 
     α u : rotation angle of elbow joint  31  around X-axis. α u =0 in reference state 
     γ u : rotation angle of elbow joint  31  around Z-axis. γ u =0 in reference state 
     [Ru]: rotation matrix of elbow joint  31 . 
     The rotation matrix [Ru] is given as follows. 
     
       
         
           
             
               
                 
                   
                     [ 
                     Ru 
                     ] 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             1 
                           
                           
                             0 
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             
                               cosα 
                                
                               u 
                             
                           
                           
                             
                               - 
                               
                                 sinα 
                                  
                                 u 
                               
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               sinα 
                                
                               u 
                             
                           
                           
                             
                               cosα 
                                
                               u 
                             
                           
                         
                       
                       ) 
                     
                      
                     
                       ( 
                       
                         
                           
                             
                               cosγ 
                                
                               u 
                             
                           
                           
                             
                               
                                 - 
                                 sin 
                               
                                
                               
                                 γ 
                                  
                                 u 
                               
                             
                           
                           
                             0 
                           
                         
                         
                           
                             
                               sinγ 
                                
                               u 
                             
                           
                           
                             
                               cosγ 
                                
                               u 
                             
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             1 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Mathematical 
                      
                     
                         
                     
                      
                     Formula 
                      
                     
                         
                     
                      
                     4 
                   
                   ] 
                 
               
             
           
         
       
     
     When [Ru] is given, P 4u  is determined by the following equation. 
     
       
         
           
             
               P 
               
                 4 
                  
                 u 
               
             
             = 
             
               
                 ( 
                 
                   
                     x 
                      
                     4 
                      
                     u 
                   
                   , 
                   
                     y 
                      
                     4 
                      
                     u 
                   
                   , 
                   
                     z 
                      
                     4 
                      
                     u 
                   
                 
                 ) 
               
               = 
               
                 
                   
                     [ 
                     Ru 
                     ] 
                   
                   * 
                   
                     P 
                     
                       4 
                        
                       
                         u 
                          
                         0 
                       
                     
                   
                 
                 = 
                 
                   
                     [ 
                     Ru 
                     ] 
                   
                   * 
                   
                     
                       ( 
                       
                         0 
                         , 
                         
                           Du 
                            
                           1 
                         
                         , 
                         
                           - 
                           
                             K 
                             
                               1 
                                
                               u 
                             
                           
                         
                       
                       ) 
                     
                     t 
                   
                 
               
             
           
         
       
     
     Because L 2u0  is constant, z2u is determined from P 4u  by the following equation. 
         L   2u   2 =( x 4 u+Wu 2) 2 +( y 4 u−Du 1) 2 +( z 4 u−z 2 u ) 2   =L   2u0   2    
         z 2 u=z 4 u+ √( L   2u0   2 −( x 4 u+Wu 2) 2 −( y 4 u−Du 1) 2 )
 
     P 3u  is determined from P 2u  and P 4u  by applying the constraint equation expressing that P 2u , P 3u , P 4u  exist on the same straight line. The expression for each variable is obtained as follows. 
         x 3 u=x 4 u −( Wu 1+ x 4 u )*( K   2u   /L   2u0 )
 
         y 3 u=y 4 u +( Du 1− y 4 u )*( K   2u   /L   2u0 )
 
         z 3 u=z 4 u +( z 2 u−z 4 u )*( K   2u   /L   2u0 ) 
     Because L 1u0  is constant, z1u is determined from P 3u  by the following equation. 
         L   1u   2 =( x 3 u−Wu 1) 2 +( y 3 u−Du 1) 2 +( z 3 u−z 1 u ) 2   =L   1u0   2    
         z 1 u=z 3 u +√( L   1u0   2 −( x 3 u−Wu 1) 2 −( y 3 u−Du 1) 2 )
 
     How to determine the lengths of the variable length links such that the designated angle can be taken with respect to wrist joint  36  is described. The distances between the joint and the link attaching units in wrist joint  36  are defined by the following variables.  FIG. 83  is a view illustrating the variables expressing the distances between the joint and the link attaching units in wrist joint  36 . 
     The variable expressing the position of each point is defined as follows. 
     P 0v : position of wrist joint  36 . 
     P 1v : position of forearm front link attaching unit J 26 . 
     P 2v : position of forearm outside link attaching unit J 27 . 
     P 3v : position of forearm inside link attaching unit J 28 . 
     P 4v : position of hand-side front link attaching unit J 29 . 
     P 4v0 : position of hand-side front link attaching unit J 29  in reference state. 
     P 5v : position of hand-side outside link attaching unit J 30 . 
     P 5v0 : position of hand-side outside link attaching unit J 30  in reference state. 
     P 6v : position of the hand-side inside link attaching unit J 31 . 
     P 6v0 : position of hand-side inside link attaching unit J 31  in reference state. 
     P 0v , P 4v , P 5v , P 6v  exist on the same plane. 
     The intervals between points are expressed by the following variables. 
     Wv1: lengths of line segment P 0v P 1v  and line segment P 0v P 2v  projected on X-axis. 
     Dv1: length of line segment P 0v P 1v  projected on Y-axis. 
     Hv1: length of line segment P 0v P 4v . 
     Dv2: length of line segment P 0v P 4v . 
     Using the variables defined above, a coordinate of each point is expressed as follows. At this point, position P 0v  of wrist joint  36  is set to the origin of the coordinate. 
         P   0v =(0, 0, 0) 
         P   1v =(0,  Dv 1, − Hv 1)
 
         P   2v =( Wv 1, 0, − Hv 1)
 
         P   3vl =(− Wv 1, 0, − Hv 1)
 
         P   4v0 =(0,  Dv 2, 0) 
         P   5v0 =( Dv 2*cos(π/6), − Dv 2*sin(π/6), 0)
 
         P   6v0 =(− Dv 2*cos(π/6), − Dv 2*sin(π/6), 0)
 
     The rotation angles of wrist joint  36  are expressed by the following variables. 
     α v : rotation angle of wrist joint  36  around X-axis. α v =0 in reference state 
     β v : rotation angle of wrist joint  36  around Y-axis. β v =0 in reference state 
     γ v : rotation angle of wrist joint  36  around Z-axis. γ v =0 in reference state 
     [Rv]: rotation matrix of wrist joint  36 . 
     The rotation matrix [Rv] is given as follows. 
     
       
         
           
             
               
                 
                   
                     [ 
                     Rv 
                     ] 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             1 
                           
                           
                             0 
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             
                               cosα 
                                
                               v 
                             
                           
                           
                             
                               - 
                               
                                 sinα 
                                  
                                 v 
                               
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               sinα 
                                
                               v 
                             
                           
                           
                             
                               cosα 
                                
                               v 
                             
                           
                         
                       
                       ) 
                     
                      
                     
                       ( 
                       
                         
                           
                             
                               cosβ 
                                
                               v 
                             
                           
                           
                             0 
                           
                           
                             
                               - 
                               
                                 sinβ 
                                  
                                 v 
                               
                             
                           
                         
                         
                           
                             0 
                           
                           
                             1 
                           
                           
                             0 
                           
                         
                         
                           
                             
                               sinβ 
                                
                               v 
                             
                           
                           
                             0 
                           
                           
                             
                               cosβ 
                                
                               v 
                             
                           
                         
                       
                       ) 
                     
                      
                     
                       ( 
                       
                         
                           
                             
                               cosγ 
                                
                               v 
                             
                           
                           
                             
                               - 
                               
                                 sinγ 
                                  
                                 v 
                               
                             
                           
                           
                             0 
                           
                         
                         
                           
                             
                               sinγ 
                                
                               v 
                             
                           
                           
                             
                               cosγ 
                                
                               v 
                             
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             1 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Mathematical 
                      
                     
                         
                     
                      
                     Formula 
                      
                     
                         
                     
                      
                     5 
                   
                   ] 
                 
               
             
           
         
       
     
     The lengths of the links are expressed by the following variables. 
     L 1v : length of forearm front link  37 L. Length of line segment P 1v P 4v . 
     L 2v : length of forearm outside link  38 L. Length of line segment P 2v P 4v . 
     L 3v : length of forearm inside link  39 L. Length of line P 3v P 6v . 
     L 1v0 : length of forearm front link  37 L in reference state. Length of line segment P 1v P 4v0 . 
     L 2v0 : length of forearm outside link  38 L in reference state. Length of line segment P 2v P 5v0 . 
     L 3v0 : length of forearm inside link  39 L in reference state. Length of line segment P 3v P 6v0 . 
     [Rv] is given, and P 4v , P 5v , P 6v  are obtained by the following expressions. 
     
       
         
           
             
               
                 
                   
                     P 
                     
                       4 
                        
                       v 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         x 
                          
                         4 
                          
                         v 
                       
                       , 
                       
                         y 
                          
                         4 
                          
                         v 
                       
                       , 
                       
                         z 
                          
                         4 
                          
                         v 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       [ 
                       Rv 
                       ] 
                     
                     * 
                     
                       
                         ( 
                         
                           0 
                           , 
                           
                             Dv 
                              
                             2 
                           
                           , 
                           0 
                         
                         ) 
                       
                       t 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     
                       5 
                        
                       v 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         x 
                          
                         5 
                          
                         v 
                       
                       , 
                       
                         y 
                          
                         5 
                          
                         v 
                       
                       , 
                       
                         z 
                          
                         5 
                          
                         v 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       [ 
                       Rv 
                       ] 
                     
                     * 
                     
                       
                         ( 
                         
                           
                             
                               Dv 
                                
                               2 
                             
                             * 
                             
                               cos 
                                
                               
                                 ( 
                                 
                                   π 
                                   / 
                                   6 
                                 
                                 ) 
                               
                             
                           
                           , 
                           
                             
                               - 
                               
                                 Dv 
                                  
                                 2 
                               
                             
                             * 
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   π 
                                   / 
                                   6 
                                 
                                 ) 
                               
                             
                           
                           , 
                           0 
                         
                         ) 
                       
                       t 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     
                       6 
                        
                       v 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         x 
                          
                         6 
                          
                         v 
                       
                       , 
                       
                         y 
                          
                         6 
                          
                         v 
                       
                       , 
                       
                         z 
                          
                         6 
                          
                         v 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       [ 
                       Rv 
                       ] 
                     
                     * 
                     
                       
                         ( 
                         
                           
                             
                               - 
                               
                                 Dv 
                                  
                                 2 
                               
                             
                             * 
                             
                               cos 
                                
                               
                                 ( 
                                 
                                   π 
                                   / 
                                   6 
                                 
                                 ) 
                               
                             
                           
                           , 
                           
                             
                               - 
                               
                                 Dv 
                                  
                                 2 
                               
                             
                             * 
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   π 
                                   / 
                                   6 
                                 
                                 ) 
                               
                             
                           
                           , 
                           0 
                         
                         ) 
                       
                       t 
                     
                   
                 
               
             
           
         
       
     
     Because P 4v , P 5v , P 6v  are obtained, the lengths L 1v , L 2v , L 3v  of the links can be calculated by the following equations. 
         L   1v =√( x 4 v   2 +( Dv 1− y 4 v ) 2 +( Hv 1+ z 4 v ) 2 )
 
         L   2v =√(( Wv 1− x 5 v ) 2   +y 5 v   2 +( Hv 1+ z 5 v ) 2 )
 
         L   3v =√(( Wv 1+ x 6 v ) 2   +y 6 v   2 +( Hv 1+ z 6 v ) 2 )
 
         L   1v0 =√(( Dv 1− Dv 2) 2   +Hv 1 2 )
 
         L   2v0 =√(( Wv 1− Dv 2*cos(π/6)) 2 +( Dv 2*sin(π/6)) 2   +Hv 1 2 )
 
         L   3v0 =√(( Wv 1− Dv 2*cos(π/6)) 2  +( Dv 2*sin(π/6)) 2   +Hv 1 2 )
 
     In the case that the rotation is performed slightly around the Z-axis from the reference state, how the length of each link is changed is examined. P 4v , P 5v , P 6v  are given as follows. Here, assuming that γv is small, approximation is performed using sin γv≈γv and cos γv≈1. 
     
       
         
           
             
               
                 
                   
                     P 
                     
                       4 
                        
                       v 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         x 
                          
                         4 
                          
                         v 
                       
                       , 
                       
                         y 
                          
                         4 
                          
                         v 
                       
                       , 
                       
                         z 
                          
                         4 
                          
                         v 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       ( 
                       
                         
                           
                             - 
                             
                               Dv 
                                
                               2 
                             
                           
                           * 
                           
                             sinγ 
                              
                             s 
                           
                         
                         , 
                         
                           
                             Dv 
                              
                             2 
                           
                           * 
                           
                             cosγ 
                              
                             s 
                           
                         
                         , 
                         0 
                       
                       ) 
                     
                     ≈ 
                     
                       ( 
                       
                         
                           
                             - 
                             
                               Dv 
                                
                               2 
                             
                           
                           * 
                           
                             γ 
                              
                             v 
                           
                         
                         , 
                         
                           Dv 
                            
                           2 
                         
                         , 
                         0 
                       
                       ) 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     
                       5 
                        
                       v 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         x 
                          
                         5 
                          
                         v 
                       
                       , 
                       
                         y 
                          
                         5 
                          
                         v 
                       
                       , 
                       
                         z 
                          
                         5 
                          
                         v 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       
                         
                           
                             ( 
                             
                               
                                 
                                   Dv 
                                    
                                   2 
                                 
                                 * 
                                 
                                   cos 
                                   ( 
                                   
                                     
                                       π 
                                       / 
                                       6 
                                     
                                     - 
                                     
                                       γ 
                                        
                                       v 
                                     
                                   
                                   ) 
                                 
                               
                               , 
                               
                                 
                                   Dv 
                                    
                                   2 
                                 
                                 * 
                                 
                                   sin 
                                   ( 
                                   
                                     
                                       π 
                                       / 
                                       6 
                                     
                                     - 
                                     
                                       γ 
                                        
                                       v 
                                     
                                   
                                   ) 
                                 
                               
                               , 
                               0 
                             
                             ) 
                           
                           ≈ 
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       
                                         Dv 
                                          
                                         2 
                                       
                                       * 
                                       
                                         cos 
                                          
                                         
                                           ( 
                                           
                                             π 
                                             / 
                                             6 
                                           
                                           ) 
                                         
                                       
                                     
                                     + 
                                     
                                       
                                         Dv 
                                          
                                         2 
                                       
                                       * 
                                       
                                         sin 
                                         ( 
                                         
                                           π 
                                           / 
                                           6 
                                         
                                         ) 
                                       
                                       * 
                                       
                                         γ 
                                          
                                         v 
                                       
                                     
                                   
                                   , 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     
                                       
                                         Dv 
                                          
                                         2 
                                       
                                       * 
                                       
                                         cos 
                                          
                                         
                                           ( 
                                           
                                             π 
                                             / 
                                             6 
                                           
                                           ) 
                                         
                                       
                                       * 
                                       
                                         γ 
                                          
                                         v 
                                       
                                     
                                     - 
                                     
                                       
                                         Dv 
                                          
                                         2 
                                       
                                       * 
                                       
                                         sin 
                                          
                                         
                                           ( 
                                           
                                             π 
                                             / 
                                             6 
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                   , 
                                   0 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     
                       6 
                        
                       v 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         x 
                          
                         6 
                          
                         v 
                       
                       , 
                       
                         y 
                          
                         6 
                          
                         v 
                       
                       , 
                       
                         z 
                          
                         6 
                          
                         v 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       
                         
                           
                             ( 
                             
                               
                                 
                                   - 
                                   
                                     Dv 
                                      
                                     2 
                                   
                                 
                                 * 
                                 
                                   cos 
                                   ( 
                                   
                                     
                                       π 
                                       / 
                                       6 
                                     
                                     + 
                                     
                                       γ 
                                        
                                       v 
                                     
                                   
                                   ) 
                                 
                               
                               , 
                               
                                 
                                   - 
                                   
                                     Dv 
                                      
                                     2 
                                   
                                 
                                 * 
                                 
                                   sin 
                                   ( 
                                   
                                     
                                       π 
                                       / 
                                       6 
                                     
                                     + 
                                     
                                       γ 
                                        
                                       v 
                                     
                                   
                                   ) 
                                 
                               
                               , 
                               0 
                             
                             ) 
                           
                           ≈ 
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       
                                         - 
                                         
                                           Dv 
                                            
                                           2 
                                         
                                       
                                       * 
                                       
                                         cos 
                                          
                                         
                                           ( 
                                           
                                             π 
                                             / 
                                             6 
                                           
                                           ) 
                                         
                                       
                                     
                                     + 
                                     
                                       
                                         Dv 
                                          
                                         2 
                                       
                                       * 
                                       
                                         sin 
                                         ( 
                                         
                                           π 
                                           / 
                                           6 
                                         
                                         ) 
                                       
                                       * 
                                       
                                         γ 
                                          
                                         v 
                                       
                                     
                                   
                                   , 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     
                                       
                                         - 
                                         
                                           Dv 
                                            
                                           2 
                                         
                                       
                                       * 
                                       
                                         cos 
                                          
                                         
                                           ( 
                                           
                                             π 
                                             / 
                                             6 
                                           
                                           ) 
                                         
                                       
                                       * 
                                       
                                         γ 
                                          
                                         v 
                                       
                                     
                                     - 
                                     
                                       
                                         Dv 
                                          
                                         2 
                                       
                                       * 
                                       
                                         sin 
                                          
                                         
                                           ( 
                                           
                                             π 
                                             / 
                                             6 
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                   , 
                                   0 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     The lengths of the links are calculated as follows. 
         L   1v =√(( Dv 2*γ v ) 2 +( Dv 1− Dv 2) 2   +Hv 1 2 )
 
         L   2v =√(( Wv 1− Dv 2*cos(π/6)−Dv2*sin(π/6)*γ v ) 2 +( Dv 2*cos(π/6)*γ v−Dv 2*sin(π/6)) 2   +Hv 1 2 )
 
         L   3v =√(( Wv 1− Dv 2*cos(π/6)+sin(π/6)*γ v ) 2 +( Dv 2*cos(π/6)*γ v+Dv 2*sin(π/6)) 2   +Hv 1 2 )
 
     Differences from the lengths of the links in the reference state are determined as follows. Here, γv&gt;0 is assumed. 
         L   1v   2   −L   1v0   2 =( Dv 2*γ v ) 2 &gt;0
 
         L   2v   2   −L   2v0   2 =( Wv 1− Dv 2* cos(π/6)− Dv 2*sin(π/6)*γ v ) 2 −( Wv 1− Dv 2*cos(π/6)) 2 +( Dv 2*sin(π/6)− Dv 2*cos(π/6)*γ v ) 2 −(Dv2*sin(π/6)) 2 &lt;0
 
         L   3v   2   −L   3v0   2 =( Wv 1− Dv 2*cos(π/6)+ Dv 2*sin(π/6)*γ v ) 2 −( Wv 1− Dv 2*cos(π/6)) 2 +( Dv 2*sin(π/6)+ Dv 2*cos(π/6)*γ v ) 2 −( Dv 2*sin(π/6)) 2 &gt;0
 
     In the reference state, it is found that one of length L 2v  of the forearm outside link  38 L and length L 3v  of the forearm inside link  39 L is lengthened while the other is shortened. Thus, while rotating around forearm bone  8 B being the torsion axis, both the force pushed by the extending link and the force drawn by the shortening link are generated, the rotation around torsion axis is performed easily. 
     Similarly to wrist joint  36 , neck joint  27  changes the connection angle with three rotational degrees of freedom by changing the lengths of the three variable length links. Even in neck joint  27 , the lengths of the three variable length links can be determined to have the determined connection angle in the same manner as wrist joint  36 . 
     How to determine the lengths of the links such that the designated angle can be taken with respect to ankle joint  41  is described. The distances between the joint and the link attaching units in ankle joint  41  are defined by the following variables.  FIG. 84  is a view illustrating the variables expressing the distances between the joint and the link attaching units in ankle joint  41 . 
     The variable expressing the position of each point is defined as follows. 
     P 0m : position of ankle joint  41 . 
     P 1m : position of foot outside link attaching unit J 41 . 
     P 2m : position of foot inside link attaching unit J 42 . 
     P 3m : position of lower leg outside link attaching unit J 39 . 
     P 3m0 : position of lower leg outside link attaching unit J 39  in reference state. 
     P 4m : position of lower leg inside link attaching unit J 40 . 
     P 4m0 : position of lower leg inside link attaching unit J 40  in reference state. 
     The intervals between points are expressed by the following variables. 
     Wm1: lengths of line segment P 0m P 1m  and line segment P 0m P 2m  projected on X-axis. 
     Wm2: lengths of line segment P 0m P 3m0  and line segment P 0m P 4m0  projected on X-axis. 
     Dm1: lengths of line segment P 0m P 1m  and line segment P 0m P 2m  projected on Y-axis. 
     Dm2: lengths of line segment P 0m P 3m0  and line segment P 0m P 4m0  projected on Y-axis. 
     Hm1: lengths of line segment P 0m P 1m  and line segment P 0m P 2m  projected on Z-axis. 
     Hm2: lengths of line segment P 0m P 3m0  and line segment P 0m P 4m0  projected on Z-axis. 
     Dm1: length of the line segment P 0m P 1m  projected on Y-axis. 
     Using the variables defined above, a coordinate of each point is expressed as follows. Position P 0m  of ankle joint  41  is set to the origin of the coordinate. 
         P   0m =(0, 0, 0) 
         P   1m =( Wm 1,  Dm 1,  −Hm 1) 
         P   2m =(− Wm 1,  Dm 1,  −Hm 1)
 
         P   3m0 =( Wm 2, − Dm 2,  Hm 2)
 
         P   4m0 =(− Wm 2, − Dm 2,  Hm 2)
 
     The rotation angles of ankle joint  41  are expressed by the following variables. 
     α m : rotation angle of ankle joint  41  around X-axis. α m =0 in reference state 
     β m : rotation angle of ankle joint  41  around Y-axis. β m =0 in reference state 
     [Rm]: rotation matrix of ankle joint  41 . 
     The rotation matrix [Rm] is given as follows. 
     
       
         
           
             
               
                 
                   
                     [ 
                     Rm 
                     ] 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             1 
                           
                           
                             0 
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             
                               cosα 
                                
                               m 
                             
                           
                           
                             
                               - 
                               
                                 sinα 
                                  
                                 m 
                               
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               sinα 
                                
                               m 
                             
                           
                           
                             
                               cosα 
                                
                               m 
                             
                           
                         
                       
                       ) 
                     
                      
                     
                       ( 
                       
                         
                           
                             
                               cosβ 
                                
                               m 
                             
                           
                           
                             0 
                           
                           
                             
                               - 
                               
                                 sinβ 
                                  
                                 m 
                               
                             
                           
                         
                         
                           
                             0 
                           
                           
                             1 
                           
                           
                             0 
                           
                         
                         
                           
                             
                               sinβ 
                                
                               m 
                             
                           
                           
                             0 
                           
                           
                             
                               cosβ 
                                
                               m 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Mathematical 
                      
                     
                         
                     
                      
                     Formula 
                      
                     
                         
                     
                      
                     6 
                   
                   ] 
                 
               
             
           
         
       
     
     The lengths of the links are expressed by the following variables. 
     L 1m : length of lower leg outside link  45 L. Length of line segment P 1m P 3m . 
     L 2m : Length of lower leg inside link  46 L. Length of line segment P 2m P 4m . 
     [Rm] is given, and P 3m , P 4m  are obtained by the following expressions. 
         P   3m =( x 3 m, y 3 m, z 3 m )=[ Rm ]*( Wm 2,  −Dm 2,  Hm 2) t    
         P   4m =( x 4 m, y 4 m, z 4 m )=[ Rm ]*(− Wm 2,  −Dm 2,  Hm 2) t  
 
     Because P 3m , P 4m  are obtained, lengths L 1m , L 2m  of the links can be calculated by the following expressions. 
         L   1m =√(( x 3 m−Wm 1) 2 +( y 3 m−Dm 1) 2 +( z 3 m+Hm 1) 2 )
 
         L   2m =√(( x 4 m+Wm 1) 2 +( y 4 m−Dm 1) 2 +( z 4 m+Hm 2) 2 )
 
     How to determine the lengths of the links such that the designated angle can be taken with respect to hip joint  22  is described. The distances between the joint and the link attaching units in hip joint  22  are defined by the following variables.  FIG. 85  is a view illustrating the variables expressing the distances between the joint and the link attaching units in hip joint  22 . 
     The variable expressing the position of each point is defined as follows. 
     P 0q : position of hip joint  22 . 
     P 1q : position of crotch front link attaching unit J 11 . 
     P 1q0 : position of crotch front link attaching unit J 11  in reference state. 
     P 2q : position of crotch outside link attaching unit J 12 . 
     P 2q0 : position of crotch outside link attaching unit J 12  in reference state. 
     P 3q : position of crotch inside link attaching unit J 13 . 
     P 3q0 : position of crotch inside link attaching unit J 13  in reference state. 
     P 4q : position of knee front link attaching unit J 32 . 
     P 5q : position of knee outside link attaching unit J 33 . 
     P 6q : position of knee inside link attaching unit J 34 . 
     The intervals between the points are defined by the following variables. A U-axis, a V-axis, and a W-axis, which are orthogonal to one another, are used as the coordinate system. The UVW-coordinate system is a coordinate system that moves along with thighbone  10 A. The W-axis is set to a direction in which thighbone  10 A extends. The U-axis is set to an axis that is matched with the X-axis in the reference state. 
     Wq2: length of line segment P 0q P 2q0  projected on U-axis. 
     Wq3: length of line segment P 0q P 3q0  projected on U-axis. 
     Dq1: length of line segment P 0q P 1q0  projected on V-axis. 
     Dq2: length of line segment P 0q P 2q0  projected on V-axis. 
     Dq3: length of line segment P 0q P 3q0  projected on V-axis. 
     Dq4: length obtained by projecting line segment P 0q P 4q  projected on V-axis. 
     Hq1: length of line segment P 0q P 1q0  projected on the W-axis. 
     Hq2: length of line segment P 0q P 2q0  projected on W-axis. 
     Hq3: length of line segment P 0q P 3q0  projected on W-axis. 
     Hq4: lengths of line segment P 0q P 4q0 , line segment P 0q P 5q0 , line segment P 0q P 6q0  projected on W-axis. 
     Using the variables defined above, the coordinate of each point in the reference state is expressed as follows in the UVW-coordinate system. The position of hip joint  22  is set to the origin of the coordinate. 
         P   0q =(0, 0, 0) 
         P   1q0=( 0, − Dq 1,  Hq 1)
 
       P 2q0 =( Wq 2,  Dq 2, − Hq 2)
 
         P   3q0 =(− Wq 3,  Dq 3, − Hq 3)
 
       P 4q =(0, − Dq 3, − Hq 4)
 
         P   5q =( Dq 4*cos(π/6),  Dq 4*sin(π/6), − Hq 4)
 
         P   6q =(− Dq 4*cos(π/6),  Dq 4*sin(π/6), − Hq 4)
 
     The lengths of the links are expressed by the following variables. 
     L 1q : length of thigh front link  23 L. Length of line segment P 1q P 4q . 
     L 2q : length of thigh outside link  24 L. Length of line segment P 2q P 5q . 
     L 3q : length of thigh inside link  25 L. Length of line segment P 3q P 6q . 
     L 1q0 : length of thigh front link  23 L in reference state. Length of line segment P 1q0 P 4q . 
     L 2q0 : length of thigh outside link  24 L in reference state. Length of line segment P 2q0 P 5q . 
     L 3q0 : length of thigh inside link  25 L in reference state. Length of line segment P 3q0 P 6q . 
     The rotation angles of hip joint  22  are defined by the following variables. 
     αq: rotation angle of hip joint  22  around X-axis. αq=αq0 in reference state. 
     βq: rotation angle of hip joint  22  around Y-axis. βq=0 in reference state. 
     γq: rotation angle of hip joint  22  around Y-axis. γq=0 in reference state. 
     [Rq]: rotation matrix of hip joint  22  in UVW-coordinate system. 
     In the case that the direction in which thighbone  10 A extends is rotated from the reference state (αq0, 0, 0) to (αq, βq, γq) in the XYZ-coordinate system, the point fixed in the XYZ-coordinate system is rotated by (αq0−αq, −βq, −γq) in the UVW-coordinate system. Thus, rotation matrix Rq is given as follows. 
     
       
         
           
             
               
                 
                   
                     [ 
                     Rq 
                     ] 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             1 
                           
                           
                             0 
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             
                               cos 
                               ( 
                               
                                 
                                   
                                     
                                       α 
                                        
                                       q 
                                     
                                   
                                   
                                     
                                       α 
                                        
                                       q 
                                        
                                       0 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                           
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   
                                     
                                       
                                         α 
                                          
                                         q 
                                       
                                     
                                     
                                       
                                         α 
                                          
                                         q 
                                          
                                         0 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   
                                     
                                       
                                         α 
                                          
                                         q 
                                       
                                     
                                     
                                       
                                         α 
                                          
                                         q 
                                          
                                         0 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           
                             
                               cos 
                                
                               
                                 ( 
                                 
                                   
                                     
                                       
                                         α 
                                          
                                         q 
                                       
                                     
                                     
                                       
                                         α 
                                          
                                         q 
                                          
                                         0 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                      
                     
                       ( 
                       
                         
                           
                             cosβq 
                           
                           
                             0 
                           
                           
                             
                               sinβ 
                                
                               q 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             1 
                           
                           
                             0 
                           
                         
                         
                           
                             
                               sinβ 
                                
                               q 
                             
                           
                           
                             0 
                           
                           
                             
                               cosβ 
                                
                               q 
                             
                           
                         
                       
                       ) 
                     
                      
                     
                       ( 
                       
                         
                           
                             
                               cosγ 
                                
                               q 
                             
                           
                           
                             
                               sinγ 
                                
                               q 
                             
                           
                           
                             0 
                           
                         
                         
                           
                             
                               - 
                               
                                 sinγ 
                                  
                                 q 
                               
                             
                           
                           
                             
                               cosγ 
                                
                               q 
                             
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             1 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Mathematical 
                      
                     
                         
                     
                      
                     Formula 
                      
                     
                         
                     
                      
                     7 
                   
                   ] 
                 
               
             
           
         
       
     
     The coordinates of the points P 1q , P 2q , P 3q  fixed in the XYZ-coordinate system are obtained as follows in the UVW-coordinate system. The coordinates of points P 4q , P 5q , P 6q  moving together with thighbone  10 A are not changed in the UVW-coordinate system. 
     
       
         
           
             
               
                 
                   
                     P 
                     
                       1 
                        
                       q 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         u 
                          
                         1 
                          
                         q 
                       
                       , 
                       
                         v 
                          
                         1 
                          
                         q 
                       
                       , 
                       
                         w 
                          
                         1 
                          
                         q 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       [ 
                       Rq 
                       ] 
                     
                     * 
                     
                       
                         ( 
                         
                           0 
                           , 
                           
                             - 
                             
                               Dq 
                                
                               1 
                             
                           
                           , 
                           
                             Hq 
                              
                             1 
                           
                         
                         ) 
                       
                       T 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     
                       2 
                        
                       q 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         u 
                          
                         2 
                          
                         q 
                       
                       , 
                       
                         v 
                          
                         2 
                          
                         q 
                       
                       , 
                       
                         w 
                          
                         2 
                          
                         q 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       [ 
                       Rq 
                       ] 
                     
                     * 
                     
                       
                         ( 
                         
                           
                             Wq 
                              
                             2 
                           
                           , 
                           
                             Dq 
                              
                             2 
                           
                           , 
                           
                             - 
                             
                               Hq 
                                
                               2 
                             
                           
                         
                         ) 
                       
                       t 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     
                       3 
                        
                       q 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         u 
                          
                         3 
                          
                         q 
                       
                       , 
                       
                         v 
                          
                         3 
                          
                         q 
                       
                       , 
                       
                         w 
                          
                         3 
                          
                         q 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       [ 
                       Rq 
                       ] 
                     
                     * 
                     
                       
                         ( 
                         
                           
                             - 
                             
                               Wq 
                                
                               3 
                             
                           
                           , 
                           
                             Dq 
                              
                             3 
                           
                           , 
                           
                             - 
                             
                               Hq 
                                
                               3 
                             
                           
                         
                         ) 
                       
                       t 
                     
                   
                 
               
             
           
         
       
     
     Because the coordinates of points P 1q , P 2q , P 3q  are obtained in the UVW-coordinate system, the lengths of the links are expressed as follows. 
         L   1q =√( u 1 q   2 +( v 1 q+Dq 4) 2 +( w 1 q+Hq 4) 2 )
 
         L   2q =√(( u 2 q−Dq 4*cos(π/6)) 2 +( v 2q −Dq 4*sin(π/6)) 2 +( w 2 q+Hq 4) 2 )
 
         L   3q =√(( u 3 q+Dq 4*cos(π/6)) 2 +( v 3 q−Dq 4*sin(π/6)) 2 +( w 3 q+Hq 4) 2 )
 
     In the case that the rotation is performed slightly around the W-axis from the reference state, how the length of each link is changed is examined. Points P 1q , P 2q , P 3q  are given as follows. Here, assuming that γq is small, approximation is performed using sin γq≈γq, cos γq≈1. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           P 
                           
                             1 
                              
                             q 
                           
                         
                         = 
                         
                           ( 
                           
                             
                               u 
                                
                               1 
                                
                               q 
                             
                             , 
                             
                               v 
                                
                               1 
                                
                               q 
                             
                             , 
                             
                               w 
                                
                               1 
                                
                               q 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             ( 
                             
                               
                                 
                                   - 
                                   
                                     Dq 
                                      
                                     1 
                                   
                                 
                                 * 
                                 
                                   sinγ 
                                    
                                   q 
                                 
                               
                               , 
                               
                                 
                                   - 
                                   
                                     Dq 
                                      
                                     1 
                                   
                                 
                                 * 
                                 
                                   cosγ 
                                    
                                   q 
                                 
                               
                               , 
                               
                                 Hq 
                                  
                                 1 
                               
                             
                             ) 
                           
                           ≈ 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   ( 
                   
                     
                       
                         - 
                         
                           Dq 
                            
                           1 
                         
                       
                       * 
                       
                         γ 
                          
                         q 
                       
                     
                     , 
                     
                       - 
                       
                         Dq 
                          
                         1 
                       
                     
                     , 
                     
                       Hq 
                        
                       1 
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     
                       2 
                        
                       q 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         u 
                          
                         2 
                          
                         q 
                       
                       , 
                       
                         v 
                          
                         2 
                          
                         q 
                       
                       , 
                       
                         w 
                          
                         2 
                          
                         q 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       
                         
                           ( 
                           
                             
                               
                                 
                                   Wq 
                                    
                                   2 
                                 
                                 * 
                                 
                                   cosγ 
                                    
                                   q 
                                 
                               
                               + 
                               
                                 
                                   Dq 
                                    
                                   2 
                                 
                                 * 
                                 
                                   sinγ 
                                    
                                   q 
                                 
                               
                             
                             , 
                             
                               
                                 
                                   - 
                                   
                                     Wq 
                                      
                                     2 
                                   
                                 
                                 * 
                                 
                                   sinγ 
                                    
                                   q 
                                 
                               
                               + 
                               
                                 
                                   Dq 
                                    
                                   2 
                                 
                                 * 
                                 
                                   cosγ 
                                    
                                   q 
                                 
                               
                             
                             , 
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               - 
                               
                                 Hq 
                                  
                                 2 
                               
                             
                             ) 
                           
                           ≈ 
                           
                             ( 
                             
                               
                                 
                                   Wq 
                                    
                                   2 
                                 
                                 + 
                                 
                                   
                                     Dq 
                                      
                                     2 
                                   
                                   * 
                                   
                                     γ 
                                      
                                     q 
                                   
                                 
                               
                               , 
                               
                                 
                                   
                                     - 
                                     
                                       Wq 
                                        
                                       2 
                                     
                                   
                                   * 
                                   
                                     γ 
                                      
                                     q 
                                   
                                 
                                 + 
                                 
                                   Dq 
                                    
                                   2 
                                 
                               
                               , 
                               
                                 Hq 
                                  
                                 2 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     P 
                     
                       3 
                        
                       q 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         u 
                          
                         3 
                          
                         q 
                       
                       , 
                       
                         v 
                          
                         3 
                          
                         q 
                       
                       , 
                       
                         w 
                          
                         3 
                          
                         q 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       
                         
                           ( 
                           
                             
                               
                                 
                                   - 
                                   
                                     Wq 
                                      
                                     3 
                                   
                                 
                                 * 
                                 
                                   cosγ 
                                    
                                   q 
                                 
                               
                               + 
                               
                                 
                                   Dq 
                                    
                                   3 
                                 
                                 * 
                                 
                                   sinγ 
                                    
                                   q 
                                 
                               
                             
                             , 
                             
                               
                                 
                                   Wq 
                                    
                                   3 
                                 
                                 * 
                                 
                                   sinγ 
                                    
                                   q 
                                 
                               
                               + 
                               
                                 
                                   Dq 
                                    
                                   3 
                                 
                                 * 
                                 
                                   cosγ 
                                    
                                   q 
                                 
                               
                             
                             , 
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               - 
                               
                                 Hq 
                                  
                                 3 
                               
                             
                             ) 
                           
                           ≈ 
                           
                             ( 
                             
                               
                                 
                                   Wq 
                                    
                                   3 
                                 
                                 + 
                                 
                                   
                                     Dq 
                                      
                                     3 
                                   
                                   * 
                                   
                                     γ 
                                      
                                     q 
                                   
                                 
                               
                               , 
                               
                                 
                                   
                                     Wq 
                                      
                                     3 
                                   
                                   * 
                                   
                                     γ 
                                      
                                     q 
                                   
                                 
                                 + 
                                 
                                   Dq 
                                    
                                   3 
                                 
                               
                               , 
                               
                                 - 
                                 
                                   Hq 
                                    
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     The lengths of the links are calculated as follows. 
         L   1q =√(( Dq 1*γ q ) 2 +(− Dq 1+ Dq 4) 2 +( Hq 1+ Hq 4) 2 )
 
         L   2q =√(( Wq 2+ Dq 2*γ q−Dq 4*cos(π/6)) 2 +(− Wq 2*γ q+Dq 2− Dq 4*sin(π/6)) 2 +(− Hq 2+ Hq 4) 2 )
 
         L   3q =√((— Wq 3+ Dq 3*γ q+Dq 4*cos(π/6)) 2 +( Wq 3*γ q+Dq 3− Dq 4*sin(π/6)) 2 +(− Hq 3+ Hq 4) 2 )
 
     Differences from the lengths of the links in the reference state are determined as follows. 
     
       
         
           
             
                 
             
              
             
               
                 
                   
                     L 
                     
                       1 
                        
                       q 
                     
                   
                   2 
                 
                 - 
                 
                   
                     L 
                     
                       1 
                        
                       
                         q 
                          
                         0 
                       
                     
                   
                   2 
                 
               
               = 
               
                 
                   
                     ( 
                     
                       
                         Dq 
                          
                         1 
                       
                       * 
                       
                         γ 
                          
                         q 
                       
                     
                     ) 
                   
                   2 
                 
                 &gt; 
                 0 
               
             
           
         
       
       
         
           
             
               
                 
                   L 
                   
                     2 
                      
                     q 
                   
                 
                 2 
               
               - 
               
                 
                   L 
                   
                     2 
                      
                     
                       q 
                        
                       0 
                     
                   
                 
                 2 
               
             
             = 
             
               
                 
                   
                     ( 
                     
                       
                         Wq 
                          
                         2 
                       
                       + 
                       
                         
                           Dq 
                            
                           2 
                         
                         * 
                         
                           γ 
                            
                           q 
                         
                       
                       - 
                       
                         
                           Dq 
                            
                           4 
                         
                         * 
                         
                           cos 
                           ( 
                           
                             π 
                             / 
                             6 
                           
                           ) 
                         
                       
                     
                     ) 
                   
                   2 
                 
                 - 
                 
                   
                     ( 
                     
                       
                         Wq 
                          
                         2 
                       
                       - 
                       
                         
                           Dq 
                            
                           4 
                         
                         * 
                         
                           cos 
                            
                           
                             ( 
                             
                               π 
                               / 
                               6 
                             
                             ) 
                           
                         
                       
                     
                     ) 
                   
                   2 
                 
                 + 
                 
                   
                     ( 
                     
                       
                         
                           - 
                           
                             Wq 
                              
                             2 
                           
                         
                         * 
                         
                           γ 
                            
                           q 
                         
                       
                       + 
                       
                         Dq 
                          
                         2 
                       
                       - 
                       
                         
                           Dq 
                            
                           4 
                         
                         * 
                         
                           sin 
                            
                           
                             ( 
                             
                               π 
                               / 
                               6 
                             
                             ) 
                           
                         
                       
                     
                     ) 
                   
                   2 
                 
                 - 
                 
                   
                     ( 
                     
                       
                         Dq 
                          
                         2 
                       
                       - 
                       
                         
                           Dq 
                            
                           4 
                         
                         * 
                         
                           sin 
                            
                           
                             ( 
                             
                               π 
                               / 
                               6 
                             
                             ) 
                           
                         
                       
                     
                     ) 
                   
                   2 
                 
               
               = 
               
                 
                   γ 
                    
                   q 
                 
                 * 
                 
                   ( 
                   
                     
                       
                         ( 
                         
                           
                             
                               Dq 
                                
                               2 
                             
                             2 
                           
                           + 
                           
                             
                               Wq 
                                
                               2 
                             
                             2 
                           
                         
                         ) 
                       
                       * 
                       
                         γ 
                          
                         q 
                       
                     
                     + 
                     
                       2 
                       * 
                       
                         ( 
                         
                           
                             
                               Wq 
                                
                               2 
                             
                             * 
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   π 
                                   / 
                                   6 
                                 
                                 ) 
                               
                             
                           
                           - 
                           
                             
                               Dq 
                                
                               2 
                             
                             * 
                             
                               cos 
                                
                               
                                 ( 
                                 
                                   π 
                                   / 
                                   6 
                                 
                                 ) 
                               
                             
                           
                         
                         ) 
                       
                       * 
                       
                         Dq 
                          
                         4 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   L 
                   
                     3 
                      
                     q 
                   
                 
                 2 
               
               - 
               
                 
                   L 
                   
                     3 
                      
                     
                       q 
                        
                       0 
                     
                   
                 
                 2 
               
             
             = 
             
               
                 
                   
                     ( 
                     
                       
                         - 
                         
                           Wq 
                            
                           3 
                         
                       
                       + 
                       
                         
                           Dq 
                            
                           3 
                         
                         * 
                         
                           γ 
                            
                           q 
                         
                       
                       + 
                       
                         
                           Dq 
                            
                           4 
                         
                         * 
                         
                           cos 
                           ( 
                           
                             π 
                             / 
                             6 
                           
                           ) 
                         
                       
                     
                     ) 
                   
                   2 
                 
                 - 
                 
                   
                     ( 
                     
                       
                         - 
                         
                           Wq 
                            
                           3 
                         
                       
                       + 
                       
                         
                           Dq 
                            
                           4 
                         
                         * 
                         
                           cos 
                            
                           
                             ( 
                             
                               π 
                               / 
                               6 
                             
                             ) 
                           
                         
                       
                     
                     ) 
                   
                   2 
                 
                 + 
                 
                   
                     ( 
                     
                       
                         
                           Wq 
                            
                           3 
                         
                         * 
                         
                           γ 
                            
                           q 
                         
                       
                       + 
                       
                         Dq 
                          
                         3 
                       
                       - 
                       
                         
                           Dq 
                            
                           4 
                         
                         * 
                         
                           sin 
                            
                           
                             ( 
                             
                               π 
                               / 
                               6 
                             
                             ) 
                           
                         
                       
                     
                     ) 
                   
                   2 
                 
                 - 
                 
                   
                     ( 
                     
                       
                         Dq 
                          
                         3 
                       
                       - 
                       
                         
                           Dq 
                            
                           4 
                         
                         * 
                         
                           sin 
                            
                           
                             ( 
                             
                               π 
                               / 
                               6 
                             
                             ) 
                           
                         
                       
                     
                     ) 
                   
                   2 
                 
               
               = 
               
                 
                   γ 
                    
                   q 
                 
                 * 
                 
                   ( 
                   
                     
                       
                         ( 
                         
                           
                             
                               Dq 
                                
                               3 
                             
                             2 
                           
                           + 
                           
                             
                               Wq 
                                
                               3 
                             
                             2 
                           
                         
                         ) 
                       
                       * 
                       
                         γ 
                          
                         q 
                       
                     
                     - 
                     
                       2 
                       * 
                       
                         ( 
                         
                           
                             
                               Wq 
                                
                               3 
                             
                             * 
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   π 
                                   / 
                                   6 
                                 
                                 ) 
                               
                             
                           
                           - 
                           
                             
                               Dq 
                                
                               3 
                             
                             * 
                             
                               cos 
                                
                               
                                 ( 
                                 
                                   π 
                                   / 
                                   6 
                                 
                                 ) 
                               
                             
                           
                         
                         ) 
                       
                       * 
                       
                         Dq 
                          
                         4 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
     As can be seen from the above equations, in the case where Wq2 *sin(π/6)−Dq2*cos(π/6)&gt;0 and Wq3*sin(π/6)−Dq3*cos(π/6)&gt;0 hold, or in the case where Wq2*sin(π/6)−Dq2*cos(π/6)&lt;0 and Wq3*sin(π/6)−Dq3*cos(π/6)&lt;0 hold, when the rotation is performed by a small angle around the W-axis from the reference state, one of length L 2q  of thigh outside link  24 L and length L 3q  of thigh inside link  25 L is lengthened and the other is shortened. As illustrated in  FIG. 85 , both the angle formed by line segment P 0q P 2q0  and the V-axis and the angle formed by the line segment P 0q P 3q0  and the V-axis are greater than π/6 (=60 degrees). That is, Wq2*sin(π/6)−Dq2*cos(π/6)&gt;0 and Wq3*sin(π/6)−Dq3*cos(π/6)&gt;0 hold. In hip joint  22 , when the rotation is performed by a small angle around the W-axis from the reference state, one of length L 2q  of thigh outside link  24 L and length L 3q  of thigh inside link  25 L is lengthened, and the other is shortened. 
     How to determine the length of knee drive link  42 L such that the designated angle can be taken with respect to knee joint  40  is described. The positions of knee joint  40 , knee drive link attaching unit J 35 , and thigh-side auxiliary tool attaching unit J 36  are determined with respect to thighbone  10 A. When angle α n  of knee joint  40  is determined, the position of lower leg-side auxiliary tool attaching unit J 38  is determined. Because the lengths of thigh-side auxiliary tool  43  and lower leg side auxiliary tool  44  are fixed, when the position of lower leg-side auxiliary tool attaching unit J 38  is determined, the position of knee drive link auxiliary tool connecting unit J 37  is determined. Knee joint  40  can be set to the designated angle α n  when the length of knee drive link  42 L is set to the determined distance between knee drive link auxiliary tool connecting unit J 37  and knee drive link attaching unit J 35 . 
     In hand  9 , the motor is driven such that the first finger joint and the second finger joint of each finger are set to the designated angle, and such that the worm gear of each finger joint is located at the position corresponding to the designated angle. Opposable finger  97  can be opposed to the ordinary fingers, and only the first finger joint can be bent, so that the fingers can hold thin paper or the like by sandwiching the thin paper with extended fingers. The fingers may previously be disposed so that one finger is opposed to other fingers without including opposable finger  97 . The number of fingers is not necessary to be five, but may be at least three. As in hand  9 , when the hand includes the opposable finger and the four ordinary fingers, it is advantageous to make the same motion as a human such as grasp of an object, pressing of a button, and operation of a lever. 
     Humanoid robot  100  uses a driving method in which each joint is driven by the expansion and contraction of the actuator. For this reason, the gear is not required to be disposed in the joint, and the joint can be made compact. When the gear is disposed in the joint, a large space is required for the gear and the joint is enlarged. When the large force is exerted in the humanoid robot in which the gear is disposed in the joint, the joint is enlarged, the humanoid robot has the appearance far away from a human, and the appearance may become distorted. Humanoid robot  100  includes the compact joint, so that appearance of the humanoid robot can be brought close to a human more naturally. The joint has the rotational degrees of freedom of the same degrees as a human, so that humanoid robot  100  can make the motion similar to a human. 
     The already-developed humanoid robots are thought to have problems in that the joint has insufficient bending rigidity and that thrust or rigidity is insufficient for actual operation. The humanoid robot of the present disclosure is considered to be one of the solutions to these problems. 
     Because the actuator using the screw rod and the nut is used, reverse efficiency of the screw is high, and the large gripping force of the joint is obtained in a stationary state. When the force less than or equal to the force corresponding to frictional force at the screw acts from the outside on the member driven by the actuator, the joint does not move. When the force larger than the force corresponding to the frictional force acts from the outside, the joint is moved by the external force while the screw functions as a damper that weakens the motion. Because of damping action, robustness against the external force and disturbance is improved. 
     Hand  9  has opposable finger  97  corresponding to the thumb. Opposable finger  97  can be opposed to four ordinary fingers  93 ,  94 ,  95 ,  96 , and the object can be gripped by opposable finger  97  and ordinary fingers  93 ,  94 ,  95 ,  96 . Each finger joint is driven by the worm gear mechanism in which the worm and the worm wheel are used, so that large force to bend the finger can be obtained . 
     Each of the first finger joint and the second finger joint are driven by the worm gear mechanism, so that only one or both of the first finger joint and the second finger joint can be bent. For this reason, the object can be held in a more fitted state by appropriately bending each finger joint of each finger according to the shape of the object held by hand  9 . When the electric power supply is interrupted, gripping force can be maintained by the worm gear mechanism. 
     The finger joint does is not rotated when the motor does not generate the drive force. The reason is that the worm gear mechanism has the large reverse efficiency and the frictional force in the worm gear mechanism is larger than the external force acting on the finger joint. Even if the force to move the member located on the side moved by the worm gear mechanism acts from the outside, when the force is less than or equal to the frictional force of the worm gear mechanism, the finger joint does not rotate. When the larger force acts on the finger joint, the finger joint is rotated while the worm gear mechanism acts as a damper that weakens the motion. For this reason, even if the robot performs such the motion that the upper arm is moved with the hand holding the object, the finger joint of the hand can generate reaction force of the force acting on the object by the motion of the upper arm, and the object can be held in the hand. The force that the finger joint is moved when the motor does not generate the drive force is the force that can be exerted by one or a plurality of humans. Consequently, the object held by, for example, the humanoid robot can be separated from the hand in the event of a disaster or the like in which power supply is cut off. 
     The humanoid robot according to the present disclosure has a structure enabling the motion close to a human. For this reason, the humanoid robot can substitute the work performed by an ordinary person. When artificial intelligence is installed in the humanoid robot, or when the humanoid robot is remotely operated by a person, it is considered that the humanoid robot can be used in industry, an aging society, and resolution of labor shortage. In particular, it is estimated that the humanoid robot can be used to resolve the labor shortage in simple work, dangerous work and work in a severe environment (such as a radiation environment, a high-temperature environment, a low-temperature environment, and a space environment) in which a person can hardly stay for a long time. 
     The three-rotational-degree-of-freedom connection mechanism may be used in chest bending unit C 1 , shoulder C 4 , elbow C 5 , knee C 8 , and ankle C 9 . The three-rotational-degree-of-freedom connection mechanism may be used in not all body bending unit C 2 , neck C 3 , wrist C 6 , crotch C 7 , but at least one of body bending unit C 2 , neck C 3 , wrist C 6 , crotch C 7 , chest bending unit C 1 , shoulder C 4 , elbow C 5 , knee C 8 , and ankle C 9 . 
     The humanoid robot may have only the chest, the head, and the upper limb. The humanoid robot may have only the waist, the chest, the head, and the upper limbs. The humanoid robot may have only the waist and lower limbs. The humanoid robot may not have the head. The three-rotational-degree-of-freedom connection mechanism may be used in at least one joint included in the humanoid robot. In the humanoid robot that includes no waist but the upper limb, the side far from the hand is set to the first member. 
     The three-rotational-degree-of-freedom connection mechanism of the present disclosure may be applied to not the humanoid robot but a robot arm including the hand and one or a plurality of arm section units connected in series from the hand. The three-rotational-degree-of-freedom connection mechanism may be used such that the second member being one of the hand and the arm section units is connected rotatably to the first member provided far from the hand with three rotational degrees of freedom. In the robot arm, the hand can be at a proper position and can be directed to a proper angle. 
     In the hand of the present disclosure, only the hand can be used as a robot hand. A hand different from that of the first embodiment may be used. 
     A biaxial gimbal having a structure different from that of the first embodiment may be used as the biaxial gimbal having two rotational degrees of freedom in the joint and the link attaching unit. The proper type of biaxial gimbal may be used according to the place to which the joint and link attachment are applied. 
     Each of features possessed by the body bending unit, the chest bending unit, the neck, the shoulder, the elbow, the wrist, the crotch, the knee, and the ankle of the first embodiment can be applied to the humanoid robot that does not include the three-rotational-degree-of-freedom connection mechanism. 
     A screw type actuator in which the screw rod is used or an actuator in which hydraulic pressure is used may be used as the actuator. The actuator may have any configuration as long as the distance between two points can be changed and maintained. In the actuator, a suitable mechanism such as a gear and a timing belt may be used as the mechanism for transmitting the rotation of the motor to the screw rod. 
     The opposable finger is movable from the position near the side of the palm plate to the position opposed to the ordinary finger across the palm plate, and may include three finger joints similarly to the ordinary finger. To that end, the opposable finger further includes a fourth dactylus and a fourth finger joint that connects the fourth dactylus rotatably to the third dactylus. The third finger joint rotates the third dactylus with respect to the second dactylus using the worm gear mechanism. The fourth finger joint may be rotated in conjunction with the third finger joint, or can be rotated independently of the third finger joint. The hand may include a finger that always exists at the position opposed to the ordinary finger. The hand may include a finger that is bent in the direction different from the ordinary finger. 
     The humanoid robot, the robot arm, and the robot hand are remotely controlled. The robot may have an automatically operating program, and be autonomously operated according to the program. The motion of the robot can be stopped from the outside even in the autonomous operation. The autonomous operation can be switched to the remote operation. When the robot comes into contact with a living thing such as a human or an unexpected object while the autonomous operation is performing, the robot has a function of automatically detecting the living thing or the unexpected object and stopping the motion. 
     The above is also applied to other embodiments. 
     Second Embodiment 
     In a second embodiment, a hydraulic mechanism is used in the variable length link. A humanoid robot  100 Z includes an actuator in which the hydraulic mechanism is used. An electric motor is used as a drive source of each actuator, a hydraulic pump is driven by the motor, and a piston is moved in the axial direction inside the hydraulic cylinder. A control method when the screw mechanism is driven by the electric motor can directly be adopted when the hydraulic mechanism is used.  FIG. 86  is a cross-sectional view illustrating a structure of the variable length link of the actuator included in the humanoid robot according to the second embodiment. 
     The structure of the actuator in which the hydraulic mechanism is used is described with a thoracolumbar center actuator  19 Z as an example. Thoracolumbar center actuator  19 Z includes a variable length link  19 LZ and a motor  19 M. Variable length link  19 LZ includes a cylinder  19 H, a piston  19 J that is moved in cylinder  19 H, a pipe  19 K, and a pump  19 N. Cylinder  19 H is filled with liquid such as mineral oil. Piston  19 J divides the inside of cylinder  19 H into a first chamber  19 P and a second chamber  19 Q. Piston  19 J can be rotated around the axis in cylinder  19 H. Pipe  19 K connects first chamber  19 P and second chamber  19 Q. Pipe  19 K is filled with the liquid. Pump  19 N is provided in the middle of pipe  19 K. Pump  19 N is driven by motor  19 M. Pump  19 N is driven by motor  19 M. Pump  19 N can move the liquid from first chamber  19 P to second chamber  19 Q, and move the liquid from second chamber  19 Q to first chamber  19 P. 
     One end of piston  19 J is attached to chest-side center link attaching unit J 5 . One end of cylinder  19 H is attached to waist-side center link attaching unit J 10 . 
     When pump  19 N moves the liquid from first chamber  19 P to second chamber  19 Q, piston  19 J is moved in the direction approaching chest-side center link attaching unit J 5 . When pump  19 N moves the liquid from second chamber  19 Q to first chamber  19 P, piston  19 J is moved in the direction away from chest-side center link attaching unit J 5 . When no liquid is moved between first chamber  19 P and second chamber  19 Q, the position of piston  19 J does not change. Thus, the length of variable length link  19 LZ can be changed, and maintain any length of variable length link  19 LZ within the movable range. 
     Instead of the screw type actuator in which the screw rod  19 A or the like is used, the actuator in which the hydraulic mechanism having pump  19 N driven by motor  19 M is used can be used. 
     A valve that switches whether the liquid flows in pipe  19 K may be provided. The valve is open in the case that the length of variable length link  19 LZ is to be changed. The valve is closed in the case that the length of variable length link  19 LZ is to be fixed. 
     With the configuration of the second embodiment, the hydraulic mechanism driven by the motor moves the piston. A rotation coupling component that transmits the rotation of the motor to the screw rod is eliminated, the rotation coupling component being required when the screw rod is used. Reliability is improved by decreasing the number of components. In the control of each drive shaft, each actuator can be controlled in the same manner as the rotation control of each shaft of the electric driven motor, and the hydraulic mechanism can be replaced directly for the screw mechanism. As a result of the case where the hydraulic actuator is used, the larger thrust can be generated as compared with the case where the screw mechanism is driven with the electric motor, and the humanoid robot having high robustness and high gripping force that can be used at the time of disaster can be constructed. 
     With the configuration of the second embodiment, the actuator in consideration of damping characteristics due to hydraulic pressure can be constructed. The configuration of the second embodiment operates while exhibiting the damping characteristics against the disturbance, which improves the robustness against the disturbance. Furthermore, a future increase in size and an increase in gripping force of the robot can be dealt with. 
     Third Embodiment 
     In a third embodiment, the humanoid robot includes the hand including an opposed finger that is always opposed to the ordinary fingers instead of the opposable finger.  FIG. 87  is a perspective view illustrating a left hand  9 A included in a humanoid robot according to the third embodiment viewing from the backside of the hand.  FIG. 88  is a perspective view illustrating left hand  9 A viewing from the palm side.  FIGS. 89, 90, and 91  are a front view of left hand  9 A, a side view of left hand  9 A viewing from the side on which first finger  83  exists, and a rear view, respectively. A view of hand  9 A viewed from the palm side is taken as a front view. Left hand  9 A is illustrated in the state in which the palm faces the front and first finger  83  to fourth finger  86  are directed upward.  FIG. 92  is a side view illustrating left hand  9 A viewing from the fingertip side.  FIG. 93  is a side view illustrating left hand  9 A viewing from the wrist side.  FIG. 94  is a side view illustrating left hand  9 A viewing from the side on which the first finger exists while an opposed finger  87  is bent. In  FIG. 93 , for convenience, left hand  9 A is illustrated while a hand attaching tool  81  is omitted. 
     The structure of hand  9 A is described. Hand  9 A is attached to wrist plate  91  by hand attaching tool  81 . Hand attaching tool  81  is an L-shaped member in side view. Hand attaching tool  81  includes a circular attaching plate  81 A attached to wrist plate  91  and a rectangular palm plate connecting part  81 B connected to a palm plate  82 . Attaching plate  81 A and palm plate connecting part  81 B are connected to each other at an angle of about 90 degrees. In this case, a cylindrical member is sandwiched between hand attaching tool  81  and wrist plate  91 . 
     The cylindrical member may not be required to be sandwiched. 
       FIG. 95  is a plan view illustrating the palm plate of the left hand. As illustrated in  FIG. 95 , in palm plate  82 , substantially rectangular portions to which first finger  83 , second finger  84 , third finger  85 , fourth finger  86 , and opposed finger  87  are attached are referred to as a first finger attaching part  82 A, a second finger attaching part  82 B, a third finger attaching part  82 C, a fourth finger attaching part  82 D, and an opposed finger attaching part  82 E. Other portions of the palm plate  82  are referred to as a palm plate main body  82 F. First finger attaching part  82 A, second finger attaching part  82 B, third finger attaching part  82 C, and fourth finger attaching part  82 D are connected to the fingertip side in the fingertip direction of palm plate main body  82 F. Opposed finger attaching part  82 E exists at a corner of the palm plate  82 , the corner exists on the wrist side in the fingertip direction and on the side where first finger attaching part  82 A exists in the hand breadth direction. 
     First finger attaching part  82 A, second finger attaching part  82 B, third finger attaching part  82 C, fourth finger attaching part  82 D, and opposed finger attaching part  82 E are a finger attaching part that is separated in each finger to which the first dactylus of the finger is connected. Palm plate main body  82 F is a main body to which the finger attaching part is connected. 
     First finger attaching part  82 A and second finger attaching part  82 B are not connected directly to each other, but are connected to each other through palm plate main body  82 F interposed therebetween. Second finger attaching part  82 B and third finger attaching part  82 C are also connected to each other through palm plate main body  82 F interposed therebetween. Third finger attaching part  82 C and fourth finger attaching part  82 D are also connected to each other through palm plate main body  82 F interposed therebetween. First finger attaching part  82 A, second finger attaching part  82 B, third finger attaching part  82 C, and fourth finger attaching part  82 D are connected to palm plate main body  82 F having spaces between adjacent ones. First finger  83 , second finger  84 , third finger  85 , and fourth finger  86  are attached to the palm plate  82  such that there exists wider space at the fingertip side. For this reason, first finger attaching part  82 A, second finger attaching part  82 B, third finger attaching part  82 C, and fourth finger attaching part  82 D are connected to palm plate main body  82 F to be oriented toward the same directions as first finger  83 , second finger  84 , third finger  85 , and fourth finger  86 , respectively. 
     Each of first finger attaching part  82 A, second finger attaching part  82 B, third finger attaching part  82 C, and fourth finger attaching part  82 D is connected to palm plate main body  82 F while a width decreasing portion in which a width in the hand breadth direction orthogonal to the fingertip direction is narrowed is interposed therebetween. For this reason, a notch or a difference in width is provided in places where first finger attaching part  82 A, second finger attaching part  82 B, third finger attaching part  82 C, and fourth finger attaching part  82 D are connected to palm plate main body  82 F. A difference in width  82 G that narrows the width of first finger attaching part  82 A is provided in first finger attaching part  82 A on the side where second finger attaching part  82 B does not exist. And a semicircular notch  82 H is provided in first finger attaching part  82 A on the side near second finger attaching part  82 B. Semicircular notches  827 ,  82 K are provided on both sides of second finger attaching part  82 B. Semicircular notches  82 L,  82 M are provided on both sides of third finger attaching part  82 C. In fourth finger attaching part  82 D, a notch  82 N is provided on the side near third finger attaching part  82 C, and a difference in width  82 P is provided on the side where third finger attaching part  82 C does not exist. 
     Notches  82 H,  82 J,  82 K,  82 L,  82 M,  82 N have the same shape. A straight line connects notches  82 H,  82 J. A straight line connects notches  82 M,  82 N. A straight line connects notches  82 K,  82 L. Notches  82 H,  82 J and the straight line connecting notches  82 H,  82 J may collectively be regarded as a notch provided in palm plate main body  82 F. Notches  82 K,  82 L may be regarded as one notch provided in palm plate main body  82 F, and notches  82 M,  82 N may be regarded as one notch provided in palm plate main body  82 F. 
     First finger attaching part  82 A, second finger attaching part  82 B, third finger attaching part  82 C, and fourth finger attaching part  82 D have the same width in the hand breadth direction and the same width of the width decreasing portion. The width decreasing portion is a place where the notch or the difference in width is provided to decrease the width. 
     When the object is gripped by hand  9 A, first finger  83 , second finger  84 , third finger  85 , fourth finger  86 , and the opposed finger attaching part  82 E are appropriately bent. This is because that first finger attaching part  82 A, second finger attaching part  82 B, third finger attaching part  82 C, fourth finger attaching part  82 D, and opposed finger attaching part  82 E are provided separately from one another. This is also because first finger attaching part  82 A, second finger attaching part  82 B, third finger attaching part  82 C, and fourth finger attaching part  82 D are connected to palm plate main body  82 F with the width decreasing portion interposed therebetween. 
     A notch  82 Q that separates opposed finger attaching part  82 E and first finger attaching part  82 A is provided in palm plate  82  on the side of first finger  83 . Notch  82 Q is formed to have a side parallel to a wrist-side outline on the side of opposed finger attaching part  82 E. However, on the side of first finger attaching part  82 A, notch  82 Q is formed to have a straight portion in which the interval is narrowed toward the inside and a portion parallel to opposed finger attaching part  82 E on the side of first finger attaching part  82 A. Notch  82 K has a semicircular shape in the portion farthest from the end in the hand breadth direction. A through-hole  82 U to be inserted by first worm  87 J is provided in opposed finger attaching part  82 E. In  FIG. 95 , a hole or the like used to attach the member to palm plate  82  is omitted. 
     Two notches  82 R are provided in a place of palm plate main body  82 F to which palm plate connecting part  81 B is attached. Palm plate main body  82 F sandwiched between two notches  82 R is referred to as a wrist attaching part  82 S. Palm plate connecting part  81 B is screwed to wrist attaching part  82 S by a single screw, and screwed to palm plate main body  82 F on the fingertip side of two notches  82 R by a single screw. Wrist attaching part  82 S is narrow because wrist attaching part  82 S is sandwiched between notches  82 R. Hand  9 A is attached to wrist plate  91  with wrist attaching part  82 S interposed therebetween, so that hand  9 A can appropriately be rotated around the axis directed toward the fingertip direction. 
     Palm plate main body  82 F is bent, and three straight lines are formed on palm plate main body  82 F by bending. One ordinary finger is connected to each bent portion. Consequently, the bent portions to which first finger attaching part  82 A, second finger attaching part  82 B, third finger attaching part  82 C, and fourth finger attaching part  82 D are connected have different angles. Each bent angle at a bending place is about 6 degrees. By bending palm plate  82 , the object is gripped easily to be enfolded by palm plate  82  as compared with the case where palm plate  82  is not bent. The direction of the line generated at three bending places is the direction substantially parallel to the fingertip direction. 
     A plurality of palm fleshes  82 T are provided on the palm side of palm plate  82 . The shape of palm flesh  82 T is a rectangular parallelepiped in which corners and edges on the side far from palm plate  82  are chamfered. Palm flesh  82 T acts as a cushion that relieves a load applied from palm plate  82  to the object when the object is gripped. Palm flesh  82 T is made of a material, such as rubber, which has moderate elasticity. 
     One palm flesh  82 T is provided in each of first finger attaching part  82 A, second finger attaching part  82 B, third finger attaching part  82 C, fourth finger attaching part  82 D, and opposed finger attaching part  82 E. Three palm fleshes  82 T are provided for each bent portion in palm plate main body  82 F. Palm flesh  82 T is not provided in palm plate main body  82 F in the portion in which the opposed finger  87  exists. 
     First finger  83 , second finger  84 , third finger  85 , and fourth finger  86 , which are the four ordinary fingers, are connected to palm plate  82  such that there exists wider space at the fingertip side as compared with the base side. As can be seen from  FIG. 91 , second finger  84  is perpendicular to attaching plate  81 A, and the center of second finger  84  and the center of attaching plate  81 A are matched with each other. First finger  83 , second finger  84 , third finger  85 , and fourth finger  86  have the same structure. 
     A largely different point between hand  9 A and hand  9  is opposed finger  87 . The structure of opposed finger  87  is described. Opposed finger  87  is provided on the palm side of palm plate  82  such that the fingertip extends in the direction intersecting with palm plate  82 . Opposed finger  87  is provided so that it faces first finger  83  to fourth finger  86 . Opposed finger  87  is provided at a position on the wrist side and close to the corner on the side where first finger  83  of palm plate  82  exists. The direction in which opposed finger  87  is rotated is the direction intersecting first finger  83  and second finger  83 . As illustrated in  FIG. 89 , when the angle between opposed finger  87 , being extended, and palm plate  82  is decreased, the fingertip is moved in the direction in which the fingertip approaches second finger  84 . 
     Similarly to first finger  83  and other fingers, in opposed finger  87 , a first dactylus  87 A, a second dactylus  87 B, and a third dactylus  87 C are connected in series from the side closer to palm plate  82 . A first finger joint  87 D exists between palm plate  82  and first dactylus  87 A. First finger joint  87 D connects first dactylus  87 A rotatably to palm plate  82 . A second finger joint  87 E exists between first dactylus  87 A and second dactylus  87 B. Second finger joint  87 E connects second dactylus  87 B rotatably to first dactylus  87 A. A third finger joint  87 F exists between second dactylus  87 B and third dactylus  87 C. Third finger joint  87 F connects third dactylus  87 C rotatably to second dactylus  87 B. The rotation axes of first finger joint  87 D, second finger joint  87 E, and third finger joint  87 F are parallel to one another. That is, in the opposed finger  87 , the direction in which first finger joint  87 D is rotated first dactylus  87 A, the direction in which second finger joint  87 E is rotated second dactylus  87 B, and the direction in which third finger joint  87 F rotate third dactylus  8 CB are identical to one another. Opposed finger  87  is always located at the position opposed to first finger  83  to fourth finger  86 , and opposed finger  87  includes three finger joints, so that hand  9 A can grip the object more adequately as compared with hand  9 . 
     Regarding adjacent two of palm plate  82 , first dactylus  87 A, second dactylus  87 B, and third dactylus  87 C, one member located on the side closer to palm plate  82  is referred to as a base-side member, and the other member located on the side on which the base-side member does not exist is referred to as a tip-side member. First finger joint  87 D, second finger joint  87 E, and third finger joint  87 F are three finger joints that connect the tip-side member being any one of first dactylus  87 A, second dactylus  87 B, and third dactylus  87 C rotatably to the base-side member. The same holds true for first finger  83 , second finger  84 , third finger  85 , and fourth finger  86 . 
     Opposed finger  87  cannot be moved in the hand breadth direction. That is, unlike hand  9  in  FIGS. 72 to 78 , opposed finger  87  cannot be moved to the position near the side of palm plate  82  and cannot orient the fingertip toward the substantially same direction as first finger  83  to fourth finger  86 . When one finger joint and one motor are further added to opposed finger  87 , opposed finger  87  can also be moved in the hand breadth direction. In hand  9 A, the number of finger joints and the number of motors are the same as those of hand  9 . 
     A finger first motor  87 H being a power source for rotating first finger joint  87 D of opposed finger  87  is perpendicularly fixed to the backside of palm plate  82 . A first gear head  87 T for converting a rotation speed is provided on the rotation shaft side of finger first motor  87 H. An outer shape of first gear head  87 T is a quadrangular prism shape. First gear head  87 T and finger first motor  87 H are fixed so as not to be moved with respect to each other. First gear head  87 T is perpendicularly fixed to palm plate  82 . Finger first motor  87 H and first gear head  87 T can be fixed to palm plate  82  with high rigidity by perpendicularly fixing first gear head  87 T. 
     A second gear head  87 U is also fixed to a finger second motor  87 L. The outer shape of second gear head  87 U is also the quadrangular prism shape. The first gear head or the second gear head of other fingers is also fixed to the finger first motor or the finger second motor. 
     Portion of opposed finger  87  on the fingertip side from a finger base yoke  87 G exists on the palm side of palm plate  82 . At a position corresponding to first worm  87 J, through-hole  82 U is provided in palm plate  82 . First worm  87 J connected directly to the rotation shaft of finger first motor  87 H meshes with and rotates first worm wheel  87 K supported rotatably by finger base yoke  87 G on the palm side. 
     In first finger joint  87 D, a worm gear mechanism rotates first dactylus  87 A with respect to palm plate  82 . The worm gear mechanism includes finger first motor  87 H disposed in palm plate  82 , first worm  87 J rotated by finger first motor  87 H, and first worm wheel  87 K meshing with first worm  87 J and rotating around the rotation axis of first finger joint  87 D. 
     When opposed finger  87  grips the object with large force, the force rotating first worm wheel  87 K also becomes large as reaction. Finger first motor  87 H generates force to prevent first worm wheel  87 K from rotating. Unless the finger first motor  87 H is firmly fixed to palm plate  82 , finger first motor  87 H and first gear head  87 T are peeled off from palm plate  82  due to the force rotating first worm wheel  87 K. Making finger first motor  87 H and first gear head  87 T perpendicular to palm plate  82  causes to generate force easily against force separating finger first motor  87 H from palm plate  82 . 
     First dactylus  87 A includes a first wheel linked part  87 AA, a first yoke  87 AB, and a second motor installation part  87 AC. First wheel linked part  87 AA is a box-shaped member that sandwiches first worm wheel  87 K and is rotated together with first worm wheel  87 K. First yoke  87 AB is a member that sandwiches and holds the rotation shaft of second finger joint  87 E. The length of first wheel linked part  87 AA is set to an extent that opposed finger  87  can sandwich the object with the fingertip of the ordinary finger. 
     Finger second motor  87 L is installed in second motor installation part  87 AC. Second motor installation part  87 AC is a member existing on the wrist side and contacting with first yoke  87 AB. First wheel linked part  87 AA and second motor installation part  87 AC are manufactured integrally. First wheel linked part  87 AA is a polygon in which the side where second finger joint  87 E exists is wider viewing from the side where opposed finger  87  exists. First yoke  87 AB being two plate materials are screwed to first wheel linked part  87 AA on the side where second finger joint  87 E exists. Protrusions  87 AD are provided at the tip of first yoke  87 AB. Protrusions  87 AD are stoppers that restrict the rotation of second finger joint  87 E toward the backside of the hand to an allowable rotation angle. 
     Second motor installation part  87 AC includes a motor installation surface perpendicular to first yoke  87 AB, sides having a distance wider than first yoke  87 AB and being parallel to first yoke  87 AB, and a bottom connected to first wheel linked part  87 AA. The sides are lower than the motor installation surface, and the corners of the sides on the finger base side are largely chamfered. The upper corners of the motor installation surface are also chamfered. Finger second motor  87 L and second gear head  87 U are fixed vertically in the motor installation surface. A through-hole is made in the motor installation surface, and the rotation shaft of second gear head  87 U is inserted in the through hole. 
     A second worm  87 M is attached to the rotation shaft of finger second motor  87 L. Second worm  87 M meshes with a second worm wheel  87 N held rotatably by first yoke  87 AB. Since the worm gear mechanism including second worm  87 M and second worm wheel  87 N is used, second dactylus  87 B is rotated around finger joint  87 E, being the rotation axis, with respect to first dactylus  87 A by rotation of finger second motor  87 L. 
     Second dactylus  87 B sandwiches and holds second worm wheel  87 N, and is rotated together with second worm wheel  87 N. Second dactylus  87 B is two plate materials. The rotation shaft of third finger joint  87 F is provided at the end of second dactylus  87 B on the side where third dactylus  87 C exists. Two plate materials included in second dactylus  87 B have a constant thickness. Second dactylus  87 B has a portion that sandwiches second worm wheel  87 N and is sandwiched by first yoke  87 AB, an intermediate portion, and a portion in which third finger joint  87 F is provided. And second dactylus  87 B is formed into a shape having different widths with a small difference. The distance between two plate materials included in second dactylus  87 B is narrow on the side where second finger joint  87 E exists, and is wide on the side where third finger joint  87 F exists. The side surfaces of stoppers  87 AD provided at the tip of first yoke  87 AB contact with the portion sandwiched by first yoke  87 AB. Stoppers  87 AD abut on the difference in width of second dactylus  87 B existing between the intermediate portion and the portion sandwiched by first yoke  87 AB, thus the angle at which second finger joint  87 E is rotated onto the side opposite to the palm is restricted. 
     In second finger joint  87 E, a worm gear mechanism rotates second dactylus  87 B with respect to first dactylus  87 A. The worm gear mechanism includes finger second motor  87 L disposed on first dactylus  87 A, second worm  87 M rotated by finger second motor  87 L, and second worm wheel  87 N that meshes with second worm  87 M to be rotated around the rotation axis of second finger joint  87 E together with second dactylus  87 B. 
     Referring to  FIG. 96 , the gear that rotates third finger joint  87 F in conjunction with second finger joint  87 E is described.  FIG. 96  is an enlarged perspective view illustrating a vicinity of second dactylus  87 B of opposed finger  87 . A plurality of gears that rotate third finger joint  87 F in conjunction with the rotation of second finger joint  87 E are provided in second dactylus  87 B. An idler gear  87 R existing outside second dactylus  87 B meshes with a partial gear  87 Q provided at the tip of first yoke  87 AB. The pair of idler gear  87 R and partial gear  87 Q exists on both sides of second dactylus  87 B. Idler gear  87 R meshing with partial gear  87 Q is rotated in the same rotation direction as second worm wheel  87 N. Idler gear  87 R meshes with an outer-idler gear  87 SA on the fingertip side. On the rotation shaft of outer-idler gear  87 SA, an inner-idler gear  87 SB is fixed by being sandwiched by second dactylus  87 B. Outer-idler gear  87 SA and inner-idler gear  87 SB are rotated in the opposite direction to idler gear  87 R. Outer-idler gear  87 SA and inner-idler gear  87 SB are rotated around the same rotation axis. Inner-idler gear  87 SB meshes with a third dactylus drive gear  87 P that is rotated around the rotation axis of third finger joint  87 F together with third dactylus  87 AC. Third dactylus drive gear  87 P is rotated in the opposite direction to inner-idler gear  87 SB. Third dactylus drive gear  87 P is rotated in the same direction as second worm wheel  87 N. 
     A gear ratio between second worm wheel  87 N and third dactylus drive gear  87 P is adjusted so that it becomes an appropriate value close to 1. 
     Idler gear  87 R is a gear that is rotated in conjunction with the rotation of second finger joint  87 B. Outer-idler gear  87 SA (including inner-idler gear  87 SB) is one of a plurality of gears that is rotated on an odd-numbered rotation shafts driven by idler gear  87 R. Third dactylus drive gear  87 P is a gear provided in third finger joint  87 F driven by inner-idler gear  87 SB. 
     Third dactylus  87 C includes a fingertip  87 CA and a fingertip base  87 CB. Fingertip  87 CA has a shape in which a hemisphere is connected to the tip of the cylinder. Fingertip base  87 CB is a member that is rotated together with third dactylus drive gear  87 P. A rectangular-plate-shaped member having a rounded corner is provided on the fingertip side of fingertip base  87 CB. Fingertip  87 CA is attached to this plate-shaped member. Consequently, fingertip  87 CA can be replaced easily with a fingertip having a shape that conforms to the application. 
     In first finger  83 , all members, including a finger first motor  83 H, exist on the backside of the hand. 
     Finger first motor  83 H is attached to a first motor fixer  83 V. First motor fixer  83 V is a rectangular parallelepiped box. First motor fixer  83 V is attached to first finger attaching part  82 A. In first motor fixer  83 V, the fingertip side and the side near first finger attaching part  82 A are open. Ribs are provided on the finger base side for the purpose of reinforcement, and the side near the finger base side of first motor fixer  83 V is seen obliquely when viewed from the side. First motor fixer  83 V is perpendicular to palm plate  82 B, and finger first motor  83 H and a first gear head  83 T are attached to the surface parallel to palm plate  82 B. A first worm  83 J attached to the rotation shaft of first gear head  83 T is inserted between first motor fixer  83 V and palm plate  82 B. 
     Finger first motor  83 H and first motor fixer  83 V can be fixed with increased rigidity by fixing finger first motor  83 H perpendicularly to first motor fixer  83 V. 
     First worm  83 J meshes with first worm wheel  83 K that is rotated around the rotation axis held by finger base yoke  83 G. First dactylus  83 A is rotated around first finger joint  83 D together with first worm wheel  83 K. 
     The structure on the fingertip side from first dactylus  83 A is the same as opposed finger  87 . First wheel linked part  83 AA is shorter than first wheel linked part  87 AA of opposed finger  87 . 
     The structures of second finger  84 , third finger  85 , and fourth finger  86  are the same as first finger  83 . 
     The disposition of the worm gear mechanism is described by taking first finger  83  as an example. In first finger joint  83 D, as illustrated in  FIG. 90 , in the direction in which palm plate  82  extends, the worm gear mechanism exists in an area in which the finger base yoke  83 G exists or an area on the side of finger base yoke  83 G on which palm plate  82  exists. At the same time, in the direction perpendicular to palm plate  82 , the worm gear mechanism exists in an area on the side of palm plate  82  on which the rotation axis exists. The worm gear mechanism is similarly disposed in second finger  84  and the like. Because the worm gear mechanism of the first finger joint is disposed in such areas, the worm gear mechanism does not obstruct the object when the object is held by hand  9 A.  FIG. 90  is a view illustrating hand  9 A viewed from the direction parallel to the rotation axes of first finger joint  83 D and first finger joint  83 E. 
     In second finger joint  83 E, as illustrated in  FIG. 90 , the worm gear mechanism exists in an area in which first dactylus  83 A exists or an area on the side of first dactylus  83 A far from palm plate  82  in the direction orthogonal to the direction in which first dactylus  83 A extends. The area on the side of first dactylus  83 A far from palm plate  82  in the direction orthogonal to the direction in which first dactylus  83 A extends is the back side of the hand. First finger  83  can be rotated onto the palm side from the state in which each finger joint is extended. When each finger joint is rotated onto the palm side, first finger  83  approaches palm plate  82 . The back side of first finger  83  is the side far from palm plate  82  than first finger  83 . Also in second finger  84  and the like, the worm gear mechanism is similarly disposed in the second finger joint. Because the worm gear mechanism of the second finger joint is disposed in such areas, the worm gear mechanism does not obstruct the object when the object is held by hand  9 A. 
     The operation is described. In hand  9 A, the motor is driven such that the first finger joint and the second finger joint of each finger are set to the designated angle, and such that the worm gear of each finger joint is located at the position corresponding to the designated angle. 
     Each finger joint is driven by the worm gear mechanism in which the worm and the worm wheel are used, so that large force to bend the finger can be generated . Each of the first finger joint and the second finger joint are driven by the worm gear mechanism, so that only one or both of the first finger joint and the second finger joint can be bent. When the electric power supply is interrupted, gripping force can be maintained by the worm gear mechanism. 
     Since opposed finger  87  includes second finger joint  87 E and third finger joint  87 F in addition to first finger joint  87 D, the object can be held by bending second finger joint  87 E as illustrated in  FIG. 102 . Second finger joint  87 E and third finger joint  87 F have the rotation axis parallel to first finger joint  87 D. For this reason, hand  9 A can hold a thin object such as paper with opposed finger  87  in the state in that only first finger joint  87 D is bent, and second finger joint  87 E and third finger joint  87 F are extended. 
     In hand  9 , first worm  93 J protrudes to the side of palm plate  92  from first dactylus  93 A. On the other hand, in hand  9 A, first worm  83 J exists on the backside of the hand. In first finger  83 , first dactylus  83 A, second dactylus  83 B, and first dactylus  83 C face palm plate  82 . In holding the object between first finger  83  or the like and palm plate  82 , the member that prevents first worm  83 J or the like from contacting with the object is necessary in hand  9 . In hand  9 A the member that prevents first worm  83 J or the like from contacting with the object is not necessary, and the structure of hand  9 A is simplified as compared with hand  9 . 
     First finger  83 , second finger  84 , third finger  85 , and fourth finger  86  have the same structure. However, the structure may be changed depending on the fingers. In all the finger joints including the worm gear mechanism, the worm driven by the motor is made perpendicular to the base-side member. Alternatively, at least one worm gear mechanism of at least one finger may be made perpendicular to the base-side member. 
     The opposed finger including the three finger joints may be rotatable in the hand breadth direction with respect to the palm plate like the opposable finger. 
     The above is also applied to other embodiments. 
     Fourth Embodiment 
     In a fourth embodiment, the third embodiment is changed such that the humanoid robot includes the hand including a hand breadth rotation finger in which the entire finger is rotated in the hand breadth direction instead of the opposed finger.  FIG. 97  is a perspective view illustrating a left hand  9 B included in a humanoid robot of the fourth embodiment when left hand  9 B is viewed from the back side of the hand while a hand breadth rotation finger  88  extends.  FIG. 98  is a perspective view illustrating left hand  9 B when left hand  9 B is viewed from the back side of the hand while hand breadth rotation finger  88  is directed in a direction intersecting with palm plate  82 .  FIGS. 99, 100, 101, 102, and 103  are a front view illustrating left hand  9 B when hand breadth rotation finger  88  extends, a side view illustrating left hand  9 B viewed from the side on which first finger  83  exists, a rear view, a side view illustrating left hand  9 B viewed from the side on which fourth finger  86  exists, and a side view illustrating left hand  9 B viewed from the fingertip side, respectively.  FIGS. 104, 105, 106, 107, and 108  are a front view illustrating left hand  9 B when hand breadth rotation finger  88  is directed in the direction intersecting with palm plate  82 , a side view illustrating left hand  9 B viewed from the side on which first finger  83  exists, a rear view, a side view illustrating left hand  9 B viewed from the side on which fourth finger  86  exists, and a side view illustrating left hand  9 B viewed from the fingertip side, respectively.  FIGS. 109 and 110  are enlarged perspective views illustrating hand breadth rotation finger  88 .  FIG. 109  is a perspective view illustrating hand breadth rotation finger  88  when hand breadth rotation finger  88  extends.  FIG. 110  is a perspective view illustrating hand breadth rotation finger  88  when hand breadth rotation finger  88  is directed in the direction intersecting palm plate  82 . 
     In  FIGS. 97 to 110 , a portion up to wrist plate  91  is illustrated. Palm plate  82 , first finger  83 , second finger  84 , third finger  85 , and fourth finger  86  have the same structure as the first embodiment. In  FIGS. 97 to 110 , the cover and the like omitted in  FIGS. 87 to 97  of the third embodiment are illustrated. 
     A first dactylus cover  83 X is a cover that covers a portion in which a first yoke  83 AB is attached to first wheel linked part  83 AA. First dactylus cover  83 X is a member formed by bending a substantially rectangular plate material into a U-shape. The substantially rectangular plate member includes a substantially rectangular protrusion in the center of one side. First dactylus cover  83 X is put on first dactylus  83 A from the palm side. The substantially rectangular protrusion has a rounded corner, and is bent such that a step can be formed in the middle of the protrusion. 
     A second dactylus cover  83 Y is a cover that covers a second worm wheel  83 N and a partial gear  83 Q, an idler gear  83 R, an outer-idler gear  83 SA, and the like, which exist on the side not sandwiched between two second dactyli  83 B. Second dactylus cover  83 Y has the same shape as first dactylus cover  83 X. Second dactylus cover  83 Y in the direction along first finger  83  is longer than first dactylus cover  83 X. 
     A second worm cover  83 Z is a cover that covers second worm  83 M from the backside of the hand. Second worm cover  83 Z has a shape in which a cylinder including a bottom only on one side and a flange on the other side is cut into a half in the axial direction. Second worm  83 M exists in the cylindrical portion. A flange is attached to the rear surface of the motor installation surface of a second motor installation part  83 AC. The outer shape of the flange has the same shape as the motor installation surface. 
     Differences from hand  9 A are described. Hand  9 B includes hand breadth rotation finger  88  instead of opposed finger  87 . Hand breadth rotation finger  88  is attached to palm plate  82  such that the entire finger can be rotated in the hand breadth direction. Hand breadth rotation finger  88  is attached to palm plate  82  at the same position as opposed finger  87 . Hand breadth rotation finger  88  is attached to a hand breadth rotation finger attaching part  82 V that is a part of palm plate  82 . Similarly to opposed finger attaching part  82 E, hand breadth rotation finger attaching part  82 V exists at the corner of palm plate  82 , the corner exists on the wrist side in the fingertip direction and on the side where first finger attaching part  82 A exists in the hand breadth direction. Hand breadth rotation finger attaching part  82 V has the same shape as opposed finger attaching part  82 E. 
     In hand breadth rotation finger  88 , a portion in the fingertip side from finger base yoke  88 G has the same structure as opposed finger  87 . Hand breadth rotation finger  88  and opposed finger  87  are different from each other only in the attaching direction to palm plate  82 . 
     Hand breadth rotation finger  88  is attached to palm plate  82  being able to be rotated in the hand breadth direction with a box-shaped hand breadth finger base  88 W which has two open sides. Hand breadth finger base  88 W is interposed between hand breadth rotation finger  88  and palm plate  82 . Hand breadth finger base  88 W is attached onto the backside of the hand of hand breadth rotation finger attaching part  82 V with an angle of about 20 degrees toward the wrist. Finger first motor  88 H and second gear head  88 T are accommodated in hand breadth finger base  88 W, and attached to the motor installation surface that is the surface in the hand breadth direction of hand breadth finger base  88 W. A through-hole is made in the motor installation surface, and the rotation shaft of second gear head  88 T is inserted in the through-hole. Finger base yoke  88 G is attached to the outer surface of the motor installation surface. Finger base yoke  88 G is attached such that the shaft member of finger base yoke  88 G is parallel to the motor installation surface and forms an angle of about 65 degrees with respect to palm plate  82 . Consequently, in the case in that first finger joint  88 D is rotated and hand breadth rotation finger  88  is extended, third dactylus  88 C is located closer to the fingertip side as compared with palm plate  82 , and the object is held easily between hand breadth rotation finger  88  and palm plate  82 . Hand breadth finger base  88 W includes the sides connected to both of the motor installation surface and the attaching surface to palm plate  82 . The corners of the two sides have a shape that is largely cut by a straight line. The side surfaces of hand breadth finger base  88 W each has a trapezoidal shape in which an upper base is short while a side is perpendicular to a lower base. On the side surface on the wrist side, the perpendicular side on the side on which the surface attached to palm plate  82  is shorter than that of the other side surface. 
     Similarly to opposed finger  87 , in hand breadth rotation finger  88 , first dactylus  88 A is longer than first dactylus  83 A and other first dactyli. For this reason, first dactylus cover  83 X is longer than second dactylus cover  83 Y. 
     The operation is described. In hand  9 B, the motor is driven such that the first finger joint and the second finger joint of each finger are set to the designated angle, and such that the worm gear of each finger joint is located at the position corresponding to the designated angle. 
     Each finger joint is driven by the worm gear mechanism in which the worm and the worm wheel are used, so that large force to bend the finger can be generated. Each of the first finger joint and the second finger joint are driven by the worm gear mechanism, so that only one or both of the first finger joint and the second finger joint can be bent. When the electric power supply is interrupted, gripping force can be maintained by the worm gear mechanism. 
     By including hand breadth rotation finger  88  that is rotated in the hand breadth direction, the length in the hand breadth direction of hand  9 B is larger than that of hand  9 A when hand breadth rotation finger  88  is extended. Consequently, hand  9 B can hold the larger object as compared with hand  9 A. When palm plate  82  faces upward and right and left hands  9 B are arranged at the same height, the large object can be held by both hands  9 B. 
     Fifth Embodiment 
     A fifth embodiment is the case where a humanoid upper half body robot is placed on a pedestal with a height that is changeable and movable. Referring to  FIGS. 111 to 113 , the whole configuration of the humanoid upper half body robot is described.  FIGS. 111, 112, and 113  are a perspective view, a front view, and a side view of the whole of a humanoid upper half body robot according to the fifth embodiment of the present disclosure. 
     A humanoid upper half body robot  100 C is a robot including an upper half body robot from the waist. Humanoid upper half body robot  100 C is placed on an upper surface of a control device container  150  containing a control device (not illustrated) that controls humanoid upper half body robot  100 C. The waist of humanoid upper half body robot  100 C is fixed to the upper surface of control device container  150 . Control device container  150  has a rectangular parallelepiped shape. Because the humanoid upper half body robot and the control device are under development, the control device container  150  is made larger such that the control device can be modified easily. When the humanoid robot is actually used, the control device is made to have a size of a small bag, and is disposed in, for example, the rear of the humanoid robot. 
     Control device container  150  is placed on a pedestal lifter  160 . Pedestal lifter  160  is placed on a cart  170 . Although pedestal lifter  160  is simply illustrated in the drawings, a height of the upper surface can be changed by changing the angle of the link connecting the upper surface and the lower surface. Cart  170  has a function of being pushed by a person or the like or having automatic drive. Pedestal lifter  160  is a height adjuster in which humanoid upper half body robot  100 C is mounted and which moves humanoid upper half body robot  100 C vertically. Cart  170  is a moving unit that moves humanoid upper half body robot  100 C and pedestal lifter  160 . The pedestal lifter and the cart may have a configuration other than those illustrated in the drawings. Humanoid upper half body robot  100 C is moved to a place to be used by cart  170 , and is made to have a height suitable for the object to be operated by pedestal lifter  160 . Furthermore, humanoid upper half body robot  100 C can take a posture suitable for the work. Humanoid upper half body robot  100 C, pedestal lifter  160 , and cart  170  can be considered as one robot. 
     The lower half body having the same shape as a human may be provided similarly to humanoid robot  100  of the first embodiment. An upper half body robot including up to the chest without the waist may be used. The upper half body robot without the waist is mounted on control device container  150  by fixing the chest to the upper surface of control device container  150 . 
     As illustrated in  FIGS. 114 to 119 , humanoid upper half body robot  100 C has the same structure as an upper structure of a human including from the waist.  FIGS. 114, 115 and 116  are perspective views of humanoid upper half body robot  100 C.  FIG. 114  is a perspective view when humanoid upper half body robot  100 C is viewed from the front.  FIG. 115  is a perspective view when humanoid upper half body robot  100 C is viewed from the left side.  FIG. 116  is a perspective view when humanoid upper half body robot  100 C is viewed from a rear side.  FIGS. 117, 118 and 119  are a front view, a plan view, and a bottom view of humanoid upper half body robot  100 C, respectively. 
     Humanoid upper half body robot  100 C includes a trunk  1 C and a pair of upper limbs  3 C protruding from the right and left of an upper part of trunk  1 C. Humanoid upper half body robot  100 C does not include a head. The head may be provided above the center of trunk  1 C. 
     Trunk  1 C is divided into an upper-side, that is, chest  5 C and a lower-side, that is, waist  6 C. In upper limb  3 C, an upper arm  7 C, a forearm  8 C,and a hand  9 C are connected in series. The pair of right and left upper limbs  3 C has a structure in which right upper limb  3 C and left upper limb  3 C have a mirror image relationship. Right and left upper limbs  3 C may have a portion in which the mirror image relationship does not hold. 
     Each joint of humanoid upper half body robot  100 C has three rotational degrees of freedom, at which the joint can be moved back and forth and right and left and twisting motion can be performed, in the wrist and a connection between chest  5 C and waist  6 C. The shoulder and the elbow have two rotational degrees of freedom, at which the joint can be moved back and forth and right and left. The shoulder, the elbow, or the like may have three rotational degrees of freedom. 
     Referring to  FIGS. 114 to 132 , a structure of trunk  1 C is described.  FIGS. 120, 121, 122, and 123  are a perspective view, a front view, a left side view, and a right side view illustrating the body bending unit of humanoid upper half body robot  100 C. In  FIGS. 120 to 123 , the humanoid upper half body robot  100 C is in the state in which the actuators that drive upper limb  3 C and a shoulder C 4 C and the like are removed.  FIGS. 127, 128, and 129  are a front view, a plan view, and a left side view illustrating the shoulder included in humanoid upper half body robot  100 C, respectively. In  FIGS. 120 to 123 , humanoid upper half body robot  100 C is in the state in which the portion from upper arm  7 C is removed from shoulder C 4 C.  FIG. 130  is a view illustrating the left shoulder of humanoid upper half body robot  100 C viewed from below.  FIGS. 131 and 132  are perspective views illustrating the left shoulder of humanoid upper half body robot  100 C.  FIG. 131  is a perspective view illustrating the left shoulder of humanoid upper half body robot  100 C viewed from the front upper side.  FIG. 132  is a perspective view illustrating the left shoulder of humanoid upper half body robot  100 C viewed from the upper rear side. 
     Chest  5 C includes a shoulder frame  51 C and a chest skeleton plate  52 C. Chest skeleton plate  52 C is a plate-shaped member extending in the right and left direction and the vertical direction of humanoid upper half body robot  100 C. Chest  5  of the humanoid robot  100  has a structure including many frames. As compared with chest  5 , chest  5 C has a simple structure. 
     Chest skeleton plate  52 C is located at the center in the front-back direction of humanoid upper half body robot  100 C. Chest skeleton plate  52 C has a substantially rectangular shape when viewed from the front. A portion in which the width in the right and left direction is gradually widened is connected onto the rectangle. Above the portion, there exists a portion in which the width in the right and left direction is narrowed so that a step-shaped portion is formed at each of right and left ends. Shoulder frame  51 C is connected to the step-shaped portion from the right and left. The height of the portion in which the width in the right and left direction is narrowed stepwise is high only in the portions being near both ends in the right and left direction and connected with shoulder frame  51 C. A semi-circularly protruding portion exists at the right and left ends of the lower end of the rectangle. 
     Chest skeleton plate  52 C includes a plate-shaped portion that extends in the vertical direction when viewed from the side, and plate-shaped portions that extend in the front-back direction above and below the vertical plate-shaped portion. In the upper plate-shaped portion, the width in the front-back direction is the same at any portion in the right and left direction. In the lower plate-shaped portion, the width in the front-back direction is large at the center in the right and left direction. Reinforcing ribs extending vertically exist in the front surface and the rear surface at two places near the center of chest skeleton plate  52 C. Chest skeleton plate  52 C includes two openings in a portion between the reinforcing ribs and one opening outside each of the right and left reinforcing ribs for the purpose of weight reduction. 
     Shoulder frame  51 C is connected to the portions located on the upper side of chest skeleton plate  52 C and near the right and left ends, namely, the portions corresponding to both the shoulders. Shoulder frame  51 C extends while being bent backward. A shoulder joint mounting hole  51 H is made at the outside end of shoulder frame  51 C. Shoulder joint  13  is mounted in shoulder joint mounting hole  51 H. 
     As illustrated in  FIGS. 120 and 121 , a shoulder first mounting hole  52 H and a shoulder second mounting hole  52 L are arranged near each of the right and left ends of chest skeleton plate  52 C vertically. Shoulder second mounting holes  52 L are made in the semi-circularly protruding portions at the right and left ends of the lower end of chest skeleton plate  52 C. Chest-side main link attaching unit J 1  is mounted from the front into upper shoulder first mounting hole  52 H. Chest-side auxiliary link attaching unit J 2  is attached from the rear into lower shoulder second mounting hole  52 L. In humanoid robot  100 , chest-side main link attaching unit J 1  is attached rearward from the front portion of thorax frame  52 . Chest-side auxiliary link attaching unit J 2  is attached forward from the rear portion of thorax frame  52 . 
     Chest-side main link attaching unit J 1  is the biaxial gimbal in which upper arm driving main link  14 L is sandwiched by the yoke provided in the rotation member that is rotated around the rotation axis perpendicular to chest skeleton plate  52 C. Chest-side auxiliary link attaching unit J 2  is the biaxial gimbal in which upper arm drive auxiliary link  15 L is sandwiched by the yoke provided on the rotation member that is rotated around the rotation axis perpendicular to chest skeleton plate  52 C. The direction of the rotation axes around which the rotation members of chest-side main link attaching unit J 1  and chest-side auxiliary link attaching unit J 2  rotate are different from the direction of the link moving plane rotation axis passing chest-side main link attaching unit J 1  and chest-side auxiliary link attaching unit J 2 . Thus, upper arm drive main link  14 L and upper arm drive auxiliary link  15 L are required to have one degree of freedom around the axis. 
     Columnar backbone  56  is provided below chest skeleton plate  52 C. Backbone  56  is perpendicular to the lower surface that is wide in the front-back direction of chest skeleton plate  52 C. A thoracolumbar joint  18  connecting backbone  56  rotatably to waist  6  with three rotational degrees of freedom is provided at a lower end of backbone  56 . A spherical bearing is used for thoracolumbar joint  18 . Backbone  56  being the torsion axis is fixed with respect to chest  5 C. 
     Waist  6 C has a disc shape. Thoracolumbar joint  18  is provided at the center of the disc. Waist  6 C around thoracolumbar joint  18  has a cylindrical shape, and is thicker than the other portions. 
     As illustrated in  FIGS. 120 to 123 , three actuators of a thoracolumbar center actuator  19 C, a thoracolumbar right actuator  20 C, and a thoracolumbar left actuator  21 C are provided between chest  5 C and waist  6 C. Thoracolumbar center actuator  19 C includes a thoracolumbar center link  19 LC. Thoracolumbar right actuator  20 C includes a thoracolumbar right link  20 LC. Thoracolumbar left actuator  21 C includes a thoracolumbar left link  21 LC. 
     A chest center link attaching unit J 5 C and a chest right link attaching unit J 6 C are provided on the lower surface of chest skeleton plate  52 C. One ends of thoracolumbar center link  19 LC and thoracolumbar right link  20 LC are connected rotatably to chest center link attaching unit J 5 C and chest right link attaching unit J 6 C with two rotational degrees of freedom. Chest center link attaching unit J 5 C has a structure in which one end of thoracolumbar center link  19 LC is sandwiched rotatably by the yoke provided on chest skeleton plate  52 C. The yoke of chest center link attaching unit J 5 C is provided on the rotation member that is rotated around the rotation axis being parallel to the Y-axis and extending from chest skeleton plate  52 C to the rear side. Chest right link attaching unit J 6 C has a structure in which one end of thoracolumbar right link  20 LC is sandwiched rotatably by the yoke provided on chest skeleton plate  52 C. The yoke of chest right link attaching unit J 6 C is provided on the rotation member that is rotated around the horizontal rotation axis forming the angle of about 25 degrees with the X-axis extending from chest skeleton plate  52 C to the front side. 
     Chest center link attaching unit J 5 C and chest right link attaching unit J 6 C exist at the same height. In backbone  56 , the place having the height of chest center link attaching unit J 5 C and chest right link attaching unit J 6 C that are provided in chest  5 C is called a backbone upper end  56 B. 
     A center-link left link attaching unit J 7 C is provided on thoracolumbar center link  19 LC at a position having a predetermined distance from chest center link attaching unit J 5 C. One end of thoracolumbar left link  21 LC is connected rotatably to center link left link attaching unit J 7 C with two rotational degrees of freedom. Center-link left link attaching unit J 7 C has a structure in which a protrusion provided on thoracolumbar center link  19 LC is sandwiched by the yoke provided at one end of thoracolumbar left link  21 LC. The protrusion is provided on the same straight line extending to both side surfaces of a rectangular parallelepiped provided on thoracolumbar center link  19 LC. The rectangular parallelepiped in which the protrusion is provided is rotatable around the axis of thoracolumbar center link  19 LC. Center-link left link attaching unit J 7 C has two rotational degrees of freedom including one rotational degree around the axis of thoracolumbar center link  19 LC. Chest center link attaching unit J 5 C, chest right link attaching unit J 6 C, and center-link left link attaching unit J 7 C are the biaxial gimbal. 
     A waist center link attaching unit J 10 C, a waist right link attaching unit J 8 C, and a waist left link attaching unit J 9 C are provided on the upper surface of waist  6 C. Waist center link attaching unit J 10 C, waist right link attaching unit J 8 C and waist left link attaching unit J 9 C are connected rotatably to the other ends of thoracolumbar center link  19 LC, thoracolumbar right link  20 LC, and thoracolumbar left link  21 LC with two rotational degrees of freedom, respectively. Waist center link attaching unit J 10 C, waist right link attaching unit J 8 C and waist left link attaching unit J 9 C, which are the biaxial gimbal, exist at the same height as thoracolumbar joint  18 . Waist center link attaching unit J 10 C has a structure in which the other end of thoracolumbar center link  19 LC is sandwiched rotatably by the yoke provided on waist  6 C. The yoke of waist center link attaching unit J 10 C is provided on the rotation member that is rotated around the rotation axis parallel to the Y-axis extending from waist  6 C to the rear side. Waist right link attaching unit J 8 C has a structure in which the other end of the thoracolumbar right link  20 LC is sandwiched rotatably by the yoke provided on waist  6 C. The yoke of waist right link attaching unit J 8 C is provided on the rotation member that is rotated around the rotation axis being parallel to the X-axis and extending from waist  6 C to the right arm side. Waist left link attaching unit J 9 C has a structure in which the other end of thoracolumbar left link  21 LC is sandwiched rotatably by the yoke provided on waist  6 C. The yoke of waist left link attaching unit J 9 C is provided on the rotation member that is rotated around the horizontal rotation axis extending onto the rear side of waist  6 C. The rotation axis and the X-axis forms the angle of about 25 degrees. 
     Each of thoracolumbar center link  19 LC, thoracolumbar right link  20 LC, and thoracolumbar left link  21 LC is attached to waist  6 C with an attachment interposed therebetween. The attachment is a member that is parallel to the screw rod. Because the attachment is used, each of thoracolumbar center link  19 LC, thoracolumbar right link  20 LC, and thoracolumbar left link  21 LC is attached to waist  6 C at a position having a predetermined distance in a predetermined direction from a straight line through which the screw rod extends. The determined direction is a direction orthogonal to the link in the plane in which there exist the link and the rotation axis around which the yoke of the link attaching unit is rotated. 
     A body bending unit C 2 C is a rotation connecting mechanism that connects chest  5 C rotatably to waist  6 C with three rotational degrees of freedom around thoracolumbar joint  18 . With reference to  FIGS. 124 and 125 , the arrangement of the link and the link attaching unit in body bending unit C 2 C is described.  FIG. 124  is a perspective view illustrating the link arrangement of body bending unit C 2 C included in humanoid upper half body robot  100 C.  FIG. 125  is a view illustrating the link arrangement in the reference state of body bending unit C 2 C when the links are viewed from the direction in which the backbone extends. 
     As can be seen from  FIG. 125 , thoracolumbar center link  19 LC exists right behind backbone  56  at the angle of several degrees or less with backbone  56 . Thoracolumbar right link  20 LC exists on the right side (left side when viewed from the front) of backbone  56 . Thoracolumbar left link  21 LC connects a point existing in the back of backbone  56  from the vicinity of the left side (right side when viewed from the front) end of waist  6 C. On the side of waist  6 C, waist center link attaching unit J 10 C, waist left link attaching unit J 9 C and waist right link attaching unit J 8 C are arranged on the back side of backbone  56  with a sufficient width in the right and left direction and the front-back direction. For this reason, a load of chest  5 C can be dispersed and supported stably by backbone  56 , thoracolumbar center link  19 LC, thoracolumbar right link  20 LC, and thoracolumbar left link  21 LC. In a triangle formed by chest center link attaching unit J 5 C, chest right link attaching unit J 6 C, and backbone upper end  56 B, the angle at a vertex corresponding to backbone upper end  56 B is about 110 degrees. Chest center link attaching unit J 5 C and chest right link attaching unit J 6 C are separated from backbone upper end  56 B by about a radius of waist  6 C. For this reason, chest  5 C can be tilted mainly in the front-back direction when thoracolumbar center link  19 LC is expanded and contracted. Chest  5 C can be tilted mainly in the right and left direction when thoracolumbar right link  20 LC is expanded and contracted. Chest  5 C can be rotated mainly around backbone  56  when thoracolumbar left link  21 LC is expanded and contracted. 
     Referring to  FIG. 126 , line segments and others are defined to express the condition regarding the arrangement of the link attaching unit in the body bending unit.  FIG. 126  is a view illustrating variables to evaluate the link arrangement in the reference state of the body bending unit.  FIG. 126(A)  illustrates the arrangement of the link attaching unit in waist  6 C.  FIG. 126(B)  illustrates the arrangement of the link attaching unit in chest  5 C. The plane determined by waist center link attaching unit J 10 C, waist left link attaching unit J 9 C, and waist right link attaching unit J 8 C is referred to as a waist reference plane.  FIG. 126(A)  illustrates the positional relationship among thoracolumbar joint  18 , waist center link attaching unit J 10 C, waist left link attaching unit J 9 C, and waist right link attaching unit J 8 C on the waist reference plane. An intersection of waist reference plane and backbone  56  is referred to as a first twist center. In body bending unit C 2 C, the first twist center is matched with thoracolumbar joint  18 . When thoracolumbar joint  18  is not located on the waist reference plane, the first twist center becomes a position different from that of thoracolumbar joint  18 . The position of the first twist center is changed slightly by changing the connection angle at thoracolumbar joint  18 . The distance between thoracolumbar joint  18  and the waist reference plane is determined to be equal to or less than an upper limit. 
     The line segment connecting waist center link attaching unit J 10 C and thoracolumbar joint  18  (first twist center) is referred to as a first line segment S 11 . The line segment connecting waist right link attaching unit J 8 C and thoracolumbar joint  18  is referred to as a third line segment S 13 . The line segment connecting waist left link attaching unit J 9 C and thoracolumbar joint  18  is referred to as a second line segment S 12 . The lengths of first line segment S 11 , second line segment S 12 , and third line segment S 13  are represented by variables L 11 , L 12 , and L 13 . The angle formed by first line segment S 11  and third line segment S 13  is represented by a variable η 1 . 
     In body bending unit C 2 C, η 1  is about 90 degrees. That is, first line segment 
     Sl 1  and third line segment S 13  are substantially orthogonal to each other. For this reason, a triangle (first member triangle) formed by waist center link attaching unit J 10 C, waist left link attaching unit J 9 C, and thoracolumbar joint  18  has a sufficient width when viewed from any direction. The load on chest  5 C can be supported by the first member triangle stably. η 1  is not required to be orthogonal (intersect at 90 degrees), but may exist within a first crossing angle range that is determined to include 90 degrees, for example, 60 degrees to 120 degrees. 
     First line segment S 11  exists between second line segment S 12  and third line segment S 13 . Thus, the width of the first member triangle can be made wider as compared with the case where first line segment S 11  does not exist between second line segment S 12  and third line segment S 13 , and the load of chest  5 C can be supported by the first member triangle stably. A value obtained by dividing shorter one of a length L 11  of first line segment S 11  and a length L 13  of third line segment S 13  by longer one is referred to as the long to short ratio. The long to short ratio is represented by a variable λ. λ=about 0.93 is obtained. Thus, the load on chest  5 C can substantially equally be supported by waist left link attaching unit J 9 C and thoracolumbar joint  18 . Long to short ratio λ may be greater than or equal to a predetermined lower limit ratio such as 0.8. 
     An intersection of backbone  56  and the plane that passes chest center link attaching unit J 5 C and is perpendicular to backbone  56  is referred to as a second twist center  56 B. Here, second twist center  56 B is also the backbone upper end  56 B. The plane passing chest center link attaching unit J 5 C, second twist center  56 B, and chest right link attaching unit J 6 C is referred to as a chest reference plane. In humanoid upper half body robot  100 C, the chest reference plane is perpendicular to backbone  56 .  FIG. 126(B)  illustrates the positional relationship among second twist center  56 B, chest center link attaching unit J 5 C, and chest right link attaching unit J 6 C on the chest reference plane. Here, on the chest reference plane, a line segment connecting second twist center  56 B and chest center link attaching unit J 5 C is referred to as a fourth line segment S 14 . The line segment connecting second twist center  56 B and chest right link attaching unit J 6 C is referred to as a fifth line segment S 15 . The angle formed by fourth line segment S 14  and fifth line segment S 15  is represented by a variable η 2 . 
     In body bending unit C 2 C,η 2  is about 119 degrees. In center link left link attaching unit J 7 C, thoracolumbar left link  21 LC is connected at an angle ξ of about 32 degrees with respect to thoracolumbar center link  19 LC. 
     η 2  is about 119 degrees, which exists within a second crossing angle range that is determined to include 90 degrees, for example, 55 degrees to 125 degrees. Thus, the direction in which chest  5 C is tilted by expanding or contracting the link to change one of the positions of chest center link attaching unit J 5 C and chest right link attaching unit J 6 C is sufficiently different from the direction in which chest  5 C is tilted by expanding or contracting the link to change the other of the positions of chest center link attaching unit J 5 C and chest right link attaching unit J 6 C. As a result, chest  5 C can be tilted adequately in any direction. Angle ξ is about 32 degrees, which is greater than or equal to a predetermined third crossing angle such as 20 degrees. For this reason, chest  5 C can be rotated efficiently around backbone  56  by expanding or contracting thoracolumbar left link  21 LC. 
     Body bending unit C 2 C is a rotation connecting mechanism that connects chest  5 C being the second member rotatably to waist  6 C being the first member by thoracolumbar joint  18 . Thoracolumbar joint  18  is a joint that connects chest  5 C rotatably to waist  6 C with three rotational degrees of freedom. Body bending unit C 2 C changes the angle of thoracolumbar joint  18  and moves chest  5 C with respect to waist  6 C. 
     Thoracolumbar center link  19 LC is the first link having five rotational degrees of freedom. Chest center link attaching unit J 5 C is the second-member first attaching unit provided on chest  5 C. The positional relationship with respect to thoracolumbar joint  18  is fixed in chest center link attaching unit J 5 C. One end of thoracolumbar center link  19 LC is attached rotatably to chest center link attaching unit J 5 C with at least two rotational degrees of freedom. Waist center link attaching unit J 10 C is the first-member first attaching unit provided in waist  6 C. The other end of thoracolumbar center link  19 LC is attached rotatably to waist center link attaching unit J 10 C with at least two rotational degrees of freedom. The positional relationship with respect to thoracolumbar joint  18  is fixed in waist center link attaching unit J 10 C. Waist center link attaching unit J 10 C is also the first reference point provided on waist  6 C. Thoracolumbar center link  19 LC itself has one rotational degree of freedom. 
     Motor  19 M is a first power source that generates the force changing the length of the thoracolumbar center link  19 LC. The length of thoracolumbar center link  19 LC is the distance between chest center link attaching unit J 5 C and waist center link attaching unit J 10 C. Thoracolumbar center actuator  19  including thoracolumbar center link  19 LC, chest center link attaching unit J 5 C, waist center link attaching unit J 10 C, and motor  19 M is the first actuator. 
     Thoracolumbar left link  21 LC is the second link having five rotational degrees of freedom. Center-link left link attaching unit J 7 C is the first-link second attaching unit provided on thoracolumbar center link  19 LC. The positional relationship with respect to chest center link attaching unit J 5 C is fixed in center link left link attaching unit J 7 C. One end of thoracolumbar left link  21 LC is attached rotatably to center link left link attaching unit J 7 C with at least two rotational degrees of freedom. Waist left link attaching unit J 9 C is the first-member second attaching unit provided on waist  6 C. The other end of thoracolumbar left link  21 LC is attached rotatably to waist right link attaching unit J 8 C with at least two rotational degrees of freedom. The positional relationship with respect to thoracolumbar joint  18  is fixed in waist left link attaching unit J 9 C. Waist left link attaching unit J 9 C is also the second reference point provided on waist  6 C. Thoracolumbar left link  21 LC itself has one rotational degree of freedom. A motor  21 M is the second power source that generates the force changing the length of thoracolumbar left link  21 LC. The length of thoracolumbar left link  21 L is the distance between center-link left link attaching unit J 7 C and waist left link attaching unit J 9 C. Thoracolumbar left actuator  21  including thoracolumbar left link  21 LC, center-link left link attaching unit J 7 C, waist left link attaching unit J 9 C, and motor  21 M is the second actuator. 
     Thoracolumbar right link  20 LC is the third link having five degrees of freedom. Chest right link attaching unit J 6 C is the second-member third attaching unit provided on chest  5 C. The positional relationship with respect to chest  5 C is fixed in chest right link attaching unit J 6 C. One end of thoracolumbar right link  20 LC is attached rotatably to chest right link attaching unit J 6 C with at least two rotational degrees of freedom. Waist right link attaching unit J 8 C is the first-member third attaching unit provided on waist  6 C. The other end of thoracolumbar right link  20 LC is attached rotatably to waist right link attaching unit J 8 C with at least two rotational degrees of freedom. Thoracolumbar right link  20 LC itself has one rotational degree of freedom. A motor  20 M is the second power source that generates the force changing the length of thoracolumbar right link  20 LC. The length of thoracolumbar right link  20 LC is the distance between chest right link attaching unit J 6 C and waist right link attaching unit J 8 C. Thoracolumbar right actuator  20  including thoracolumbar right link  20 LC, chest right link attaching unit J 6 C, waist right link attaching unit J 8 C, and motor  20 M is a third actuator. 
     The waist reference plane is a first-member reference plane that is a plane passing the first-member first attaching unit, the first-member second attaching unit, and the first-member third attaching unit. The first twist center is the intersection of the first-member reference plane and the torsion axis. The first line segment is a line segment connecting the first twist center and the first-member first attaching unit. The second line segment is a line segment connecting the first twist center and the first-member second attaching unit. The third line segment is a line segment connecting the first twist center and the first-member third attaching unit. 
     In the second member, which has the fixed angle with the torsion axis like chest  5 C, the intersection of the torsion axis and the plane that passes the second-member first attaching unit and is perpendicular to the torsion axis is referred to as the second twist center. The plane passing the second twist center, the second-member first attaching unit, and the second-member second attaching unit is referred to as a second-member reference plane. In chest  5 C, the chest reference plane is the second-member reference plane. On the second-member reference plane, the line segment connecting the second twist center and the second-member first attaching unit is the fourth line segment. The fifth line segment is a line segment connecting the second twist center and the second-member first attaching unit. 
     Thoracolumbar center link  19 LC, thoracolumbar right link  20 LC, and thoracolumbar left link  21 LC may not have one rotational degree of freedom around the axis, and the link attaching unit provided on chest  5 C or waist  6 C may have three rotational degrees of freedom. 
     The structure of shoulder C 4 C is basically the same as that of shoulder C 4 . Chest-side main link attaching unit J 1  has the substantially same height as upper arm main link attaching unit J 20 . Chest-side auxiliary link attaching unit J 2  is located lower than chest-side main link attaching unit J 1 , namely, closer to waist  6 C. Upper arm drive auxiliary link  15 L extends obliquely upward. Upper arm drive auxiliary link  15 L is connected to upper arm drive main link  14 L from obliquely below by upper arm drive main-link-side auxiliary link attaching unit J 21 . When upper arm  7 C is moved up and down, upper arm drive auxiliary link  15 L expands or contracts mainly. When upper arm  7 C is moved in the right and left direction, upper arm drive main link  14 L expands or contracts mainly. Because upper arm drive auxiliary link  15 L is connected to upper arm drive main link  14 L from obliquely below, upper arm drive auxiliary actuator  15  generates the force necessary for raising upper arm  7 C easily. Chest-side auxiliary link attaching unit J 2  is disposed at a position lower than chest-side main link attaching unit J 1 . That is, upper arm driving auxiliary link  15 L supports upper arm  7 C so that it pushes up upper arm  7 C from below with upper arm drive main link  14 L interposed therebetween. Consequently, humanoid upper half body robot  100 C can hold the vertical position of upper limb  3 C including upper arm  7 C more stably. 
     Referring to  FIGS. 134 to 137 , the structure of elbow C 5 C is described.  FIGS. 134, 135, and 136  are a perspective view, a front view, and a side view illustrating elbow C 5 C included in humanoid upper half body robot  100 C.  FIG. 137  is a perspective view illustrating the link arrangement of elbow C 5 C. 
     Humerus  7 B is fitted in humerus mounting unit  7 H provided on the upper surface of humerus inside frame  34 F. An elbow tip  8 D connected to forearm  8 C is provided in elbow drive inside link attaching unit J 24 . Elbow tip  8 D is mounted in an elbow mounting hole  8 H (illustrated in  FIG. 138 ) of forearm  8 C. An elbow joint tip  31 D is provided on the base side in the yoke of elbow joint  31 . Elbow joint tip  31 D is mounted in an elbow joint connecting hole  8 J (illustrated in  FIG. 138 ) of forearm  8 C. 
     The structure of elbow C 5 C is basically the same as elbow C 5 . The points in which elbow C 5 C differs from elbow C 5  are described. An upper arm outside actuator  34 P does not include nut  34 B, rail  34 C, and gripper  34 D that engages with rail  34 C. Instead of them, upper arm outside actuator  34 P includes a spline shaft  34 E and a nut  34 J. Nut  34 J is a perforated member including a guide hole through which spline shaft  34 E passes and a drive shaft hole (through-hole) through which screw rod  34 A passes. The guide hole is made so as to penetrate nut  34 J. Screw rod  34 A and spline shaft  34 E are parallel to each other. Because spline shaft  34 E and screw rod  34 A pass through nut  34 J, nut  34 J is not rotated when screw rod  34 A is rotated. Spline shaft  34 E is a guide shaft, which passes through the guide hole and is provided in parallel with screw rod  34 A. The guide hole and spline shaft  34 E constitute the second rotation preventing unit to prevent nut  34 J from rotating. Upper arm outside link attaching unit J 22  is provided in a portion sandwiched by the guide hole and the drive shaft hole of nut  34 J. 
     A female screw that meshes with a male screw provided on an outer surface of screw rod  34 A is provided on an inner surface of the drive shaft hole. When motor  34 M rotates, the rotation is transmitted to screw rod  34 A by a timing belt. When screw rod  34 A is rotated, nut  34 J is moved along screw rod  34 A and spline shaft  34 E because nut  34 J cannot be rotated . 
     Spline shaft  34 E is a metal cylinder having a smooth surface. A bearing or the like is provided on the inner surface of the guide hole to decrease friction with spline shaft  34 E. 
     An upper arm outside linear guide  34 GC includes screw rod  34 A, spline shaft  34 E, nut  34 J, and upper arm outside frame  34 F. Upper arm outside frame  34 F contains screw rod  34 A, spline shaft  34 E, and nut  34 J. A point where a straight line passing through screw rod  34 A intersects with a portion closest to the shoulder in upper arm outside frame  34 F is defined as a second reference point P 2N . The second reference point P 2N  is illustrated in  FIG. 135 . Upper arm outside linear guide  34 GC constitutes the second guide that guides nut  34 J to be moved along screw rod  34 A. Upper arm outside linear guide  34 GC is provided in upper arm  7 C so that it has a fixed positional relationship with respect to elbow joint  31  and second reference point P 2N . 
     Similarly to upper arm outside actuator  34 P, an upper arm inside actuator  35 P includes a spline shaft  35 E and a nut  35 J. The guide hole made in nut  35 J and spline shaft  35 E constitute the first rotation preventing unit to prevent nut  35 J from rotating. An upper arm inside linear guide  35 GC has the same structure as upper arm outside linear guide  34 GC. Upper arm inside linear guide  35 GC includes a screw rod  35 A, spline shaft  35 E, nut  35 J, and upper arm inside frame  35 F. Upper arm outside frame  35 F contains screw rod  35 A, spline shaft  35 E, and nut  35 J. A point where a straight line passing through screw rod  35 A intersects with a portion closest to the shoulder in upper arm inside frame  35 F is defined as a first reference point P 1N . First reference point P 1N  is illustrated in  FIG. 135 . Upper arm inside link attaching unit J 23  is provided in a portion between the guide hole and the drive shaft hole of nut  34 J. Upper arm inside linear guide  35 GC constitutes the first guide portion that guides nut  35 J to be moved along screw rod  35 A. Upper arm inside linear guide  35 GC is provided in upper arm  7 C so that it has a fixed positional relationship with respect to elbow joint  31  and first reference point P 1N  fixed. 
     Screw rod  34 A and spline shaft  34 E pass through nut  34 J, so that the force acting on nut  34 J can be distributed and received by the two rods. The same holds true for nut  35 J. 
     The elbow joint may have three rotational degrees of freedom. When the elbow joint has three rotational degrees of freedom, the upper arm and the forearm are connected to each other by a variable length link (third link) being the third link. The variable length link has five rotational degrees of freedom, is attached rotatably to the upper arm with at least two rotational degrees of freedom, and is attached rotatably to the forearm with at least two rotational degrees of freedom. The variable length link being the third link may use a screw mechanism or a hydraulic mechanism. The third link may use a linear actuator that moves the other end of the link. 
     Referring to  FIGS. 138 to 144 , the structure of a wrist C 6 C is described.  FIG. 138  is a perspective view illustrating wrist C 6 C included in humanoid upper half body robot  100 C.  FIG. 139  is another perspective view of wrist C 6 C.  FIG. 140  is a front view of wrist C 6 C.  FIG. 141  is a right side view of wrist C 6 C.  FIG. 142  is a perspective view illustrating the link arrangement of wrist C 6 C.  FIG. 143  is a view illustrating the link arrangement of wrist C 6 C in the reference state when the link arrangement is viewed from the direction in which the forearm extends.  FIG. 144  is a view illustrating variables evaluating the link arrangement of wrist C 6 C in the reference state. 
     Wrist C 6 C is different from wrist C 6  in that a forearm outside link  38 LC is attached not to a wrist plate  91 C but in a middle of a forearm front link  37 LC. One end of forearm front link  37 LC is attached to wrist plate  91 C by a hand-side front link attaching unit J 29 C. The other end of forearm front link  37 LC is attached to forearm  8 C by a forearm front link attaching unit J 26 C. One end of a forearm outside link  38 LC is attached to forearm front link  37 LC by a front-link-side outside link attaching unit J 30 C. The other end of forearm outside link  38 LC is attached to forearm  8 C by a forearm outside link attaching unit J 27 C. One end of a forearm inside link  39 LC is attached to wrist plate  91 C by a hand-side inside link attaching unit J 31 C. The other end of forearm inside link  39 LC is attached to forearm  8 C by a forearm outside link attaching unit J 27 C. 
     As illustrated in  FIG. 143 , wrist plate  91 C has an octagonal plate shape which is shaped by cutting corners of a substantially square shape so that one corner is cut largely, and the remaining three corners are cut small into a similar shape. In wrist plate  91 C, wrist joint  36 , hand-side front link attaching unit J 29 C, and hand-side inside link attaching unit J 31 C are arranged so that they form an isosceles right triangle. In the isosceles right triangle, the distance from an octagonal side of wrist plate  91 C is almost the same on each side. The angle of wrist plate  91 C with forearm bone  8 B, which is the torsion axis, can be changed. 
     Wrist joint  36  is a spherical bearing. Wrist joint  36  has three rotational degrees of freedom. In wrist plate  91 C, two protrusions are provided on the surface on which wrist joint  36  is provided. The two protrusions have substantially the same distance from wrist joint  36 . Two line segments connecting each of the two protrusions and wrist joint  36  are substantially orthogonal to each other in wrist joint  36 . The rotation member and the yoke that is rotated together with the rotation member are provided in each of the two protrusions. The rotation member is rotated around the rotation axis being parallel to wrist plate  91 C and being directed in the direction toward wrist joint  36 . One of the yokes constitutes hand-side front link attaching unit J 29 C. The other yoke constitutes hand-side inside link attaching unit J 31 C. The yoke included in hand-side front link attaching unit J 29 C sandwiches and holds the shaft member passing through a through-hole made at the other end of forearm front link  37 LC. The yoke included in hand-side inside link attaching unit J 31 C sandwiches and holds the shaft member passing through a through-hole made at the other end of forearm inside link  39 LC. In front-link-side outside link attaching unit J 30 C, the yoke is provided at one end of forearm outside link  38 LC. Forearm front link  37 LC is equipped with a member rotatable around the axis that is the extending direction of forearm front link  37 LC. The yoke included in front-link-side outside link attaching unit J 30 C sandwiches and holds rotatably the protrusion protruding from the rotatable member. Front-link-side outside link attaching unit J 30 C has two rotational degrees of freedom including one rotational degree of rotation around the axis provided on forearm front link  37 LC. 
     Forearm front link attaching unit J 26 C, forearm outside link attaching unit J 27 C, and forearm inside link attaching unit J 28 C are provided in portions of forearm  8 C that protrude in three directions. The portions protruding in the three directions are provided at positions of the same length from wrist joint  36 . Each of forearm front link attaching unit J 26 C, forearm outside link attaching unit J 27 C, and forearm inside link attaching unit J 28 C includes the yoke that is rotated around the rotation axis extending from the protruding portion to the outside perpendicular to forearm  8 C. Forearm front link attaching unit J 26 C has a structure in which the yoke sandwiches and holds the shaft member passing through a through-hole made at one end of forearm front link  37 LC. Forearm outside link attaching unit J 27 C and forearm inside link attaching unit J 28 C have the same structure. In forearm front link attaching unit  26 C, forearm outside link attaching unit J 27 C, and forearm inside link attaching unit J 28 C, the directions in which the rotation axis of the yoke faces are the directions that are set to have at equal intervals of about 70 degrees. The rotation axis of forearm front link attaching unit  26 C is disposed at the center. 
     With reference to  FIG. 144 , a line segment or the like is defined in order to express the condition regarding the arrangement of the link attaching unit in the wrist.  FIG. 144  is a view illustrating variables used for evaluating the link arrangement of the wrist in the reference state.  FIG. 144(A)  illustrates the arrangement of the link attaching unit in upper arm  8 C.  FIG. 144(B)  illustrates the arrangement of the link attaching unit on the side of wrist joint  36 . A plane determined by forearm front link attaching unit J 26 C, forearm outside link attaching unit J 27 C, and forearm inside link attaching unit J 28 C is referred to as a forearm reference plane.  FIG. 144(A)  illustrates the positional relationship among forearm bone  8 B, waist forearm front link attaching unit J 26 C, forearm outside link attaching unit J 27 C, and forearm inside link attaching unit J 28 C on the forearm reference plane. The intersection of the forearm reference plane and forearm bone  8 B is referred to as the first twist center. A sign of first twist center is set to  8 B that is the same as forearm bone. The direction of forearm bone  8 B being the torsion axis is fixed to forearm  8  being the first member. For this reason, when the connection angle of wrist joint  36  is changed, the position of the first twist center is not changed. 
     The line segment connecting forearm front link attaching unit J 26 C and first twist center  8 B is referred to as a first line segment S 21 . The line segment connecting forearm outside link attaching unit J 27 C and first twist center  8 B is referred to as a third line segment S 23 . The line segment connecting forearm inside link attaching unit J 28 C and first twist center  8 B is referred to as a second line segment S 22 . The lengths of first line segment S 21 , second line segment S 22 , and third line segment S 23  are represented by variables L 21 , L 22 , and L 23 . The angle formed by first line segment S 21  and third line segment S 23  is represented by a variable η 1A . 
     In wrist C 6 C, η 1A  is about 90 degrees. That is, first line segment S 21  and third line segment S 23  are substantially orthogonal to each other. That is, η 1A  is the angle within the first crossing angle range that is set to, for example, 60 degrees to 120 degrees. First line segment S 21  exists between second line segment S 22  and third line segment S 23 . Long to short ratio λ, which is a value obtained by dividing shorter one of L 21  and L 23  by longer one, is λ=0.99. Long to short ratio λ is greater than or equal to the lower limit ratio determined to be, for example, 0.8. Similarly to body bending unit C 2 C, in wrist C 6 C, the load on hand  9 C can be supported stably by the link attaching units at three places of forearm  8 C. 
     The plane passing wrist joint  36 , hand-side front link attaching unit J 29 C, and hand-side inside link attaching unit J 31 C is referred to as a wrist reference plane. The wrist reference plane is the second-member reference plane.  FIG. 144(B)  illustrates the positional relationship among wrist joint  36 , hand-side front link attaching unit J 29 C, and hand-side inside link attaching unit J 31 C on the wrist reference plane. The line segment connecting wrist joint  36  and hand-side front link attaching unit J 29 C is referred to as a fourth line segment S 24 . The line segment connecting wrist joint  36  and hand-side inside link attaching unit J 31 C is referred to as a fifth line segment S 25 . The angle formed by fourth line segment S 24  and fifth line segment S 25  is represented by a variable η 2A . 
     In wrist C 6 C, η 2A  is about 92 degrees. η 2A  is the angle within the second crossing angle range that is set to, for example 55 degrees to 125 degrees. Similarly to body bending unit C 2 C, in wrist C 6 C, hand  9 C can also be tilted adequately in any direction. An angle ζ A  formed by forearm front link  37 LC and forearm outside link  38 LC holds ζ A =about 26 degrees in front-link-side outside link attaching unit J 30 C. Angle ζ A  is greater than or equal to the determined third crossing angle such as 20 degrees. For this reason, hand  9 C can be rotated efficiently around forearm bone  8 B. 
     Wrist C 6 C is a rotation connecting mechanism that connects hand  9 C being the second member rotatably to forearm  8 C being the first member by wrist joint  36 . Wrist joint  36  is a joint, which allows hand  9 C to be rotated with respect to forearm  8 C around the torsion axis in which the direction with respect to forearm  8 C is fixed and connects hand  9 C rotatably to forearm  8 C with three rotational degrees of freedom. 
     Forearm front link  37 LC is the first link having five rotational degrees of freedom. Forearm front link attaching unit J 26 C is the first-member first attaching unit provided in forearm  8 C. The positional relationship with respect to wrist joint  36  is fixed in forearm front link attaching unit J 26 C. Forearm front link attaching unit J 26 C is also the first reference point provided in forearm  8 C. The other end of forearm front link  37 LC is attached rotatably to forearm front link attaching unit J 26 C with at least two rotational degrees of freedom. Hand-side front link attaching unit J 29 C is the second-member first attaching unit provided in hand  9 C. One end of forearm front link  37 LC is attached rotatably to hand-side front link attaching unit J 29 C with at least two rotational degrees of freedom. The positional relationship with respect to wrist joint  36  is fixed in hand-side front link attaching unit J 29 C. Forearm front link  37 LC itself has one rotational degree of freedom. Motor  37 M is the first power source that generates the force changing the length of forearm front link  37 LC. The length of forearm front link  37 LC is the distance between forearm front link attaching unit J 26 C and hand-side front link attaching unit J 29 C. Forearm front actuator  37  including forearm front link  37 LC, forearm front link attaching unit J 26 C, hand-side front link attaching unit J 29 C, and motor  37 M is the first actuator. 
     Forearm outside link  38 LC is the second link having five rotational degrees of freedom. Forearm outside link attaching unit J 27 C is the first-member second attaching unit provided in forearm  8 C. The positional relationship with respect to wrist joint  36  is fixed in forearm outside link attaching unit J 27 C. Forearm outside link attaching unit J 27 C is also the second reference point provided in forearm  8 C. The other end of forearm outside link  38 LC is attached rotatably to forearm outside link attaching unit J 27 C with at least two rotational degrees of freedom. Hand-side outside link attaching unit J 30 C is the first-link second attaching unit provided in forearm front link  37 LC. The positional relationship with respect to hand-side front link attaching unit J 29 C is fixed in hand-side outside link attaching unit J 30 C. One end of forearm outside link  38 LC is attached rotatably to the hand-side outside link attaching unit J 30 C with at least two rotational degrees of freedom. Forearm outside link  38 LC itself has one rotational degree of freedom. A motor  38 M is the second power source that generates the force changing the length of forearm outside link  38 LC. The length of forearm outside link  38 LC is the distance between forearm outside link attaching unit J 27 C and hand-side outside link attaching unit J 30 C. Forearm outer actuator  38  including forearm outside link  38 LC, forearm outside link attaching unit J 27 C, hand-side outside link attaching unit J 30 C, and motor  38 M is the second actuator. 
     Forearm inside link  39 LC is the third link having five rotational degrees of freedom. Forearm inside link attaching unit J 28 C is the first-member third attaching unit provided in forearm  8 C. The positional relationship with respect to wrist joint  36  is fixed in forearm inside link attaching unit J 28 C. The other end of forearm inside link  39 LC is attached rotatably to forearm inside link attaching unit J 28 C with at least two rotational degrees of freedom. Hand-side inside link attaching unit J 31 C is the second-member third attaching unit provided in hand  9 C. The positional relationship with respect to wrist joint  36  is fixed in hand-side inside link attaching unit J 31 C. One end of forearm inside link  39 LC is attached rotatably to hand-side inside link attaching unit J 31 C with at least two rotational degrees of freedom. Forearm inside link  39 LC itself has one rotational degree of freedom. A motor  39 M is the third power source that generates the force changing the length of forearm inside link  39 LC. The length of forearm inside link  39 LC is the distance between forearm inside link attaching unit J 28 C and hand-side inside link attaching unit J 31 C. Forearm outer actuator  38  including forearm inside link  39 LC, forearm inside link mount J 28 C, hand-side inside link mount J 31 C, and motor  39 M is the third actuator. 
     The forearm reference plane is the first member reference plane. Hand  9 C is the second member, which has the changeable angle with forearm bone  8 B being the torsion axis. The hand reference plane is the second-member reference plane passing the second-member first attaching unit, the second-member third attaching unit, and the joint. On the second-member reference plane, the line segment connecting the joint and the second-member first attaching unit is the fourth line segment. The line segment connecting the joint and the second-member third attaching unit is the fifth line segment. When the direction of the torsion axis is fixed with respect to the second member, the fourth line segment and the fifth line segment are defined using the second twist center, instead of the joint. The second twist center is the intersection of the torsion axis and the plane being perpendicular to the torsion axis and passing the second-member first attaching unit. That is, the line segment connecting the second twist center and the second-member first attaching unit is the fourth line segment. The line segment connecting the second twist center and the second-member third attaching unit is the fifth line segment. 
     Referring to  FIGS. 145 to 152 , the structure of hand  9 C is described.  FIG. 145  is a view illustrating hand  9 C including the wrist viewing from the backside of the hand.  FIG. 146  is a side view illustrating hand  9 C including the wrist when hand  9 C is viewed from the side.  FIGS. 147 to 149  are views illustrating hand  9 C viewed from the back side of the hand, the palm side, and the side surface, respectively.  FIGS. 150 and 151  are perspective views illustrating the finger base of hand  9 C that rotates a two-way rotation finger around the axis of the finger base.  FIGS. 150 and 151  illustrate a state in which a finger base  80  is separated from palm plate  82 .  FIG. 151  is a perspective view illustrating finger base  80  viewed from the side of first finger  83 .  FIG. 152  is a perspective view illustrating finger base  80  viewed from the side of palm plate  82 . 
     In hand  9 C, first finger  83 , second finger  84 , third finger  85 , and fourth finger  86  are the same as hand  9 B of the fourth embodiment. Hand  9 C includes a two-way rotation finger  89  instead of hand breadth rotation finger  88  corresponding to the thumb of hand  9 B. The portion including from fingertip to a first finger joint  89 D provided in two-way rotation finger  89  is the same as the portion including from fingertip to first finger joint  88 D provided in hand breadth rotation finger  88 . Two-way rotation finger  89  includes finger base  80  that rotates the portion of the fingertip side including first finger joint  89 D and that is provided between first finger joint  89 D and palm plate  82 . 
     Finger base  80  includes a finger base dactylus  80 A, a finger base motor fixer  80 B, a finger-base finger joint  80 C, a finger base motor  80 D, a finger base gear head  80 E, a finger base worm  80 F, and a finger base worm wheel  80 G. Finger base dactylus  80 A extends in the direction being substantially parallel to palm plate  82  and being substantially orthogonal to the direction in which first finger  83  extends. Finger base motor fixer  80 B having a space inside thereof is fixed to palm plate  82 . Finger base dactylus  80 A is connected to the side surface of finger base motor fixer  80 B. A first dactylus  89 A is connected rotatably to finger base dactylus  80 A by first finger joint  89 D. 
     Finger-base finger joint  80 C has a rotation axis Rx 3  directed in the direction in which the finger base dactylus  80 A extends. Finger base motor  80 D and finger base gear head  80 E are fixed to the outer surface of finger base motor fixer  80 B so as to be orthogonal to palm plate  82 . Finger base worm  80 F is connected to the rotation shaft driven by finger base motor  80 D. Finger base worm  80 F and finger base worm wheel  80 G, in which teeth mesh with each other, exist inside finger base motor fixer  80 B. Rotation axis Rx 3  connected to finger base worm wheel  80 G is connected to finger base dactylus  80 A through a through-hole made in a wall of finger base motor fixer  80 B. When finger base motor  80 D rotates, the finger base dactylus  80 A is rotated around the rotation axis Rx 3 . That is, finger-base finger joint  80 C rotates finger base dactylus  80 A with respect to finger base motor fixer  80 B and palm plate  82  by the worm gear mechanism having rotation axis Rx 3 . Finger-base finger joint  80 C can generate the large force because the worm gear mechanism is used. Furthermore, the rotation angle around rotation axis Rx 3  can be maintained when power supply is cut off. 
     Rotation axis Rx 3  is a finger base rotation axis being the rotation axis extending in the direction having a predetermined angle with respect to first dactylus  89 A. The direction having the determined angle is a direction in which first dactylus  89 A forms an angle of about 30 degrees with respect to rotation axis Rx 3  parallel to the Y-axis. Finger base  80  rotates finger base dactylus  80 A around rotation axis Rx 3 . 
     Two projections  80 AA and  80 AB are provided in finger base dactylus  80 A. A protrusion  80 BA is provided in finger base motor fixer  80 B. Protrusion  80 BA exists between protrusions  80 AA and  80 AB that are rotated around rotation axis Rx 3  together with finger base dactylus  80 A. Protrusion  80 BA and protrusions  80 AA and  80 AB restrict the range in which finger base dactylus  80 A can be rotated around rotation axis Rx 3 . 
     Finger base dactylus  80 A is connected to a first motor fixer  89 V such that first motor fixer  89 VB faces to the palm side of the hand with respect to palm plate  82 . First motor fixer  89 V is connected to finger base dactylus  80 A while inclined onto the palm side of the hand. First motor fixer  89 V is a plate member bent in an L-shape when viewed from the side. Finger base dactylus  80 A is obliquely connected to first motor fixer  89 V on one surface of the L-shape. A finger base yoke  89 G is connected to the inside of the two surface constituting the L-shape of first motor fixer  89 V. A first worm wheel  89 K, a first wheel linked part  89 AA, and a first worm  89 J, which are rotated in conjunction with the rotation shaft of first finger joint  89 D, exist in finger base yoke  89 G. A finger first motor  89 H and a first gear head  89 T are fixed to the other surface of the L-shape of first motor fixer  89 V. A rotation axis Rz 3  of first finger joint  89 D is perpendicular to finger base yoke  89 G and rotation axis Rx 3 . A worm tip holder  89 VB is attached to finger base yoke  89 G as a surface facing the surface to which finger first motor  89 H and first gear head  89 T are fixed. A hole into which the tip of first worm  89 J is inserted is made in worm tip holder  89 VB. 
     First worm  89 J is connected to the rotation shaft of finger first motor  89 H at the position surrounded by finger base yoke  89 G and first motor fixer  89 V. The teeth of first worm  89 J mesh with the teeth of first worm wheel  89 K. When finger first motor  89 H rotates, first worm  89 J and first worm wheel  89 K are rotated to change the angle between first wheel linked part  89 AA and finger base yoke  89 G. Thus, first dactylus  89 A can be bent and extended by first finger joint  89 D. 
     Two-way rotation finger  89  can be rotated in two directions around rotation axis Rx 3  and rotation axis Rz 3  that are orthogonal to each other. When rotating around rotation axis Rz 3 , two-way rotating finger  89  is rotated in the direction in which the fingertip is moved away from palm plate  82 . When rotating around rotation axis Rx 3 , two-way rotating finger  89  can be rotated from the direction being parallel with first finger  83  to the direction orthogonal to palm plate  82 . 
     Two-way rotation finger  89  is rotated in two directions, so that hand  9 C can bend five fingers adequately according to the shape of the object to hold the object adequately. For the large object, two-way rotation finger  89  can be moved to the position being parallel with first finger  83 , and the object can be placed on palm plate  82  and five fingers. Hand  9 C including two-way rotation finger  89  performs finger drive equivalent to that of a human, and has an effect that can perform various and advanced work using hands. At least two fingers may be used as the two-way rotation finger including the finger base. 
     The operation is described. The posture of humanoid upper half body robot  100 C is determined by the angles taken by thoracolumbar joint  18 , shoulder joint  13 , elbow joint  31 , wrist joint  36 , and knee joint  40 . The angles of these joints are determined by the lengths of the links that drive the joints. The link that drives each joint of humanoid upper half body robot  100 C is set to a value determined from a designated angle that is the angle of each joint that allow to take the designated posture. Consequently, humanoid upper half body robot  100 C can take the designated posture. When humanoid upper half body robot  100 C is moved, a time series of the designated angle corresponding to a change in the posture is converted into a time series of the link length, and the link length is changed according to the determined time series, which allow humanoid upper half body robot  100 C to be moved as designated. 
     How to determine the length of the variable length link such that the joint can take a designated angle, and how to determine the position of the link attaching unit in the linear guide are described for each joint. The designated angle is required to be within the movable range of the joint. First, thoracolumbar joint  18  is described. Thoracolumbar joint  18  changes the direction in which chest  5 C is connected to waist  6 C. 
     The positions of the joint and the link attaching units in thoracolumbar joint  18  are expressed by the following variables.  FIG. 153  is a view illustrating the variables expressing the positions of the joint and the link attaching units in the thoracolumbar joint. 
     The variable representing the position of each point is defined as follows. 
     P 0s : position of thoracolumbar joint  18 . 
     P 1s : position of waist-side center link attaching unit J 10 C. 
     P 2s : position of waist-side right link attaching unit J 8 C. 
     P 3s : position of waist-side left link attaching unit J 9 C. 
     P 4s : position of chest-side center link attaching unit JSC. 
     P 4s0 : position of chest-side center link attaching unit J 5  in reference state. 
     P 5s : position of chest-side right link attaching unit J 6 C. 
     P 5s0 : position of chest-side right link attaching unit J 6 C in reference state. 
     P 6sA : position of center-link left link attaching unit J 7 C. 
     P 10s : position of intersection of thoracolumbar center link  19 LC and plane, which passes waist-side center link attaching unit J 10 C and is perpendicular to thoracolumbar center link  19 LC. 
     P 11s : position of intersection of thoracolumbar left link  21 LC and plane, which passes waist-side left link attaching unit J 9 C and is perpendicular to thoracolumbar left link  21 LC. 
     P 12s : position of intersection of thoracolumbar right link  20 LC and plane, which passes waist-side right link attaching unit J 8 C and is perpendicular to thoracolumbar right link  20 LC. 
     The rotation angle of the thoracolumbar joint  18  is expressed by the following variables as in the case of the first embodiment. 
     α s : rotation angle around X-axis of thoracolumbar joint  18 . α s =0 in reference state 
     β s : rotation angle around Y-axis of thoracolumbar joint  18 . β s =0 in reference state 
     γ s : rotation angle around Z-axis of thoracolumbar joint  18 . γ s =0 in reference state 
     [Rs]: rotation matrix of thoracolumbar joint  18 . The rotation matrix [R 2 ] is given as follows. 
     
       
         
           
             
               
                 
                   
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     The lengths of the links are expressed by the following variables. 
     L 1s : length of thoracolumbar center link  19 LC. Length of line segment P 10s P 4S . 
     L 1sd : length of line segment P 1s P 4s . 
     L 2s : length of thoracolumbar right link  20 LC. Length of line segment P 11s P 5s . 
     L 2sd : length of line segment P 2s P 5s . 
     L 3s : length of thoracolumbar left link  21 LC. Length of line segment P 12s P 6sA . 
     L 3sd : length of line segment P 3s P 6sA . 
     Hd: distance between the link attaching unit and the screw rod, which are provided in waist  6 C in thoracolumbar center link  19 LC, thoracolumbar right link  20 LC, and thoracolumbar left link  21 LC. 
     A procedure for calculating each point and the length of each link is described. The positions of points P 0s , P 1s , P 2s , P 3s  are fixed. [Rs] is determined when the angle of thoracolumbar joint  18  is determined. The positions of points P 4s , P 5s  are determined as follows. 
         P   4s =[ Rs ]* P   4s0    
         P   5s =[ Rs ]* P   5s0    
     L 1sd , L 2sd  are also determined when the positions of points P 4s , P 5s  are determined. 
     The position of point P 10s  is determined from the positions of points P 1s , P 4s . A plane including point P 1s  and the rotation axis around which the yoke of the waist-side center link attaching unit J 10 C is rotated is referred to as a first link plane. Point P 10s  exists on the first link plane. Based on the Pythagorean theorem, L 1s  is determined as follows. 
         L   1s =√( L   1sd   2   −Hd   2 )
 
     The position of point P 10s  is the point having the distance of Hd from point P 1s  and the distance of L 1s  from point P 4s  on the first link plane. 
     When the position of point P 10s  is determined, the position of point P 6sA  is determined. The position of point P 6sA  is the position at the predetermined distance from point P 4s  on a straight line passing points P 4s , P 10s . L 3sd  is also determined when the position of point P 6sA  is determined. 
     The position of point P 12s  is determined from the positions of points P 3s , P 6sA . 
     A plane including point P 3s  and the rotation axis around which the yoke of waist right link attaching unit J 8 C is rotated is referred to as a second link plane. Point P 12s  exists on the second link plane. Based on the Pythagorean theorem, L 3s  is determined as follows. 
         L   3s =√( L   3sd   2   −Hd   2 )
 
     The position of point P 12s  is the position having the distance of Hd from point P 3s  and the distance of L 3s  from point P 6sA  on the second link plane. 
     The position of point P 11s  is determined from the positions of points P 2s , P 5s . A plane including point P 2s  and the rotation axis around which the yoke of waist left link attaching unit J 9 C is rotated is referred to as a third link plane. Point P 11s  exists on the third link plane. Based on the Pythagorean theorem, L 2s  is determined as follows. 
         L   2s =√( L   2sd   2   −Hd   2 )
 
     The position of point P 12s  is the point of the distance of Hd from point P 2s  and the distance of L 2s  from point P 5s  on the third link plane. In this way, the positions of all the link attaching units and the length of each link can be determined. 
     When the length of each link is determined, how to determine the rotation angle of thoracolumbar joint  18  is studied. In body bending unit C 2 C, an influence of the change in the link length on the rotation angle of thoracolumbar joint  18  is considered easily as compared with body bending unit C 2 . 
       FIG. 154  is a view illustrating a point where the position is fixed by determining the link length in body bending unit C 2 C included in humanoid upper half body robot  100 C.  FIG. 154(A)  illustrates a state in which the lengths of the three links are not determined.  FIG. 154(B)  illustrates a state in which the lengths of thoracolumbar center link  19 LC being the first link and thoracolumbar left link  21 LC being the second link are determined.  FIG. 154(C)  illustrates a state in which the lengths of the three links are determined. In  FIG. 154 , the link having the determined length is expressed by a thick solid line, and the link of which length is not determined is expressed by a thin dotted line. A point with the position that is determined is expressed by a double circle, and a point with the position that is not determined is expressed by a white circle. The point representing thoracolumbar joint  18  being the joint is expressed by a double circle when the rotation angle of thoracolumbar joint  18  is determined. 
     As illustrated in  FIG. 154(A) , the rotation angle of thoracolumbar joint  18  and the position of the point existing in chest  5 C being the second member are not determined in the state in which the lengths of the three variable-length links are not determined. When the lengths of first link  19 LC and second link  21 LC are determined, the distance of point P 4s  from points P 0S , P 1S , P 3S  is determined. As a result, as illustrated in  FIG. 154(B) , the position of point P 4S  is determined uniquely. The fact that the position of point P 4S  is determined means that the rotation angle around the backbone  56  being the torsion axis of chest  5 C and the tilt angle of backbone  56  in the direction toward waist-side center link attaching unit J 10 C being the second-member first attaching unit are determined. 
     In the state of  FIG. 154(B) , thoracolumbar joint  18  can be rotated around a rotation axis R 11  passing points P 0S , P 4S . For this reason, point P 5S  is rotated around rotation axis R 11  while the distance from point P 0S  and the distance from point P 4S  are kept unchanged. Rotation axis R 11  connecting point P 0S  (joint) and point P 4S  (second-member first attaching unit) is referred to as a first attaching unit direction axis. In  FIG. 154(B) , rotation axis R 11  is illustrated as existing on an XZ-plane. However, rotation axis R 11  does not necessarily exist on the XZ-plane. When the position of point P 4S  determined by the lengths of first link  19 LC and second link  21 LC does not exist on the XZ-plane, rotation axis R 11  is in the direction intersecting the XZ-plane. 
     Furthermore, when the length of third link  20 LC is determined, point P 5S  and the rotation angle of thoracolumbar joint  18  are determined. Thus, the state shown in  FIG. 154(C)  is obtained. 
     In the rotation connecting mechanism of the present disclosure including the joint having three rotational degrees of freedom, the rotation angle around the torsion axis and the tilt angle (referred to as a first attaching unit tilt angle) of the torsion axis within the plane (referred to as a first attaching unit existing plane) including the torsion axis and the second-member first attaching unit can be determined by determining the lengths of the first link and the second link. The rotation axis orthogonal to the first attaching unit existing plane is referred to as a first attaching unit tilt axis. The first attaching unit tilt angle is a rotation angle around the first attaching unit tilt axis. 
     In the state where the lengths of the first link and the second link are determined, the joint can be rotated around the first attaching unit direction axis by changing the length of the third link. 
     When the length of thoracolumbar right link  20 LC being the third link is determined, the state shown in  FIG. 154(C)  is obtained. Point P 5S  is also determined by the distance from point P 2S  in addition to distances from points P 0S , P 4S . Because the distance from the three points is determined, the position of point P 5S  is determined uniquely. When the position of point P 5S  is determined, the angle of joint  18  is also determined. 
     Thus, the rotation angle around the torsion axis and the first attaching unit tilt angle can be determined by determining the lengths of the first link and the second link. Furthermore, the rotation angle around the first attaching unit direction axis can be determined when the length of the third link is determined. The shape of the triangle determined by three points P 0S , P 1S , P 4S  is determined in the state in which only the length of the first link is determined. When the length of the second link is changed in this state, vertex P 4S  of the triangle is rotated around the rotation axis passing points P 0S , P 1S . Body bending unit C 2 C has a characteristic that the relationship of the joint angle with respect to the length of each link is analyzed easily. 
     The case of body bending unit C 2  in the first embodiment is described as a comparative example.  FIG. 155  is a view illustrating a point where the position is fixed by determining the link length in body bending unit C 2  included in humanoid robot  100 .  FIG. 155(A)  illustrates a state in which the lengths of the three links are not determined.  FIG. 155(B)  illustrates a state in which the lengths of thoracolumbar center link  19 L being the first link and thoracolumbar left link  21 L being the second link are determined.  FIG. 155(C)  illustrates a state in which the lengths of the three links are determined. 
     As illustrated in  FIG. 155(A) , the position of the point existing on chest  5  being the second member is not determined in the state in which the lengths of the three variable-length links are not determined. When the lengths of first link  19 L and second link  21 L are determined, the state shown in  FIG. 155(B)  is obtained. First link  19 L is connected to chest  5  at point P 4S . Second link  21 L is connected to chest  5  at point P 6S . For this reason, neither the position of point P 4S  nor the position of point P 5S  can be determined uniquely. 
     In the state of  FIG. 155(B) , a first triangle that is a triangle determined by three points P 1S , P 2S , P 4S  and a second triangle that is a triangle determined by three points P 2S , P 4S , P 6S  are formed while sharing a bottom side S 30  connecting points P 2S , P 4S . The angle of vertex P 1S  against bottom side S 30  of the first triangle is set to ε 1 . The angle of vertex P 6S  against bottom side S 30  of the second triangle is set to ε 2 . Angles ε 1 , ε 2  must be determined to keep a constraint condition that bottom side S 30  have the same length. Angles ε 1 , ε 2  can be changed when the constraint condition is kept. 
     The position of point P 5S  is also changed when angles ε 1 , ε 2  change. The length of thoracolumbar right link  20 L being the third link is changed when the position of point P 5S  is changed. Thus, when the length of third link  20 L is determined, the positions of points P 5S , P 4S , P 6S  and the angle of thoracolumbar joint  18  being the joint are also determined uniquely.  FIG. 155(C)  illustrates the state in which the length of third link  20 L is also determined. As described above, in body bending unit C 2 , the angle of the joint can be determined only when the lengths of the three variable length links are determined. In body bending unit C 2 , part of the three components of the joint angle cannot be determined at a point of time when the lengths of the two variable length links are determined. 
     The connection relationship between the link of shoulder C 4 C and the link attaching unit is the same as shoulder C 4 . In shoulder C 4 C, the method for determining the length of the variable-length link such that shoulder joint  13  takes the designated angle is the same as shoulder C 4 . Shoulder joint  13  is a joint having two rotational degrees of freedom. Because upper arm drive auxiliary link  15 L being the second link is connected to upper arm drive main link  14 L being the first link, the rotation angle of joint  13  can be determined uniquely by determining the lengths of first link  14 L and second link  15 L. 
     When second link  15 L is connected to humerus  7 B being the second member, the rotation angle of joint  13  can be determined uniquely by determining the lengths of first link  14 L and second link  15 L. However, because two link attaching units are provided in second member  7 B, the method for determining the rotation angle of joint  13  becomes slightly complicated. 
     The connection relationship between the link and the link attaching unit in elbow C 5 C is the same as elbow C 5 . In elbow C 5 C, the method for determining the attaching positions of the first link and the second link such that elbow joint  31  takes the designated angle is the same as elbow C 5 . Elbow joint  31  is a joint having two rotational degrees of freedom. 
     Wrist C 6 C has the same link arrangement as body bending unit C 2 C. Thus, the lengths of the three variable length links such that wrist joint  36  being a joint having three rotational degrees of freedom takes a designated angle can be determined by the same method as body bending unit C 2 C. In wrist C 6 C, because the link attaching units on both sides of the link exist on the same straight line, processing is simplified as compared with body bending unit C 2 C. 
     In hand  9 C, the motor is driven such that the worm gear of each finger joint is located at the position corresponding to the designated angle. In hand  9 C, when the worm gear of each finger joint is located at the position corresponding to the designated angle, the first finger joint and the second finger joint of each finger are set to the designated angle. Two-way rotation finger  89  includes finger base  80  that rotates the entire finger including the first finger joint. In two-way rotation finger  89 , the motor is driven such that the finger is directed in the designated direction, and such that the worm gear at the finger base is located at the position corresponding to the designated angle. The number of fingers including the finger base may be two or more. 
     The rotation connecting mechanism of the present disclosure including the joint having two rotational degrees of freedom or three rotational degrees of freedom may be applied to at least one of neck C 3 , crotch C 7 , knee C 8 , and ankle C 9  of humanoid robot  100 . 
     The rotation connecting mechanism of the present disclosure may be applied to not the humanoid robot but a robot arm including the hand and one or a plurality of arm section units connected in series from the hand. The rotation connecting mechanism may be used such that the second member being one of the hand and the arm section unit is connected rotatably to the first member located on the side far from the hand with two rotational degrees of freedom or three rotational degrees of freedom. In the robot arm, the hand can be at a proper position and can be directed to a proper angle. 
     Hand  9  of the first embodiment, hand  9 A of the third embodiment, hand  9 B of the fourth embodiment, or another hand may be used as the hand. 
     The above is also applied to other embodiments. 
     Sixth Embodiment 
     A sixth embodiment is the case where the fifth embodiment is modified such that the position of the joint of the body bending unit of the humanoid upper half body robot is moved to the upper end of the backbone.  FIG. 156  is a front view illustrating a humanoid upper half body robot according to the sixth embodiment of the present disclosure. In a humanoid upper half body robot  100 D, a thoracolumbar joint  18 D is provided at the end (upper end) connecting backbone  56  and a chest  5 E. For this reason, the axial direction of backbone  56  is fixed in a direction perpendicular to a waist  6 D. In backbone  56 , a place at the height of waist center link attaching unit J 10 C is referred to as a backbone lower end  56 D. Backbone lower end  56 D is the first twist center that is the intersection of the waist reference plane and backbone  56  being the torsion axis. 
     Thoracolumbar joint  18 D includes a spherical bearing. Thoracolumbar joint  18 D connects chest  5 E rotatably to waist  6 D with three rotational degrees of freedom. The angle formed by backbone  56  and chest  5 E being the second member can be changed. In other respects, humanoid upper half body robot  100 D is the same as humanoid upper half body robot  100 C. 
       FIG. 157  is a perspective view illustrating the link arrangement of the body bending unit included in the humanoid upper half body robot of the sixth embodiment. As compared with  FIG. 124  for humanoid upper half body robot  100 C, the difference is that thoracolumbar joint  18 D is located at the upper end of backbone  56 . Because thoracolumbar joint  18 D is located at the upper end of backbone  56 , the X-axis and the Y-axis that rotate chest  5 E are located at a higher position than the case in  FIG. 124 . 
     A body bending unit C 2 D of humanoid upper half body robot  100 D is a rotation connecting mechanism that connects chest  5 E being the second member rotatably to waist  6 D being the first member by thoracolumbar joint  18  being the joint. 
     The operation is described. The posture of humanoid upper half body robot  100 D is determined by the angles taken by thoracolumbar joint  18 D, shoulder joint  13 , elbow joint  31 , wrist joint  36 , and knee joint  40 . For each joint, how to determine the length of the variable length link such that the joint can take a designated angle and how to determine the position of the link attaching unit in the linear guide are the same as humanoid upper half body robot  100 C. 
     Even in body bending unit C 2 D, the influence of the change in the link length on the rotation angle of thoracolumbar joint  18 D is considered easily.  FIG. 158  is a view illustrating a point where the position is fixed by determining the link length in body bending unit C 2 D included in humanoid upper half body robot  100 D.  FIG. 158(A)  illustrates a state in which the lengths of the three links are not determined.  FIG. 158(B)  illustrates a state in which the lengths of thoracolumbar center link  19 LC being the first link and thoracolumbar left link  21 LC being the second link are determined.  FIG. 158(C)  illustrates a state in which the lengths of the three links are determined. The meaning of the sign illustrated in the drawing as the same as the case in  FIG. 154 . 
     As illustrated in  FIG. 158(A) , the rotation angle of thoracolumbar joint  18 D being the joint and the position of the point existing in chest  5 E being the second member are not determined in the state in which the lengths of the three variable-length links are not determined. The position of point P 0S  corresponding to joint  18 D is not changed when the length of each link is changed. When the lengths of first link  19 LC and second link  21 LC are determined, the distance between point P 4S  and each of three points P 0S , P 1S , P 3S  is determined, so that the position of point P 4S  is determined uniquely as illustrated in  FIG. 158(B) . The fact that the position of point P 4S  is determined means that the rotation angle around the backbone  56  being the torsion axis of chest  5 E and the tilt angle of backbone  56  in the direction toward waist-side center link attaching unit J 10 C being the second-member first attaching unit are determined. 
     In the state of  FIG. 158(B) , joint  18 D can be rotated around a rotation axis R 21  passing two points P 0S , P 4S . For this reason, point P 5S  is rotated around rotation axis R 21  while the distance from point P 0S  and the distance from point P 0S  are kept unchanged. Rotation axis R 21  is referred to as the first attaching unit direction axis. In  FIG. 158(B) , rotation axis R 21  is illustrated as existing on the XZ-plane and to be parallel to the X-axis. However, rotation axis R 21  does not necessarily exist on the XZ-plane and is not necessarily parallel to the X-axis. 
     Furthermore, when the length of third link  20 LC is determined, point P 5S  and the rotation angles of thoracolumbar joint  18 D are determined. Thus, the state shown in  FIG. 158(C)  is obtained. 
     As described above, in humanoid upper half body robot  100 D, similarly to humanoid upper half body robot  100 C, the rotation angle around the torsion axis and the first attaching unit tilt angle can be determined by determining the lengths of the first link and the second link. Furthermore, the rotation angle around the first attaching unit direction axis can be determined when the length of the third link is determined. Humanoid upper half body robot  100 D also has the characteristic that the relationship of the joint angle with respect to the length of each link is analyzed easily. 
     The positions of not only the thoracolumbar joint  18 D but also other joints can be changed. As long as the positions with respect to the first member and the second member are fixed, and as long as the second member  2  is connected rotatably to the first member with predetermined rotational degrees of freedom, the joint may be located anywhere. For the joint having three rotational degrees of freedom, the direction of the torsion axis may be fixed to either the first member or the second member. 
     The above is also applied to other embodiments. 
     The freely combination of the embodiments or the modification or omission of each embodiment can be made without departing from the scope of the present disclosure. 
     REFERENCE SIGNS LIST 
       100 ,  100 Z: humanoid robot 
       100 C,  100 D: humanoid upper half body robot 
       150 : control device container 
       160 : pedestal lifter 
       170 : cart 
       1 : trunk 
       2 : head (second member) 
       2 A: head base plate 
       3 : upper limb 
       4 : lower limb 
       5 ,  5 C,  5 E: chest (first member, second member) 
       5 U: chest upper portion 
       5 D: chest lower portion 
       6 ,  6 C,  6 D: waist (first member) 
       7 ,  7 C: upper arm 
       7 A: motor holder 
       7 B: humerus 
       7 H: humerus mounting unit 
       8 ,  8 C: forearm (first member) 
       8 B: forearm bone (torsion axis) 
       8 D: elbow tip 
       8 H: elbow mounting hole 
       8 J: elbow joint connecting hole 
       9 ,  9 A,  9 B,  9 C: hand (second member) 
       10 : thigh (second member) 
       10 A: thighbone (torsion axis) 
       10 B: knee-side link attaching plate 
       10 C: knee connecting frame 
       10 D: thigh-side auxiliary tool attaching unit 
       11 : lower leg 
       12 : foot 
       12 A: foot main body 
       12 B: toe 
       12 C: toe joint 
       12 D: heel wheel 
       12 E: foot side-surface wheel 
       13 : shoulder joint (joint) 
       14 : upper arm drive main actuator (first actuator) 
       14 L: upper arm drive main link (first link) 
       14 M: motor (power source, first power source) 
       15 : upper arm drive auxiliary actuator (second actuator) 
       15 L: upper arm drive auxiliary link (second link) 
       15 M: motor (power source, second power source) 
       16 : intrathoracic joint 
       17 : intrathoracic actuator 
       17 L: intrathoracic link 
       17 M: motor (power source) 
       18 ,  18 D: thoracolumbar joint (joint) 
       19 : thoracolumbar center actuator 
       19 A: screw rod 
       19 B: nut (perforated member) 
       19 C: cylinder (tube) 
       19 D: nut position fixer (perforated member position fixer) 
       19 E: nut rotation holder (perforated member holder) 
       19 F: nut gear 
       19 G: drive gear 
       19 ,  19 Z: thoracolumbar center actuator 
       19 C: thoracolumbar center actuator (first actuator) 
       19 L: thoracolumbar center link (variable length link) 
       19 LC: thoracolumbar center link (first link) 
       19 LZ: thoracolumbar center link (variable length link) 
       19 H: cylinder 
       19 J: piston 
       19 K: pipe 
       19 N: pump 
       19 P: first chamber 
       19 Q: second chamber 
       19 M: motor (power source, first power source) 
       20 : thoracolumbar right actuator 
       20 C: thoracolumbar right actuator (third actuator) 
       20 L: thoracolumbar right link (variable length link) 
       20 LC: thoracolumbar right link (third link) 
       20 M: motor (power source, third power source) 
       21 : thoracolumbar left actuator 
       21 C: thoracolumbar left actuator (second actuator) 
       21 L: thoracolumbar left link (variable length link) 
       21 LC: thoracolumbar left link (second link) 
       21 M: motor (power source, third power source) 
       22 : hip joint (joint) 
       23 : thigh front actuator 
       23 L: thigh front link (variable length link) 
       23 M: motor 
       24 : thigh outside actuator 
       24 L: thigh outside link (variable length link) 
       24 M: motor (power source) 
       25 : thigh inside actuator 
       25 L: thigh inside link (variable length link) 
       25 M: motor (power source) 
       26 : neck center rod (torsion axis) 
       27 : neck joint (joint) 
       28 : neck rear actuator 
       28 L: neck rear link (variable length link) 
       28 M: motor (power source) 
       28 N: link attachment 
       29 : neck right-side actuator 
       29 L: neck right-side link (variable length link) 
       29 M: motor (power source) 
       29 N: link attachment 
       30 : neck left-side actuator 
       30 L: neck left-side link (variable length link) 
       30 M: motor (power source) 
       30 N: link attachment 
       31 : elbow joint (joint) 
       31 D: elbow joint tip 
       32 : elbow drive outside link (second link) 
       33 : elbow drive inside link (first link) 
       34 ,  34 P: upper arm outside actuator (second actuator) 
       34 A: screw rod (second moving shaft) 
       34 B,  34 J: nut (second moving member) 
       34 C: rail (second rotation preventing unit) 
       34 D: gripper (second rotation preventing unit) 
       34 E: spline shaft (guide shaft, second rotation preventing unit) 
       34 F: upper arm outside frame 
       34 G,  34 GC: upper arm outside linear guide (second guide) 
       34 M: motor (power source, second power source) 
       35 ,  35 P: upper arm inside actuator (first actuator) 
       35 A: screw rod (first moving shaft) 
       35 B,  35 J: nut (first moving member) 
       35 C: rail (first rotation preventing unit) 
       35 D: gripper (first rotation preventing unit) 
       35 E: spline shaft (guide shaft, first rotation preventing unit) 
       35 F: upper arm inside frame 
       35 G,  35 GC: upper arm inside linear guide (first guide) 
       35 M: motor (power source, first power source) 
       36 : wrist joint (joint) 
       37 : forearm front actuator 
       37 C: forearm front actuator (first actuator) 
       37 L: forearm front link (variable length link) 
       37 LC: forearm front link (first link) 
       37 M: motor (power source, first power source) 
       37 N: link attachment 
       38 : forearm outside actuator 
       38 C: forearm outside actuator (second actuator) 
       38 L: forearm outside link (variable length link) 
       38 LC: forearm outside link (second link) 
       38 M: motor (power source, second power source) 
       38 N: link attachment 
       39 : forearm inside actuator 
       39 C: forearm inside actuator (third actuator) 
       39 L: forearm inside link (variable length link) 
       39 LC: forearm inside link (third link) 
       39 M: motor (power source, third power source) 
       39 N: link attachment 
       40 : knee joint (joint) 
       41 : ankle joint (joint) 
       41 A: front-back rotation yoke 
       41 B: right and left rotation yoke 
       42 : knee drive actuator 
       42 L: knee drive link 
       42 M: motor (power source) 
       43 : thigh-side auxiliary tool 
       44 : lower leg-side auxiliary tool 
       45 : lower leg outside actuator 
       45 L: lower leg outside link 
       45 M: motor (power source) 
       46 : lower leg inside actuator 
       46 L: lower leg inside link 
       46 M: motor (power source) 
       51 : shoulder frame 
       51 H: shoulder joint mounting hole 
       52 : thorax frame 
       52 C,  52 D: chest skeleton plate 
       52 H: shoulder first mounting hole 
       52 L: shoulder second mounting hole 
       53 : thorax front-back coupling frame 
       54 : chest center coupling frame 
       55 : intrathoracic joint frame 
       56 : backbone (torsion axis, coupling rod) 
       56 B: backbone upper end (second twist center) 
       56 D: backbone lower end (first twist center) 
       56 T: intrathoracic rotation shaft 
       57 : link attaching frame 
       58 : neck lower frame 
       61 : waist main frame 
       62 : lower limb connecting frame 
       63 : waist cover 
       64 : protrusion 
       65 : protrusion 
       66 : protrusion 
       67 : protrusion 
       81 : hand attaching tool 
       81 A: attaching plate 
       81 B: palm plate connecting part 
       82 : palm plate (base) 
       82 A: first finger attaching part (finger attaching part) 
       82 B: second finger attaching part (finger attaching part) 
       82 C: third finger attaching part (finger attaching part) 
       82 D: fourth finger attaching part (finger attaching part) 
       82 E: opposed finger attaching part (finger attaching part) 
       82 F: palm plate main body (main body) 
       82 G,  82 P: difference in width 
       82 H,  82 J,  82 K,  82 L,  82 M,  82 N,  82 Q,  82 R: notch 
       82 S: wrist attaching part 
       82 T: palm flesh 
       82 U: through-hole 
       82 V: hand breadth rotation finger attaching part (finger attaching part) 
       83 : first finger (ordinary finger) 
       84 : second finger (ordinary finger) 
       85 : third finger (ordinary finger) 
       86 : fourth finger (ordinary finger) 
       87 : opposed finger 
       88 : hand breadth rotation finger 
       83 A,  84 A,  85 A,  86 A,  87 A,  88 A: first dactylus 
       83 AA,  84 AA,  85 AA,  86 AA,  87 AA,  88 AA: first wheel linked part 
       83 AB,  84 AB,  85 AB,  86 AB,  87 AB,  88 AB: first yoke 
       83 AC,  84 AC,  85 AC,  86 AC,  87 AC,  88 AC: second motor installation part 
       83 AD,  84 AD,  85 AD,  86 AD,  87 AD,  88 AD: protrusion 
       83 B,  84 B,  85 B,  86 B,  87 B,  88 B: second dactylus 
       83 C,  84 C,  85 C,  86 C,  87 C,  88 C: third dactylus 
       83 CA,  84 CA,  85 CA,  86 CA,  87 CA,  88 CA: fingertip 
       83 CB,  84 CB,  85 CB,  86 CB,  87 CB,  88 CB: fingertip base 
       83 D,  84 D,  85 D,  86 D,  87 D,  88 D: first finger joint 
       83 E,  84 E,  85 E,  86 E,  87 E,  88 E: second finger joint 
       83 F,  84 F,  85 F,  86 F,  87 F,  88 F: third finger joint 
       83 G,  84 G,  85 G,  86 G,  87 G,  88 G: finger base yoke 
       83 H,  84 H,  85 H,  86 H,  87 H,  88 H: finger first motor 
       83 J,  84 J,  85 J,  86 J,  87 J,  88 J: first worm 
       83 K,  84 K,  85 K,  86 K,  87 K,  88 K: first worm wheel 
       83 L,  84 L,  85 L,  86 L,  87 L,  88 L: finger second motor 
       83 M,  84 M,  85 M,  86 M,  87 M,  88 M: second worm 
       83 N,  84 N,  85 N,  86 N,  87 N,  88 N: second worm wheel 
       83 P,  84 P,  85 P,  86 P,  87 P,  88 P: third dactylus drive gear 
       83 Q,  84 Q,  85 Q,  86 Q,  87 Q,  88 Q: partial gear 
       83 R,  84 R,  85 R,  86 R,  87 R,  88 R: idler gear 
       83 SA,  84 SA,  85 SA,  86 SA,  87 SA,  88 SA: outer-idler gear 
       83 SB,  84 SB,  85 SB,  86 SB,  87 SB,  88 SB: inner-idler gear 
       83 T,  84 T,  85 T,  86 T,  87 T,  88 T: first gear head 
       83 U,  84 U,  85 U,  86 U,  87 U,  88 U: second gear head 
       83 V,  84 V,  85 V,  86 V: first motor fixer 
       88 W: hand breadth finger base 
       89 : two-way rotation finger 
       89 A: first dactylus 
       89 AA: first wheel linked part 
       89 AB: first yoke 
       89 AC: second motor installation part 
       89 AD: protrusion 
       89 B: second dactylus 
       89 C: third dactylus 
       89 CA: fingertip 
       89 CB: fingertip base 
       89 D: first finger joint 
       89 E: second finger joint 
       89 F: third finger joint 
       89 G: finger base yoke 
       89 H: finger first motor 
       89 J: first worm 
       89 K: first worm wheel 
       89 L: finger second motor 
       89 M: second worm 
       89 N: second worm wheel 
       89 P: third dactylus drive gear 
       89 Q: partial gear 
       89 R: idler gear 
       89 SA: outer-idler gear 
       89 SB: inner-idler gear 
       89 T: first gear head 
       89 U: second gear head 
       89 V: first motor fixer 
       89 VB: worm tip holder 
       80 : finger base 
       80 A: finger base dactylus 
       80 AA: protrusion 
       80 AB: protrusion 
       80 B: finger base motor fixer 
       80 BA: protrusion 
       80 C: finger-base finger joint 
       80 D: finger base motor 
       80 E: finger base gear head 
       80 F: finger base worm 
       80 G: finger base worm wheel 
       83 X,  84 X,  85 X,  86 X,  88 X,  89 X: first dactylus cover 
       83 Y,  84 Y,  85 Y,  86 Y,  88 Y,  89 Y: second dactylus cover 
       83 Z,  84 Z,  85 Z,  86 Z,  88 Z,  89 Z: second worm cover 
       91 ,  91 C: wrist plate 
       98 : hand attaching tool 
       98 A: attaching plate 
       98 B: palm plate connecting part 
       92 : palm plate (base) 
       93 : first finger (ordinary finger) 
       94 : second finger (ordinary finger) 
       95 : third finger (ordinary finger) 
       96 : fourth finger (ordinary finger) 
       97 : opposable finger 
       97 T: first dactylus base 
       9715 : first dactylus tip 
       93 A,  94 A,  95 A,  96 A,  97 A: first dactylus 
       93 B,  94 B,  95 B,  96 B,  97 B: second dactylus 
       93 C,  94 C,  95 C,  96 C,  97 C: third dactylus 
       93 D,  94 D,  95 D,  96 D,  97 D: first finger joint 
       93 E,  94 E,  95 E,  96 E,  97 E: second finger joint 
       93 F,  94 F,  95 F,  96 F,  97 F: third finger joint 
       93 G,  94 G,  95 G,  96 G,  97 G: finger base yoke 
       93 H,  94 H,  95 H,  96 H,  97 H: finger first motor 
       93 J,  94 J,  95 J,  96 J,  97 J: first worm 
       93 K,  94 K,  95 K,  96 K,  97 : first worm wheel 
       93 L,  94 L,  95 L,  96 L,  97 L: finger second motor 
       93 M,  94 M,  95 M,  96 M,  97 M: second worm 
       93 N,  94 N,  95 N,  96 N,  97 N: second worm wheel 
       93 P,  94 P,  95 P,  96 P,  97 P: third dactylus drive gear 
       93 Q,  94 Q,  95 Q,  96 Q,  97 Q: idler gear 
       93 R,  94 R,  95 R,  96 R,  97 R: idler gear 
       93 S,  94 S,  95 S,  96 S,  97 S: idler gear 
     J 1 : chest-side main link attaching unit (first-member first attaching unit) 
     J 2 : chest-side auxiliary link attaching unit (first-member second attaching unit) 
     J 3 : lower intrathoracic link attaching unit 
     J 4 : upper intrathoracic link attaching unit 
     J 5 : chest center link attaching unit (second-member-side link attaching unit) 
     J 5 C: chest center link attaching unit (second-member first attaching unit) 
     J 6 : chest right link attaching unit (second-member-side link attaching unit) 
     J 6 C: chest right link attaching unit (second-member third attaching unit) 
     J 7 : chest left link attaching unit (second-member-side link attaching unit) 
     J 7 C: center-link left link attaching unit (first-link second attaching unit) 
     J 8 : waist right link attaching unit (first-member-side link attaching unit) 
     J 8 C: waist right link attaching unit (first-member third attaching unit) 
     J 9 : waist left link attaching unit (first-member-side link attaching unit) 
     J 9 C: waist left link attaching unit (first-member second attaching unit) 
     J 10 : waist center link attaching unit (first-member-side link attaching unit) 
     J 10 C: waist center link attaching unit (first-member first attaching unit) 
     J 11 : crotch front link attaching unit (first-member-side link attaching unit) 
     J 12 : crotch outside link attaching unit (first-member-side link attaching unit) 
     J 12 : crotch outside link attaching unit (first-member-side link attaching unit) 
     J 13 : crotch inside link attaching unit (first-member-side link attaching unit) 
     J 14 : neck rear link attaching unit (first-member-side link attaching unit) 
     J 15 : neck right-side link attaching unit (first-member-side link attaching unit) 
     J 16 : neck left-side link attaching unit (first-member-side link attaching unit) 
     J 17 : head rear link attaching unit (second-member-side link attaching unit) 
     J 18 : head right-side link attaching unit (second-member-side link attaching unit) 
     J 19 : head left-side link attaching unit (second-member-side link attaching unit) 
     J 20 : upper arm main link attaching unit (second-member first attaching unit) 
     J 21 : upper arm drive main-link-side auxiliary link attaching unit (first-link second attaching unit) 
     J 22 : upper arm outside link attaching unit (upper-arm-side link attaching unit, first-member second attaching unit) 
     J 23 : upper arm inside link attaching unit (upper-arm-side link attaching unit, first-member first attaching unit) 
     J 24 : elbow drive inside link attaching unit (forearm-side main link attaching unit, second-member first attaching unit) 
     J 25 : elbow drive outside link attaching unit (elbow drive main-link-side auxiliary link attaching unit, first-link second attaching unit) 
     J 26 : forearm front link attaching unit (first-member-side link attaching unit) 
     J 26 C: forearm front link attaching unit (first-member first attaching unit) 
     J 27 : forearm outside link attaching unit (first-member-side link attaching unit) 
     J 27 C: forearm outside link attaching unit (first-member second attaching unit) 
     J 28 : forearm inside link attaching unit (first-member-side link attaching unit) 
     J 28 C: forearm inside link attaching unit (first-member third attaching unit) 
     J 29 : hand-side front link attaching unit (second-member-side link attaching 
     J 29 C: hand-side front link attaching unit (second-member first attaching unit) 
     J 30 : hand-side outside link attaching unit (second-member-side link attaching unit) 
     J 30 C: hand-side outside link attaching unit (first-link second attaching unit) 
     J 31 : hand-side inside link attaching unit (second-member-side link attaching unit) 
     J 31 C: hand-side inside link attaching unit (second-member third attaching unit) 
     J 32 : knee front link attaching unit (second-member-side link attaching unit) 
     J 33 : knee outside link attaching unit (second-member-side link attaching unit) 
     J 34 : knee inside link attaching unit (second-member-side link attaching unit) 
     J 35 : knee drive link attaching unit 
     J 36 : thigh-side auxiliary tool attaching unit 
     J 37 : knee drive link auxiliary tool connecting unit 
     J 38 : lower leg-side auxiliary tool attaching unit 
     J 39 : lower leg outside link attaching unit (lower leg-side link attaching unit) 
     J 40 : lower leg inside link attaching unit (lower leg-side link attaching unit) 
     J 41 : foot outside link attaching unit (foot-side link attaching unit) 
     J 42 : foot inside link attaching unit (foot-side link attaching unit) 
     C 1 : chest bending unit 
     C 2 : body bending unit (three-rotational-degree-of-freedom connection mechanism) 
     C 2 C, C 2 D: body bending unit (rotation connecting mechanism) 
     C 3 : neck (three-rotational-degree-of-freedom connection mechanism) 
     C 4 , C 4 C: shoulder (rotation connecting mechanism) 
     C 5 , C 5 C: elbow (rotation connecting mechanism) 
     C 6 : wrist (three-rotational-degree-of-freedom connection mechanism) 
     C 6 C: wrist (rotation connecting mechanism) 
     C 7 : crotch (three-rotational-degree-of-freedom connection mechanism) 
     C 8 : knee 
     C 9 : ankle 
     G 1 , G 2 , G 3 : torsion axis 
     L 1 , L 2 , L 3 : variable length link 
     T 1 , T 2 , T 3 , T 4 : second-member-side triangle 
     Rx 1 : rotation axis of shoulder joint  13   
     Rz 2 : rotation axis of elbow joint  22   
     Rx 3 : rotation axis around which whole two-way finger rotation axis  89  is rotated 
     Rz 3 : rotation axis of first finger joint  89 D of two-way finger rotation axis  89   
     Rz 4 : rotation axis of second finger joint  89 E of two-way finger rotation axis  89   
     Rz 5 : rotation axis of third finger joint  89 F of two-way finger rotation axis  89   
     R 11 : rotation axis of rotation due to expansion and contraction of third link  20 LC of body bending unit C 2 C 
     R 21 : rotation axis of rotation due to expansion and contraction of third link  20 LC of body bending unit C 2 D 
     S 30 : base common to first triangle and second triangle, which can be formed by determining lengths of two links using body bending unit C 2   
     ε 1 : angle of vertex with respect to base S 30  of first triangle formed using body bending unit C 2   
     ε 2 : angle of vertex with respect to base S 30  of second triangle formed using body bending unit C 2   
     S 11 , S 21 : first line segment 
     S 12 , S 22 : second line segment 
     S 13 , S 23 : third line segment 
     S 14 , S 24 : fourth line segment 
     S 15 , S 25 : fifth line segment 
     η 1 , η 1A : angle formed by first line segment and third line segment 
     η 2 , η 2A : angle formed by fourth line segment and fifth line segment 
     ζ, ζ A : angle formed by first link and second link at first link second attaching unit 
     P 1N : first reference point 
     P 2N : second reference point