Patent Publication Number: US-2023136316-A1

Title: Robot

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a division of U.S. application Ser. No. 16/341,821 filed Apr. 12, 2019, the entire contents of which is incorporated herein by reference. U.S. application Ser. No. 16/341,821 is a 371 of International Application No. PCT/JP2017/032667 filed Sep. 11, 2017, and claims the benefit of priority from prior Japanese Application No. 2016-205947 filed Oct. 20, 2016. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates to a robot capable of making a motion close to a human. 
     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 joint. 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. 
     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 
     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, a motion accompanied by torsion cannot be made 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. The ankle and the wrist cannot be made thick because a shape similar to a human is required to be obtained, and a distance between the joint being a fulcrum and the connection point of the link being an action point is short. For this reason, it is considered that sometimes the robot cannot output enough power. 
     The parallel link mechanism described in Patent Document 3 can take a state in which three variable length links and one fixed length link are parallel to each other. In the state in which the three variable length links and the one fixed length link are parallel to each other, the variable length links cannot be rotated around the fixed length link even if a length of the variable length link is changed. The parallel link mechanism described in Patent Document 3 has a restriction on the motion. 
     An object of the present disclosure is to obtain a robot having upper limbs capable of making a motion close to a human. 
     Solution to Problems 
     According to one aspect of the present disclosure, a robot includes: a chest; a pair of right and left upper limbs, each of the upper limbs including an upper arm, a forearm, and a hand, the upper arm, the forearm, and the hand being connected in series to either a right or a left of an upper portion of the chest; and a pair of right and left elbows connecting the right and left forearms rotatably to the right and left upper arms with two rotational degrees of freedom, respectively. The elbow includes: an elbow joint connecting the forearm and the upper arm rotatably with two rotational degrees of freedom; an elbow drive main link having a fixed length; an elbow drive auxiliary link having a fixed length; a forearm-side main link attaching unit being attached rotatably with one end of the elbow drive main link with at least two rotational degrees of freedom, and being provided in the forearm; an elbow-drive-main-link-side auxiliary link attaching unit being attached rotatably with one end of the elbow drive auxiliary link with at least two rotational degrees of freedom, and being provided on the elbow drive main link; two upper-arm-side link attaching units each of the two upper-arm-side link attaching units being attached rotatably with the other end of either the elbow drive main link or the elbow drive auxiliary link with at least two rotational degrees of freedom, and being provided in the upper arm so as to be movable along the upper arm; and two linear actuators, each of the two linear actuators including a moving member for moving each of the two upper-arm-side link attaching units, a guide for guiding the moving member to be moved along the upper arm, and a power source for generating force changing a position of the moving member with respect to the guide. 
     Further, a robot includes: a chest; a pair of right and left upper limbs, each of the upper limbs including an upper arm, a forearm, and a hand, the upper arm, the forearm, and the hand being connected in series to either a right or a left of an upper portion of the chest; and a pair of right and left shoulders connecting the right and left upper arms rotatably to the chest with two rotational degrees of freedom, respectively. The shoulder includes: a shoulder joint connecting the upper arm rotatably to the chest with two rotational degrees of freedom, the shoulder joint including a rotation axis extending from either a right end or a left end of the upper portion of the chest to the side far from the center of the chest and the rear side, the shoulder joint allowing rotation around the rotation axis and rotation changing an angle formed by the rotation axis and the upper arm; a chest-side main link attaching unit provided in the chest at a position below the shoulder joint; an upper arm main link attaching unit provided in the upper arm; an upper arm drive main actuator including an upper arm drive main link having a variable length and a power source for generating force changing the length, one end of the upper arm drive main link being attached rotatably to the upper arm main link attaching unit, the other end of the upper arm drive main link being attached rotatably to the chest-side main link attaching unit; a chest-side auxiliary link attaching unit provided in the chest at a position being below the shoulder joint and sandwiching the shoulder joint in a front-back direction together with the upper arm main link attaching unit; an upper-arm-drive-main-link-side auxiliary link attaching unit provided in the upper arm drive main link; and an upper arm drive auxiliary actuator including an upper arm drive auxiliary link having a variable length and a power source for generating force changing the length of the upper arm drive auxiliary link, one end of the upper arm drive auxiliary link being attached rotatably to the upper-arm-drive-main-link-side auxiliary link attaching unit, the other end of the upper arm drive auxiliary link being attached rotatably to the chest-side auxiliary link attaching unit. 
     Advantageous Effects of Invention 
     The present disclosure can obtain the robot having upper limbs capable of making a motion close to a human. 
    
    
     
       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 disposition 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 disposition 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 disposition 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 disposition 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 disposition 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 disposition of the variable length links at a neck included in the humanoid robot of the first embodiment. 
         FIG.  35    is a view illustrating the disposition 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 disposition 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 disposition 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 disposition 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 disposition 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 disposition 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 disposition 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 disposition of the variable length links in a left crotch of the humanoid robot of the first embodiment. 
         FIG.  63    is a view illustrating the disposition 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 disposition 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 disposition 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 disposition 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 existing an opposable finger. 
         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 not existing the opposable finger. 
         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 perspective view illustrating a humanoid robot according to a second embodiment of the present disclosure. 
         FIG.  87    is a front view illustrating the humanoid robot of the second embodiment. 
         FIG.  88    is a left side view illustrating the humanoid robot of the second embodiment. 
         FIG.  89    is a rear view illustrating the humanoid robot of the second embodiment. 
         FIG.  90    is a plan view illustrating a left foot included in a humanoid robot according to a third embodiment of the present disclosure. 
         FIG.  91    is a left side view illustrating the left foot included in the humanoid robot of the third embodiment. 
         FIG.  92    is a front view illustrating the left foot included in the humanoid robot of the third embodiment. 
         FIG.  93    is a perspective view illustrating the left foot included in the humanoid robot of the third embodiment. 
         FIG.  94    is a cross-sectional view illustrating a structure of a variable length link of an actuator included in a humanoid robot according to a fourth embodiment of the present disclosure. 
         FIG.  95    is a perspective view illustrating a left hand included in a humanoid robot according to a fifth embodiment of the present disclosure viewing from the backside of the hand. 
         FIG.  96    is a perspective view illustrating the left hand included in the humanoid robot of the fifth embodiment viewing from the palm side. 
         FIG.  97    is a front view illustrating the left hand included in the humanoid robot of the fifth embodiment. 
         FIG.  98    is a side view illustrating the left hand included in the humanoid robot of the fifth embodiment viewing from the side existing the first finger. 
         FIG.  99    is a rear view illustrating the left hand included in the humanoid robot of the fifth embodiment. 
         FIG.  100    is a side view illustrating the left hand included in the humanoid robot of the fifth embodiment viewing from the fingertip side. 
         FIG.  101    is a side view illustrating the left hand included in the humanoid robot of the fifth embodiment viewing from the wrist side. 
         FIG.  102    is a side view illustrating the left hand included in the humanoid robot of the fifth embodiment when an opposed finger of the left hand is bent viewing from the side existing the first finger. 
         FIG.  103    is a plan view illustrating a palm plate of the left hand included in the humanoid robot of the fifth embodiment. 
         FIG.  104    is an enlarged perspective view illustrating a vicinity of the second dactylus of the opposed finger of the left hand included in the humanoid robot of the fifth embodiment. 
         FIG.  105    is a perspective view illustrating a left hand included in a humanoid robot according to a sixth embodiment of the present disclosure when a hand breadth rotation finger extends viewing from the backside of the hand. 
         FIG.  106    is a perspective view illustrating the left hand included in the humanoid robot of the sixth embodiment when the hand breadth rotation finger is directed in the direction intersecting the palm plate viewing from the backside of the hand. 
         FIG.  107    is a front view illustrating the left hand included in the humanoid robot of the sixth embodiment when the hand breadth rotation finger extends. 
         FIG.  108    is a side view illustrating the left hand included in the humanoid robot of the sixth embodiment when the hand breadth rotation finger extends viewing from the side existing the first finger. 
         FIG.  109    is a rear view illustrating the left hand included in the humanoid robot of the sixth embodiment when the hand breadth rotation finger extends. 
         FIG.  110    is a side view illustrating the left hand included in the humanoid robot of the sixth embodiment when the hand breadth rotation finger extends viewing from the side existing the fourth finger. 
         FIG.  111    is a side view illustrating the left hand included in the humanoid robot of the sixth embodiment when the hand breadth rotation finger extends viewing from the fingertip side. 
         FIG.  112    is a front view illustrating the left hand included in the humanoid robot of the sixth embodiment when the hand breadth rotation finger is directed in the direction intersecting the palm plate. 
         FIG.  113    is a side view illustrating the left hand included in the humanoid robot of the sixth embodiment when the hand breadth rotation finger is directed in the direction intersecting the palm plate viewing from the side existing first finger. 
         FIG.  114    is a rear view illustrating the left hand included in the humanoid robot of the sixth embodiment when the hand breadth rotation finger is directed in the direction intersecting the palm plate. 
         FIG.  115    is a side view illustrating the left hand included in the humanoid robot of the sixth embodiment when the hand breadth rotation finger is directed in the direction intersecting the palm plate viewing from the side existing a fourth finger. 
         FIG.  116    is a side view illustrating the left hand included in the humanoid robot of the sixth embodiment when the hand breadth rotation finger is directed in the direction intersecting the palm plate viewing from the fingertip side. 
         FIG.  117    is an enlarged perspective view illustrating the left hand included in the humanoid robot of the sixth embodiment when the hand breadth rotation finger extends viewing from the backside of the hand. 
         FIG.  118    is an enlarged perspective view illustrating the left hand included in the humanoid robot of the sixth embodiment when the hand breadth rotation finger is directed in the direction intersecting the palm plate viewing from the backside of the hand. 
     
    
    
     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. 
     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 . Left and right upper limbs  3  may have a portion in which the mirror image relationship does not hold. Left and right 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 constituting a neck, a shoulder, an elbow, a wrist, a crotch, a knee, an ankle, or the like is moved by changing a length of a link (variable length link) having a variable length included in an actuator that corresponds to a muscle. A 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. A reference sign XX of the actuator is not illustrated in the drawings. 
     In many conventional humanoid robots, the motor and the gear are disposed in each joint, and joint intersection is disposed on the axis. 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. 
     Each joint of humanoid robot  100  has three rotational degrees of freedom, at which the joint can be moved back and forth, right and left and also be twisted, in the neck, the wrist, the crotch, and a space between chest  5  and waist  6 . The joint has two rotational degrees of freedom, at which the joint can be moved back and forth and right and left, in the shoulder, the elbow, and the ankle. The joint has one rotational degree of freedom, at which the joint can be moved back and forth, in the knee. The joint may have three rotational degrees of freedom in the shoulder, the elbow, and the ankle. 
     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 vertically be changed 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 at least 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 a side existing a right hand  9 .  FIG.  13    is a perspective view illustrating the upper half body in the skeletal structure viewing down from the oblique rear on the side existing right hand  9 .  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 the oblique front on the side existing left hand  9 .  FIG.  23    is a perspective view illustrating trunk  1  viewing from the oblique rear on the side existing left hand  9 .  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 vertically be rotated. 
     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 an 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 the 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  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 .  FIGS.  16  to  20    illustrate chest upper portion  5 U and link attaching frame  57  such that the attaching position of the variable length link that rotates chest  5  with respect to waist  6  can be seen. 
     As illustrated in  FIG.  10   , portions near right and left ends of shoulder frame  51  are bent backward by an angle ξ1 with respect to the X-axis. Shoulder joint  13  connecting upper arm  7  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. The biaxial gimbal of shoulder joint  13  has a structure in which a member (referred to as a rotation member) that rotates around a rotation axis existing in a direction in which shoulder frame extends  51  is sandwiched by a yoke such that the yoke provided on upper arm  7  can change (rotate) an angle formed by upper arm  7  and the rotating member. The yoke has members opposed to each other, and holes or protrusions for holding rotatably other member are provided in the yoke. A member, which is held in holes provided in the yoke and can 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 rotate 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  extends horizontally toward the center side while being bent into the L-shape. A portion extending horizontally at the front side and the rear side of thorax frame  52  is coupled at the center side by thorax front-back coupling frame  53 . Left and right 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 in 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 the variable length link of 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 in the L-shaped corner portion on a rear side. Chest-side auxiliary link attaching unit J 2  is a biaxial gimbal being attached rotatably with an upper arm drive auxiliary link  15 L 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 the yoke provided in the rotation member holds columnar protrusions (shaft member) provided in upper arm drive main link  14 L. The rotation member rotates around the rotation axis (Y-axis) perpendicular to thorax frame  52 . The columnar protrusions (shaft member) provided perpendicularly from the both sides of a square tubular portion included in upper arm drive main link  14 L. The columnar protrusions are sandwiched rotatably by the yoke. 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 . 
     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 intrathoracic rotation shaft  56 T that is a horizontally cylindrical portion provided in the upper portion of backbone  56  is provided in intrathoracic joint frame  55 . 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 a 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 behind thoracolumbar joint  18  of the waist  6 . A thoracolumbar right link  20 L connects a right 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 as to 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 as to be 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 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 rotates 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 rotates 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 rotates 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 fixing unit  19 D, a nut rotation holding unit  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 fixing unit  19 D fixes the axial position of nut  19 B with respect to cylinder  19 C. Nut rotation holding unit  19 E holds rotatably nut  19 B with respect to cylinder  19 C. Nut gear  19 F is a gear that rotates together with nut  19 B. 
     Nut position fixing unit  19 D is protrusions circumferentially provided in cylinder  19 C so as not to move nut  19 B. The protrusions being nut position fixing unit  19 D are provided so as to sandwich the circumferentially-provided protrusion provided included in nut  19 B. Nut position fixing unit  19 D is provided at three places, that are, both sides of nut rotation holding unit  19 E and a connection portion between nut gear  19 F and nut  19 B. Any nut position fixing unit  19 D may be used as long as nut position fixing unit  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 rotate when drive gear  19 G rotates. Nut  19 B moves with respect to screw rod  19 A when nut  19 B rotates. Because the position of nut  19 B is fixed with respect to the length direction of cylinder  19 C, screw rod  19 A moves with respect to nut  19 B and cylinder  19 C when nut  19 B rotates. 
     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 moves 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 moves 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 on the side existing screw rod  19 A of thoracolumbar center link  19 L 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 in screw rod  19 A is provided on an inner surface. Nut  19 B is a rotation member that rotates by transmitting force from motor  19 M to the rotation member. Cylinder  19 C is a tube that accommodates screw rod  19 A and nut  19 B. Nut position fixing unit  19 D is a rotation member position fixing unit that fixes a relative position of nut  19 B with respect to cylinder  19 C in the axial direction of screw rod  19 A. Nut rotation holding unit  19 E is a rotation member holding unit, which is provided between nut  19 B and cylinder  19 C and holds nut  19 B rotatably with respect to cylinder  19 C. Because the rotation member holding unit is included, thoracolumbar center link  19 L being the variable length link has one rotational degree of freedom at which thoracolumbar center link  19 L can rotate 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. The case in that the variable length link has one rotational degree of freedom around the axis and both ends of the variable length link are attached to the attaching units with two rotational degrees of freedom, and the case in that one end of the variable length link is attached to the attaching unit with three rotational degrees of freedom and the other end is attached to the 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 during the rotation, 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 does not rotate 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. The pitch of the threads and the magnitude of the friction coefficient are determined such that the minimum value of the force that can change the length of the variable length link with which the nut is rotated becomes proper magnitude. 
     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 change 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 existing the tube or motor is attached to the link attaching unit with at least two rotational degrees of freedom. The end on the side existing the tube or the motor may be attached to the link attaching unit with a link attachment interposed therebetween. When the link attachment is used, the screw rod, the tube, and the link attachment become the variable length link. 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  being connected with lower limb  4 , 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 arranged, wiring and the like are routed. 
     Viewing from above, waist main frame  61  includes a rectangle, a circle connected to and overlapped on the front side of the rectangle and two thick plate-shaped portions extending rearward at symmetrical positions on the rear side of the rectangle. The circular portion, existing on the front side, viewed from above is a cylinder in which thoracolumbar joint  18  exists. Thoracolumbar joint  18  is constructed with 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 the other end of thoracolumbar left link  21 L are attached 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  being attached with thoracolumbar center link  19 L 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. In waist right link attaching unit J 8  and waist left link attaching unit J 9 , the yoke including the through-hole is provided rotatably and facing upward. To the through-hole included in the yoke, the shaft member provided in the variable length link is inserted. In waist center link attaching unit J 10 , the yoke having the through-hole is provided rotatably so as to be 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 disposition 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 disposition viewing from the front. Chest lower portion  5 D is illustrated with hatching. Chest lower portion  5 D can rotate 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 rotate 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  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 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 a second member on a connecting side rotatably to waist  6  being a first member on a connected side with three rotational degrees of freedom. Thoracolumbar joint  18  is a joint that connects chest  5  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 farther from waist  6  is defined as the second member. 
     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 disposed such that the maximum value of three angles formed by three links and the torsion axis is greater than or equal to an angle δ0 (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 disposition 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 connecting three second-member-side link attaching units J 5 , J 6 , J 7  provided on chest lower portion  5 D and three first-member-side link attaching units J 10 , J 8 , J 9  provided on waist  6 . The positions of three second-member-side link attaching units J 5 , J 6 , J 7  provided on 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 on waist  6  are fixed with respect to thoracolumbar joint  18 . For this reason, the 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 rotate 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 disposition 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 easily performed around torsion axis  56 . 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. When the length of variable length link  19 L is kept constant, when variable length link  20 L is lengthened, and when variable length link  21 L is shortened, or when the length of variable length link  19 L is kept constant, when variable length link  20 L is shortened, and when 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 disposition of the links that allows the second member to rotate 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  changes 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 δ0 (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 δ0. The link reference plane is a plane that is determined in each variable length link. Specifically, the link reference plane is the plane including the torsion axis and the first-member-side link attaching unit of the variable length link provided in the first member when the direction of the torsion axis is fixed to the first member, or the plane including the torsion axis and the second-member-side link attaching unit of the variable length link provided in the second member when the direction of the torsion axis is fixed to the second member. 
     In the case of tilt angle θ, a torque TA by the variable length link L 3  is given as follows. 
         TA∝K*W *sin θ= 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 δ0 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 is located on the same plane as torsion axis  56 , and a tilt angle θs1 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 θs2 and θs3 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 δ0. 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 θs2 and θs3 are about 41 degrees, at least one of θs2 and θs3 is greater than or equal to δ0 even if chest  5  is largely tilted. 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 the twisted relationship with torsion axis  56 . The tilt angle formed by the link reference plane and variable length link  20 L is greater than or equal to δ0. The link reference plane is a plane including torsion axis  56  and the each of second-member-side link attaching units J 6 , J 7  provided in second member  5  in which the direction of torsion axis  56  is fixed. 
       FIG.  31    is a view illustrating the disposition 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 the second member, when torsion axis  56  is tilted, waist  6  (first member) is expanded and contracted in the direction in which waist  6  (first member) is tilted by viewing the direction in which torsion axis  56  extends depending on the tilted angle. In  FIG.  31   , it is contracted by 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 θs2, θs3 of variable length links  20 L,  21 L are decreased. In the case that torsion axis  56  is tilted to the right, tilt angle θs2 of variable length link  20 L is increased and tilt angle θs3 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 δ0 in the vicinity of the boundary within the movable range It. 
     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 so as 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 including a spherical surface and a spherical receiving member provided an end of thigh  10  that holds the spherical surface of the spherical member rotatably with three rotational degrees of freedom. The spherical member protrudes outward and obliquely 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 being provided with crotch front link attaching unit J 11  and being 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 in 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 in 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 outside 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 inside 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  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 actuators  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. The 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 in the bent portion. Neck rear link attaching unit J 14  is located in 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 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 are attached to neck rear link attaching unit J 14 , neck right-side link attaching unit J 15 , and neck left-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 lengths of the screw rod and the cylinder included in neck rear link  28 L are shorter than the distance between head rear link attaching unit J 17  and neck rear link attaching unit J 14 . Link attachment  28 N is a member, which extends along motor  28 M from a gap existing between the cylinder included in neck rear link  28 L and motor  28 M. Link attachment  28 N is bent into an L-shape in the side view. The tip of L-shaped link attachment  28 N is attached to the head rear link attaching unit  17  at the position where the screw rod 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 disposition of the variable length links in neck C 3  is described.  FIG.  34    is a perspective view illustrating the disposition 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 disposed 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 disposed 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 disposition 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 θp1 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 θp2, θp3 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 δ0 (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 δ0.  FIG.  36    is a view illustrating the disposition 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 disposition 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 θp1, θp3 of variable length links  28 L,  30 L are increased, and tilt angle θp2 of variable length link  29 L is decreased. In the case that the rotation around torsion axis  26  is not performed, tilt angles θp2, θp3 of variable length links  29 L,  30 L are kept constant 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 θp2, θp3 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 disposed 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 disposed 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 do not exist on the same plane as torsion axis  26  even if neck joint  27  rotates 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 rotates 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 easily performed around torsion axis. 
     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 to chest  5  with two rotational degrees of freedom by shoulder joint  13 . Upper arm  7  and forearm  8  have a straight rod shape. An upper arm main link attaching unit J 20  being attached with upper arm drive main link  14 L with two rotational degrees of freedom is provided at a position of a predetermined distance from shoulder joint  13  of upper arm  7 . Upper arm main link attaching unit J 20  is a biaxial gimbal having the structure in which the rotation member that rotates around the direction in which the upper arm  7  is sandwiched by the semi-circular yoke being provided at one end of upper arm drive main link  14 L such that the angle formed with upper arm  7  is rotatable. Two columnar protrusions existing on the same straight line perpendicular to the rotation member protrude toward both sides, and the protrusions are sandwiched rotatably by the yoke provided on upper arm drive main link  14 L. 
     A main-link-side auxiliary link attaching unit J 21  being attached with one end of upper arm drive auxiliary link  15 L with one rotational degree of freedom is provided at a position having a distance determined from upper arm main link attaching unit J 20  of upper arm drive main link  14 L. 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 is referred to as an upper arm drive link plane. In main-link-side auxiliary link attaching unit J 21 , upper arm drive auxiliary link  15 L is attached to upper arm drive main link  14 L so as to be rotatable with one rotational degree of freedom at which the angle on the upper arm drive link plane can be changed. Main-link-side auxiliary link attaching unit J 21  has the structure in which protrusions (shaft member) perpendicular to the upper arm drive link plane 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 plane determined by chest-side main link attaching unit J 1 , chest-side auxiliary link attaching unit J 2 , and main-link-side auxiliary link attaching unit J 21  is referred to as the upper arm drive link plane. When the lengths of upper arm drive main link  14 L and upper arm drive auxiliary link  15 L change, the upper arm drive link plane rotates around the straight line passing through chest-side main link attaching unit J 1  and chest-side auxiliary link attaching unit J 2 . Upper arm drive main link  14 L and upper arm drive auxiliary link  15 L exist on the upper arm drive link plane. About the relative positional relationship between upper arm drive main link  14 L and upper arm drive auxiliary link  15 L, only the angle formed by upper arm drive main link  14 L and upper arm drive auxiliary link  15 L is changed at main-link-side auxiliary link attaching unit J 21 . Thus, main-link-side auxiliary link attaching unit J 21  may have only one rotational degree of freedom at which only the rotation can be performed in the upper arm drive link plane. Main-link-side auxiliary link attaching unit J 21  may have two rotational degrees of freedom. 
       FIG.  38    is a perspective view illustrating the disposition 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. Main-link-side auxiliary link attaching unit J 21  exists on upper arm drive main link  14 L and at the position of the distance predetermined from upper arm main link attaching unit J 20 . When the position of upper arm main link attaching unit J 20  is determined, upper arm  7  is directed in the direction from shoulder joint  13  toward upper arm main link attaching unit J 20 . Upper arm  7  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. 
     Upper arm  7  is raised by lengthening upper arm drive main link  14 L, and upper arm  7  is lowered by shortening upper arm drive main link  14 L. Upper arm  7  moves forward by lengthening upper arm drive auxiliary link  15 L, and upper arm  7  moves rearward by shortening upper arm drive auxiliary link  15 L. Upper arm  7  can move freely within the movable range that is determined under a situation in that shoulder joint  13  is used as the center of the rotation. For example, when the downward direction is set to 0 degrees and the forward direction is set to 90 degrees with respect to the vertical direction and the front-back direction, upper arm  7  can be rotated from −30 degrees to 95 degrees. In the right and left direction, upper arm  7  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 that upper arm  7  is directed in the direction of a rotation axis Rx 1  rotating the rotation member of the biaxial gimbal (referred to as a singular point), upper arm  7  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 ξ1 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 upper arm  7  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. 
     Shoulder joint  13  exists at either a right end of a left 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 angle formed by rotation axis Rx 1  and upper arm  7  is allowed to be changed by shoulder joint  13 . Shoulder joint  13  connects upper arm  7  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. 
     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 so as to be far from trunk  1 , left upper arm  7  has moved so as 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   , right and left forearms  8  each is directed in the direction being 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 ξ2 with respect to the front direction (Y-axis) of trunk  1 . 
     The front direction of upper limb  3  is the direction in which the forearm  8  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 ξ2 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. 
     The forearm  8  is connected to upper arm  7  with two rotational degrees of freedom by elbow joint  31 . 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, the angle between upper arm  7  and forearm  8  can be changed. And forearm  8  can be rotated around rotation axis Rz 2 . In elbow joint  31 , the rotation member is provided in upper arm  7 , and the yoke is provided in forearm  8 . An elbow drive outside links  32  and an elbow drive inside link  33  in each of which the length is fixed are attached to upper arm  7  and forearm  8 . Elbow drive outside link  32  and elbow drive inside link  33  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, upper arm outside actuator  34  and upper arm inside actuator  35 , being two linear actuators, are provided on both sides of upper arm  7  in parallel with upper arm  7 . As illustrated in  FIG.  11    and other figures, actuator holder  7 A that holds a motor  34 M of upper arm outside actuator  34  and a motor  35 M of upper arm inside actuator  35  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. Motor  34 M of upper arm outside actuator  34  transmits the power to a screw rod  34 A by a timing belt provided on the side closer to shoulder joint  13 , and rotates screw rod  34 A. 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 does not rotate nut  34 B around screw rod  34 A is provided. For this reason, nut  34 B moves along screw rod  34 A when screw rod  34 A rotates. Upper arm outside link attaching unit J 22  is attached to nut  34 B, and upper arm outside link attaching unit J 22  also moves when nut  34 B moves. Nut  34 B is a moving member that is moved by upper arm outside actuator  34 . 
     The mechanism that does not rotate nut  34 B 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 as to have low friction with rail  34 C. Because gripper  34 D sandwiches rail  34 C, gripper  34 D and nut  34 B do not rotate around screw rod  34 A. Another mechanism that does not rotate nut  34 B around screw rod  34 A may be used. 
     Upper arm inside actuator  35  and upper arm inside link attaching unit J 23  have the same structure. Upper arm inside actuator  35  includes motor  35 M, screw rod  35 A, nut  35 B, rail  35 C and gripper  35 D. 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 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. 
     An elbow drive inside link attaching unit J 24  being attached with elbow drive inside link  33  with two rotational degrees of freedom is provided at a position of a predetermined distance from elbow joint  31  of forearm  8 . 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 . An elbow drive outside link attaching unit J 25  being attached with elbow drive outside link  32  with two rotational degrees of freedom is provided at a position having a distance predetermined from elbow drive inside link attaching unit J 24  of elbow drive inside link  33 . Elbow drive outside link attaching unit J 25 , has the structure in which the protrusions provided in 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 sufficient length so as 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. 
     At least one of upper arm outside link attaching unit J 22  and elbow drive inside link attaching unit J 24  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 disposition 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 upper arm  7  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 in 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  move along upper arm  7 , and the position of elbow drive inside link attaching unit J 24  is changed. 
     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 main-link-side auxiliary link attaching unit provided in elbow drive inside link  33 , upper arm inside link attaching unit J 23  and upper arm outside link attaching unit J 22  being two upper-arm-side link attaching units, and upper arm outside actuator  34  and upper arm inside actuator  35  being two linear actuators. 
     When both upper arm outside link attaching unit J 22  and upper arm inside link attaching unit J 23  move so as 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  move so as to be far from shoulder joint  13 , elbow joint  31  extends and forearm  8  moves to be far from upper arm  7 . When upper arm outside link attaching unit J 22  is moved so as to come close to shoulder joint  13 , and upper arm inside link attaching unit J 23  is moved so as to be far from shoulder joint  13 , forearm  8  is directed outside. When upper arm inside link attaching unit J 23  is moved so as to come close to shoulder joint  13 , and upper arm outside link attaching unit J 22  is moved so as 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 upper arm  7  can be changed from the state in which upper arm  7  and forearm  8  exist on one straight line to the state in which the angle formed by upper arm  7  and forearm  8  becomes, for example, 70 degrees. In the plane (elbow auxiliary drive plane) perpendicular to upper arm  7 , 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 each of the two links for driving elbow joint  31  have a fixed length and the position of the link attaching unit on the upper arm side is moved. 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. For this purpose, the interval between the attaching positions of the two variable length links is required to be wider than the interval between the two linear actuators 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 the main-link-side auxiliary link attaching unit being attached rotatably with one end of elbow drive outside link  32  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, being attached rotatably with the other ends of elbow drive inside link  33  and elbow drive outside link  32  with at least two rotational degrees of freedom and being provided in upper arm  7  so as to be movable along upper arm  7 . 
     One end of elbow driving outside link  32  on the side existing forearm  8  may be attached to forearm  8  instead of elbow drive inside link  33 . In this case, two forearm-side link attaching units are provided in forearm  8 . One ends of elbow drive outside link  32  and elbow drive inside link  33 , which are the two elbow drive links, each is attached rotatably to each of 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 upper arm  7 , 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 actuator  34  is the linear actuator including nut  34 B, screw rod  34 A, and motor  34 M. Upper arm inside actuator  35  is the linear actuator including nut  35 B, screw rod  35 A, and motor  35 M. 
     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 to forearm  8  with three rotational degrees of freedom by a wrist joint  36 . The spherical bearing that holds rotatably the spherical surface provided at one end of rod-shaped forearm  8  is used as wrist joint  36 . A member that holds the spherical surface is provided in wrist plate  91 . Hand  9  can rotate around wrist joint  36  with three rotational degrees of freedom. The angle between hand  9  and forearm  8  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 by about 20 degrees in the direction (front direction) to the palm side, tilted by about 20 degrees in the direction (rear direction) to the backside of the hand, and tilted by about 20 degrees in the both directions that are perpendicular to the direction of forearm  8  and the direction directed from the front toward the rear. Hand  9  can be rotated by about 70 degrees in both directions around forearm  8 . 
     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 in parallel with 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 in 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 attaching tool  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 move to the position opposed to the ordinary fingers. Wrist plate  91  is connected to forearm  8  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 surface, the backside of the hand is set to the rear surface. 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. 
     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 existing hand  9 . 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  8  and 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 in the surface on the side existing forearm  8  of wrist plate  91  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 disposed 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  8  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 in the surface on the forearm side of the wrist plate  91 . Hand-side outside link attaching unit J 30  and hand-side inside link attaching unit J 31  are also the biaxial gimbal having the a same structure. 
     One ends of forearm front link  37 L, forearm outside link  38 L, and forearm inside link  39 L are attached 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 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. 
     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  8  being the first member is also the torsion axis. The angle of forearm  8  can be changed with respect to hand  9 . 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 disposition of the variable length links in wrist C 6  is described.  FIG.  50    is a perspective view illustrating the disposition 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  8  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 through second-member-side link attaching unit J 29  and the torsion center. 
       FIG.  51    is a view illustrating the disposition 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 θv2, θv3 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 δ0 (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  8 , 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 angle is greater than or equal to δ0. 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 of tilt angles θv2, θv3 of variable length links  38 L,  39 L and to keep variable length link  37 L in the same plane as torsion axis  8 , hand  9  is tilted onto the side existing fourth finger  96 .  FIG.  52    is a view illustrating the disposition of the variable length links when left wrist C 6  is tilted toward the side existing fourth finger  96  viewing from the direction in which forearm  8  extends. In  FIG.  52   , hand  9  is tilted by 20 degrees toward the fourth finger portion side. Tilt angles θv2, θv3 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 θv2, θv3 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  relative 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 ξ3 (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 in 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 in knee-side link attaching plate  10 B 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 in 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, three thigh front links  23 L, thigh outside link  24 L, and thigh inside link  25 L, being 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 , being three first-member-side link attaching unit, and knee front link attaching units J 32 , knee outside link attaching unit J 33 , and a knee inside link attaching unit J 34 , being 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. The relative positional relationships with hip joint  22  are fixed by lower limb connecting frame  62  in crotch front link attaching unit J 11 , crotch outside link attaching unit J 12 , and crotch inside link attaching unit J 13 . 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 disposition of the variable length links that move hip joint  22  is described.  FIG.  62    is a perspective view illustrating the disposition 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  with respect 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 disposition 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 θq1 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 θq2 of variable length link  24 L is about 1.9 degrees. A tilt angle θq3 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 δ0 (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 disposition 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 θq3 of variable length link  25 L is larger than that in the case of  FIG.  63   . Tilt angle θq1 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 δ0 (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 rotate 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 also 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 existing knee joint  40 . 
     A knee drive link attaching unit J 35  being attached with one end of knee drive link  42 L with one rotational degree of freedom is provided on the rear 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 existing knee joint  40 . 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 L. 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 rotate with one rotational degree of freedom by the rotation shaft 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 existing knee joint  40 . 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 to lower leg  11  with one rotational degree of freedom by the lower leg-side auxiliary tool attaching unit J 38 . 
       FIG.  66    is a perspective view illustrating the disposition 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  move 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  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 disposed 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 easily transmitted 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 more smoothly be performed. 
     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 connects foot  12  to lower leg  11  with two rotational degrees of freedom, that are, 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 rotate 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 rotate in the front-back direction with respect to front-back rotation yoke  41 A. Columnar portions (shaft member) are provided in 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 move in the right and left direction with respect to foot  12 . 
     Foot  12  can rotate 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  that attach one ends of a lower leg outside link  45 L and a lower leg inside link  46 L with two rotational degrees of freedom are provided in 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 existing foot  12 . 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  being attached with 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 on the rear side 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 easily in the right and left direction. 
     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. Between foot main body  12 A and toe  12 B, there exists a toe joint  12 C. Toe joint  12 C changes vertical angle of toe  12 B with respect to foot main body  12 A. 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 smoothly landed 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 existing foot  12  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 . During the movement, 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 disposition 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  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 existing opposable finger  97 , a rear view of left hand  9 , and a side view of left hand  9  viewing from the side not existing opposable finger  97 .  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 in 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 palm plate  92  on the side closer to attaching plate  98 A than first finger  93  and other fingers and on the side existing first finger  93 . 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 easily added in the drawing. 
     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 close 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 the adjacent two of palm plate  92 , first dactylus  96 A, second dactylus  96 B, and third dactylus  96 C, one member provided on the side close to palm plate  92  is referred to as a base-side member, and the other member provided on the side not existing the base-side member 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 that is 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 the 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 forearm  8  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 rotates 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 rotates, and first worm wheel  96 K rotates 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 rotate 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 rotates 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 rotates, and second worm wheel  96 N rotates 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 rotate 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. 
     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 rotates 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 rotates in the opposite direction when second worm wheel  94 N rotates. Idler gear  94 R meshes with idler gear  94 Q, and idler gear  94 R rotates in the opposite direction when idler gear  94 Q rotates. Idler gear  94 S meshes with idler gear  94 R, and idler gear  94 S rotates in the opposite direction when idler gear  94 R rotates. Third dactylus drive gear  94 P meshes with idler gear  94 S, and third dactylus drive gear  94  rotates in the opposite direction when idler gear  94 S rotates. Because a number of three idler gears  94 Q,  94 R,  94 S is an odd number, third dactylus drive gear  94 P rotates in the same direction when second worm wheel  94 N rotates. 
     Idler gears  94 Q,  94 R,  94 S are the gears that rotate 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 rotates 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 ϕ2 of second worm wheel  94 N and a rotation angle ϕ3 of third dactylus drive gear  94 P are equal to each other. That is, a value f=ϕ3/ϕ2 being a ratio of ϕ3 to ϕ2 is set to f=1. Value f=ϕ3/ϕ2 of the ratio of third dactylus drive gear  94 P, namely, rotation angle ϕ3 of third dactylus  94 C to second worm wheel  94 N, namely, rotation angle ϕ2 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 a 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 K that rotates around the rotation axis of first finger joint  97 D. First worm wheel  97 K is attached to second dactylus  97 B. When finger first motor  97 H rotates, first worm wheel  97 K rotates together with first dactylus  97 A. When first dactylus  97 A rotates, second dactylus  97 B and third dactylus  97 C move 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 rotates together with first worm wheel  97 K 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 motion 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  moves, 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 lengths of the links such that each joint can take the designated angle is explained. 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 0s P 3s  projected on Y-axis. 
     Ws2: lengths of line segment P 0As0 P 5s0  and line segment P 0As 0P 6s0  projected on X-axis. 
     Ds3: length of line segment P 0As P 4s0  projected on Y-axis. 
     Ds4: lengths of line segment P 0As P 5s0  and line segment P 0As 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, Ds1, −Hs2) 
     P 2s =(Ws1, Ds2, −Hs2) 
     P 3s =(−Ws1, Ds2, −Hs2) 
     P 4s0 =(0, Ds3, Hs1) 
     P 5s0 =(Ws2, −Ds4, Hs1) 
     P 6s0 =(−Ws2, −Ds4, Hs1) 
     P 7s0 =(0, 0, Hs1) 
     P 8s0 =(0, −Ds5, Hs1−Hs3) 
     P 9s0 =(0, −Ds5, Hs1+Hs3) 
     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 
                           
                           
                             
                               cos 
                               ⁢ 
                               α 
                               ⁢ 
                               s 
                             
                           
                           
                             
                               
                                 - 
                                 sin 
                               
                               ⁢ 
                               α 
                               ⁢ 
                               s 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               sin 
                               ⁢ 
                               α 
                               ⁢ 
                               s 
                             
                           
                           
                             
                               cos 
                               ⁢ 
                               α 
                               ⁢ 
                               s 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               cos 
                               ⁢ 
                               β 
                               ⁢ 
                               s 
                             
                           
                           
                             0 
                           
                           
                             
                               
                                 - 
                                 sin 
                               
                               ⁢ 
                               β 
                               ⁢ 
                               s 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             1 
                           
                           
                             0 
                           
                         
                         
                           
                             
                               sin 
                               ⁢ 
                               β 
                               ⁢ 
                               s 
                             
                           
                           
                             0 
                           
                           
                             
                               cos 
                               ⁢ 
                               β 
                               ⁢ 
                               s 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               cos 
                               ⁢ 
                               γ 
                               ⁢ 
                               s 
                             
                           
                           
                             
                               
                                 - 
                                 sin 
                               
                               ⁢ 
                               γ 
                               ⁢ 
                               s 
                             
                           
                           
                             0 
                           
                         
                         
                           
                             
                               sin 
                               ⁢ 
                               γ 
                               ⁢ 
                               s 
                             
                           
                           
                             
                               cos 
                               ⁢ 
                               γ 
                               ⁢ 
                               s 
                             
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             1 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Mathematical 
                     ⁢ 
                         
                     Formula 
                     ⁢ 
                         
                     1 
                   
                   ] 
                 
               
             
           
         
       
     
     The rotation matrix [Rs2] of intrathoracic joint  16  is given as follows. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       Rs 
                       ⁢ 
                       2 
                     
                     ] 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           1 
                         
                         
                           0 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           
                             cos 
                             ⁢ 
                             ψ 
                           
                         
                         
                           
                             
                               - 
                               sin 
                             
                             ⁢ 
                             ψ 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             sin 
                             ⁢ 
                             ψ 
                           
                         
                         
                           
                             cos 
                             ⁢ 
                             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 the point P D  after rotation in thoracolumbar joint  18  can be given as follows. 
         P   D =[ Rs ]* P   D0    
     Assuming that 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 the 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 4s . 
     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. 
         x 9 s= 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 slightly performed around the Z-axis from the reference state, how the length of each link changes 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 
                         * 
                         sin 
                         ⁢ 
                         γ 
                         ⁢ 
                         s 
                       
                       , 
                       
                         Ds 
                         ⁢ 
                         3 
                         * 
                         cos 
                         ⁢ 
                         γ 
                         ⁢ 
                         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 
                           * 
                           cos 
                           ⁢ 
                           γ 
                           ⁢ 
                           s 
                         
                         + 
                         
                           Ds 
                           ⁢ 
                           4 
                           * 
                           sin 
                           ⁢ 
                           γ 
                           ⁢ 
                           s 
                         
                       
                       , 
                       
 
                       
                         
                           Ws 
                           ⁢ 
                           2 
                           * 
                           sin 
                           ⁢ 
                           γ 
                           ⁢ 
                           s 
                         
                         - 
                         
                           Ds 
                           ⁢ 
                           4 
                           * 
                           cos 
                           ⁢ 
                           γ 
                           ⁢ 
                           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 
                           * 
                           cos 
                           ⁢ 
                           γ 
                           ⁢ 
                           s 
                         
                         + 
                         
                           Ds 
                           ⁢ 
                           4 
                           * 
                           sin 
                           ⁢ 
                           γ 
                           ⁢ 
                           s 
                         
                       
                       , 
                       
 
                       
                         
                           
                             - 
                             Ws 
                           
                           ⁢ 
                           2 
                           * 
                           sin 
                           ⁢ 
                           γ 
                           ⁢ 
                           s 
                         
                         - 
                         
                           Ds 
                           ⁢ 
                           4 
                           * 
                           cos 
                           ⁢ 
                           γ 
                           ⁢ 
                           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 easily performed around torsion axis. 
     How to determine the lengths of the 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-side main link attaching unit J 20 . Q 1t =(x1t, y1t, z1t) 
     Q 1t0 : position of upper-arm-side main link attaching unit J 20  in reference state. 
     Q 2t : position of main-link-side auxiliary link attaching unit J 21 . Q 2t =(x2t, y2t, z2t) 
     Q 2t0 : position in reference state of main-link-side auxiliary link attaching unit J 21 . 
     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 
                           
                           
                             
                               cos 
                               ⁢ 
                               α 
                               ⁢ 
                               t 
                             
                           
                           
                             
                               
                                 - 
                                 sin 
                               
                               ⁢ 
                               α 
                               ⁢ 
                               t 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               sin 
                               ⁢ 
                               α 
                               ⁢ 
                               t 
                             
                           
                           
                             
                               cos 
                               ⁢ 
                               α 
                               ⁢ 
                               t 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               cos 
                               ⁢ 
                               β 
                               ⁢ 
                               t 
                             
                           
                           
                             0 
                           
                           
                             
                               
                                 - 
                                 sin 
                               
                               ⁢ 
                               βt 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             1 
                           
                           
                             0 
                           
                         
                         
                           
                             
                               sin 
                               ⁢ 
                               βt 
                             
                           
                           
                             0 
                           
                           
                             
                               cos 
                               ⁢ 
                               β 
                               ⁢ 
                               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 the shoulder joint  13 , because main-link-side auxiliary link attaching unit J 21  is located on upper arm drive main link  14 L, position Q 2t  of 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   2t =√(( x 2 t+Wt 1) 2 +( y 2 t−Dt 2) 2 +( z 2 t+Ht 1) 2 )
 
     How to determine the link attachment position at the upper arm such that a designated angle can be taken with respect to the 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 , move 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 )*( H   u1   +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 
                           
                           
                             
                               cos 
                               ⁢ 
                               α 
                               ⁢ 
                               u 
                             
                           
                           
                             
                               
                                 - 
                                 sin 
                               
                               ⁢ 
                               α 
                               ⁢ 
                               u 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               sin 
                               ⁢ 
                               α 
                               ⁢ 
                               u 
                             
                           
                           
                             
                               cos 
                               ⁢ 
                               α 
                               ⁢ 
                               u 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               cos 
                               ⁢ 
                               γ 
                               ⁢ 
                               u 
                             
                           
                           
                             
                               
                                 - 
                                 sin 
                               
                               ⁢ 
                               γ 
                               ⁢ 
                               u 
                             
                           
                           
                             0 
                           
                         
                         
                           
                             
                               sin 
                               ⁢ 
                               γ 
                               ⁢ 
                               u 
                             
                           
                           
                             
                               cos 
                               ⁢ 
                               γ 
                               ⁢ 
                               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 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 2v . 
     Dv2: length of line segment P 0v P 4v . 
     Using the variables defined above, a coordinate of each point is expressed as follows. 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   3v =(− 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 
                           
                           
                             
                               cos 
                               ⁢ 
                               α 
                               ⁢ 
                               v 
                             
                           
                           
                             
                               
                                 - 
                                 sin 
                               
                               ⁢ 
                               α 
                               ⁢ 
                               v 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               sin 
                               ⁢ 
                               α 
                               ⁢ 
                               v 
                             
                           
                           
                             
                               cos 
                               ⁢ 
                               α 
                               ⁢ 
                               v 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               cos 
                               ⁢ 
                               β 
                               ⁢ 
                               v 
                             
                           
                           
                             0 
                           
                           
                             
                               
                                 - 
                                 sin 
                               
                               ⁢ 
                               β 
                               ⁢ 
                               v 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             1 
                           
                           
                             0 
                           
                         
                         
                           
                             
                               sin 
                               ⁢ 
                               β 
                               ⁢ 
                               v 
                             
                           
                           
                             0 
                           
                           
                             
                               cos 
                               ⁢ 
                               β 
                               ⁢ 
                               v 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               cos 
                               ⁢ 
                               γ 
                               ⁢ 
                               v 
                             
                           
                           
                             
                               
                                 - 
                                 sin 
                               
                               ⁢ 
                               γ 
                               ⁢ 
                               v 
                             
                           
                           
                             0 
                           
                         
                         
                           
                             
                               sin 
                               ⁢ 
                               γ 
                               ⁢ 
                               v 
                             
                           
                           
                             
                               cos 
                               ⁢ 
                               γ 
                               ⁢ 
                               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 Liv, L 1v , 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 slightly performed around the Z-axis from the reference state, how the length of each link changes 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 
                         * 
                         sin 
                         ⁢ 
                         γ 
                         ⁢ 
                         v 
                       
                       , 
                       
 
                       
                         Dv 
                         ⁢ 
                         2 
                         * 
                         cos 
                         ⁢ 
                         γ 
                         ⁢ 
                         v 
                       
                       , 
                       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 
                       ⁢ 
                       b 
                     
                     , 
                     
                       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 
                             ⁡ 
                             ( 
                             
                                
                               / 
                               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)− Dv 2*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  
 
       −( Dv 2*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, in the rotation around forearm  8  being the torsion axis, both the force pushed by the extending link and the force drawn by the shortening link are generated, the rotation is easily performed around torsion axis. 
     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 so as 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 
                           
                           
                             
                               cos 
                               ⁢ 
                               α 
                               ⁢ 
                               m 
                             
                           
                           
                             
                               
                                 - 
                                 sin 
                               
                               ⁢ 
                               α 
                               ⁢ 
                               m 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               sin 
                               ⁢ 
                               α 
                               ⁢ 
                               m 
                             
                           
                           
                             
                               cos 
                               ⁢ 
                               α 
                               ⁢ 
                               m 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               cos 
                               ⁢ 
                               β 
                               ⁢ 
                               m 
                             
                           
                           
                             0 
                           
                           
                             
                               
                                 - 
                                 sin 
                               
                               ⁢ 
                               β 
                               ⁢ 
                               m 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             1 
                           
                           
                             0 
                           
                         
                         
                           
                             
                               sin 
                               ⁢ 
                               β 
                               ⁢ 
                               m 
                             
                           
                           
                             0 
                           
                           
                             
                               cos 
                               ⁢ 
                               β 
                               ⁢ 
                               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 rotates from the reference state (αq0, 0, 0) to (αq, βq, γq) in the XYZ-coordinate system, the point fixed in the XYZ-coordinate system rotates 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 
                                 
                               
                               ) 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               cos 
                               ⁢ 
                               β 
                               ⁢ 
                               q 
                             
                           
                           
                             0 
                           
                           
                             
                               sin 
                               ⁢ 
                               β 
                               ⁢ 
                               q 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             1 
                           
                           
                             0 
                           
                         
                         
                           
                             
                               
                                 - 
                                 sin 
                               
                               ⁢ 
                               β 
                               ⁢ 
                               q 
                             
                           
                           
                             0 
                           
                           
                             
                               cos 
                               ⁢ 
                               β 
                               ⁢ 
                               q 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               cos 
                               ⁢ 
                               γ 
                               ⁢ 
                               q 
                             
                           
                           
                             
                               sin 
                               ⁢ 
                               γ 
                               ⁢ 
                               q 
                             
                           
                           
                             0 
                           
                         
                         
                           
                             
                               
                                 - 
                                 sin 
                               
                               ⁢ 
                               γ 
                               ⁢ 
                               q 
                             
                           
                           
                             
                               cos 
                               ⁢ 
                               γ 
                               ⁢ 
                               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 do not change 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 2 q−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 slightly performed around the W-axis from the reference state, how the length of each link changes 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. 
     
       
         
           
             
               
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     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   1z   2   −L   1q0   2 =( Dq 1*γ q ) 2 &gt;0
 
         L   2q   2   −L   2q0   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   3q   2   −L   3q0   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)
 
     From the above equations, in the case that 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 that Wq2*sin(π/6)−Dq2*cos (π/6)&lt;0 and Wq3*sin(π/6)−Dq3*cos(π/6)&lt;0 hold, it is understood that 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 when the rotation is performed by a small angle around the W-axis from the reference state. As shown in  FIG.  85   , the angle formed by line segment P 0q P 2q0  and the V-axis and the angle formed by the line P 0q P 3q0  and the V-axis are larger 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 of the ordinary fingers can be bent, so that the fingers can hold a thin paper or the like by sandwiching the thin paper with extended fingertips. The fingers may previously be disposed so that one finger is opposed to other fingers without including opposable finger  97 . The number of fingers need not 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 disposition of the gear in the joint is not necessary, and the joint can be made compact. The joint has the rotational degree of freedom of the same order as a human, humanoid robot  100  can make the similar motion to a human. 
     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 a worm gear mechanism in which a worm and a worm wheel are used, so that strong 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. When the electric power supply is interrupted, gripping force can be maintained by the worm gear mechanism. 
     The humanoid robot according to the present disclosure has a structure enabling the motion close to a human. Consequently, the humanoid robot can perform work performed by an ordinary person. When artificial intelligence is installed, it is understood that the humanoid robot can be used in industry, an aging society, and solving labor shortage. In particular, it is estimated that the humanoid robot can be used to solve the labor shortage in simple work and work that is performed under the environment that is severe for a human to stay for a long time (radiation environment, high-temperature environment, low-temperature environment, and the like). 
     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 rotate in conjunction with the third finger joint, or can rotate 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 above is also applied to other embodiments. 
     Second Embodiment 
     In a second embodiment, knee drive link  42 L that drives knee joint  40  is connected only to lower leg  11 .  FIG.  86    is a perspective view illustrating a humanoid robot  100 X according to the second embodiment of the present disclosure  FIGS.  87 ,  88  and  89    are a front view, a left side view, and a rear view of humanoid robot  100 X, respectively. 
     In humanoid robot  100 X, one end of knee drive link  42 L is not attached to a thigh  10 X. One end of knee drive link  42 L is attached only to a lower leg  11 X. In humanoid robot  100 X, a knee joint  40 X is largely bent until thigh  10 X and lower leg  11 X become substantially parallel, sometimes sufficient force for extending knee joint  40 X cannot be obtained. When the posture that knee joint  40 X is largely bent is not necessary, humanoid robot  100 X can be used similarly to humanoid robot  100  of the first embodiment. The structure of knee joint  40 X is simplified in humanoid robot  100 X, so that humanoid robot  100  can be manufactured at a lower cost than humanoid robot  100 . 
     Third Embodiment 
     In a third embodiment, an actuator that changes the angle formed by the toe and the foot main body is provided.  FIGS.  90 ,  91 ,  92 , and  93    are a plan view, a left side view, a front view, and a perspective view illustrating the left foot of a humanoid robot  100 Y according to a third embodiment of the present disclosure. 
     A foot  12 Y of humanoid robot  100 Y has a toe drive actuator  47  that changes the angle formed by foot main body  12 A and toe  12 B. Toe drive actuator  47  is disposed on the side existing toe  12 B of foot  12 Y longitudinally side by side with ankle joint  41 . A foot-main-body-side link attaching unit J 43  is provided in foot main body  12 A. One end of toe drive link  47 L is attached rotatably to foot-main-body-side link attaching unit J 43 . A toe-side link attaching unit J 44  being attached rotatably with the other end of toe drive link  47 L is provided in toe  12 B. In foot-main-body-side link attaching unit J 43  and toe-side link attaching unit J 44 , toe drive link  47 L is attached with one rotational degree of freedom around the rotation axis parallel to the right and left direction of foot  12 Y. A motor  47 M is disposed above toe drive link  47 L. 
     An intra-foot bending unit C 10  connects toe  12 B rotatably to foot main body  12 A. Toe  12 B is connected to the front of foot main body  12 A. Intra-foot bending unit C 10  includes a toe joint  12 C, toe drive actuator  47  including toe drive link  47 L and motor  47 M, toe-side link attaching unit J 44  provided in toe  12 B, and foot-main-body-side link attaching unit J 43  provided in foot main body  12 A. Toe joint  12 C connects toe  12 B and foot main body  12 A with one rotational degree of freedom. Toe drive link  47 L is located above toe  12 B and foot main body  12 A, and the length of toe drive link  47 L can be changed. One end of toe drive link  47 L is attached rotatably to toe-side link attaching unit J 44 . The other end of toe drive link  44 L is attached rotatably to foot-main-body-side link attaching unit J 43 . 
     When toe drive link  47 L is shortened, the angle formed by toe  12 B and foot main body  12 A is decreased, and toe  12 B moves upward. When toe drive link  47 L is lengthened, the angle formed by toe  12 B and foot main body  12 A is increased, and toe  12 B moves downward. 
     Since foot  12 Y includes toe drive link  47 L, the angle between toe  12 B and foot main body  12 A can be set to the designated angle. Consequently, when humanoid robot  100 Y walks or runs, the motion of humanoid robot  100 Y can be made closer to human motion. 
     When the space where toe drive actuator  47  is disposed in foot  12  is insufficient, the force changing the angle of toe joint  12 C may be transmitted from a motor or the like provided in lower leg  11  or the like using a wire or the like. 
     Fourth Embodiment 
     In a fourth embodiment, a hydraulic mechanism is used for the variable length link. A humanoid robot  100 Z includes an actuator in which the hydraulic mechanism is used.  FIG.  94    is a cross-sectional view illustrating a structure of the variable length link of the actuator included in the humanoid robot according to the fourth 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 moves inside of 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. 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 moves 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 moves in the direction away from chest-side center link attaching unit J 5 . When no liquid moves 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. 
     Fifth Embodiment 
     In a fifth embodiment, the humanoid robot includes a hand including an opposed finger that is always opposed to the ordinary fingers instead of the opposable finger.  FIG.  95    is a perspective view illustrating a left hand  9 A included in a humanoid robot according to the fifth embodiment viewing from the backside of the hand.  FIG.  96    is a perspective view illustrating left hand  9 A viewing from the palm side.  FIGS.  97 ,  98 , and  99    are a front view of left hand  9 A, a side view of left hand  9 A viewing from the side existing first finger  83 , 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.  100    is a side view illustrating left hand  9 A viewing from the fingertip side.  FIG.  101    is a side view illustrating left hand  9 A viewing from the wrist side.  FIG.  102    is a side view illustrating left hand  9 A viewing from the side existing the first finger when an opposed finger  87  is bent. In  FIG.  101   , 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 the 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 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. 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.  103    is a plan view illustrating the palm plate of the left hand. As illustrated in  FIG.  103   , in palm plate  82 , substantially rectangular portions being attached with first finger  83 , second finger  84 , third finger  85 , fourth finger  86 , and opposed finger  87  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 existing first finger attaching part  82 A 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 base being provided separately for each finger and being connected with the first dactylus of the finger. Palm plate main body  82 F is a main body being connected with the finger bases. 
     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 so as to be oriented toward the same directions as first finger  83 , second finger  84 , third finger  85 , and fourth finger  86 , respectively. 
     Between palm plate main body  82 F and 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, a width decreasing portion having a narrowed width in the hand breadth direction orthogonal to the fingertip direction is interposed to connect each of first finger attaching part  82 A, second finger attaching part  82 B, third finger attaching part  82 C, or fourth finger attaching part  82 D to palm plate main body  82 F. For this reason, a notch or 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 not existing second finger attaching part  82 B. 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  82 J,  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 not existing third finger attaching part  82 C. 
     Notches  82 H,  82 J,  82 K,  82 L,  82 M,  82 N have the same shape. Notches  82 H,  82 J are connected with a straight line. 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. 
     The widths in the hand breadth direction 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 are the same, and the widths of the width decreasing portions are also the same. The width decreasing portion is the place in which the notch or the difference in width is provided. 
     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 existing 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.  103   , a hole or the like used to attach the member to the 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 , it becomes easier to grip the object to be enfolded by palm plate  82  compared with the case that 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.  99   , 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. 
     The structure of opposed finger  87  in which hand  9 A differs largely from hand  9  is described. Opposed finger  87  is provided on the palm side of palm plate  82  such that the fingertip extends in the direction intersecting palm plate  82 . Opposed finger  87  is provided so as to face 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 existing first finger  83  of palm plate  82 . The direction in which opposed finger  87  rotates is the direction intersecting first finger  83  and second finger  84 . As illustrated in  FIG.  97   , when the angle between opposed finger  87 , being extended, and palm plate  82  is decreased, the fingertip moves in the direction approaching 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 close 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 rotates first dactylus  87 A, the direction in which second finger joint  87 E rotates 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 more properly grip the object as compared with hand  9 . 
     Regarding the adjacent two of palm plate  82 , first dactylus  87 A, second dactylus  87 B, and third dactylus  87 C, one member provided on the side close to palm plate  82  is referred to as a base-side member, and the other member provided on the side not existing the base-side member 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 that is 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 move 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 move 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 easily to generate force against force separating finger first motor  87 H from palm plate  82 . 
     First dactylus  87 A is constructed with 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 rotates 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 integrally manufactured. First wheel linked part  87 AA is a polygon in which the side existing second finger joint  87 E is wider viewing from the side existing opposed finger  87 . First yoke  87 AB being two plate materials are screwed to first wheel linked part  87 AA on the side existing second finger joint  87 E. 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 vertically fixed 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 constructed with 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 rotates 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 existing third dactylus  87 C. 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 existing second finger joint  87 E, and is wide on the side existing third finger joint  87 F. 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. When 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, the angle at which second finger joint  87 E rotates 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 rotate around the rotation axis of second finger joint  87 E together with second dactylus  87 B. 
     Referring to  FIG.  104   , the gear that rotates third finger joint  87 F in conjunction with second finger joint  87 E is described.  FIG.  104    is an enlarged perspective view illustrating the 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 rotates 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 rotate in the opposite direction to idler gear  87 R. Outer-idler gear  87 SA and inner-idler gear  87 SB rotate around the same rotation axis. Inner-idler gear  87 SB meshes with a third dactylus drive gear  87 P that rotates around the rotation axis of third finger joint  87 F together with third dactylus  87 AC. Third dactylus drive gear  87 P rotates in the opposite direction to inner-idler gear  87 SB. Third dactylus drive gear  87 P rotates 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 as to become an appropriate value close to 1. 
     Idler gear  87 R is a gear that rotates 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 rotates 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 is constructed with 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 rotates 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 easily be replaced 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 fixing unit  83 V. First motor fixing unit  83 V is a rectangular parallelepiped box. First motor fixing unit  83 V is attached to first finger attaching part  82 A. In first motor fixing unit  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 fixing unit  83 V is seen obliquely when viewed from the side. First motor fixing unit  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 fixing unit  83 V and palm plate  82 B. 
     Finger first motor  83 H and first motor fixing unit  83 V can be fixed with increased rigidity by fixing finger first motor  83 H perpendicularly to first motor fixing unit  83 V. 
     First worm  83 J meshes with first worm wheel  83 K that rotates around the rotation axis held by finger base yoke  83 G. First dactylus  83 A rotates 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 motion 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 a worm gear mechanism in which a worm and a worm wheel are used, so that strong 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. 
     In addition to first finger joint  87 D, opposed finger  87  also includes second finger joint  87 E and third finger joint  87 F, which have the rotation axis parallel to first finger joint  87 D, so that the object can be held by bending second finger joint  87 E as illustrated in FIG.  102 . 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 third dactylus  83 C face palm plate  92 . In holding the object between first finger  83  or other first dactyli and palm plate  92 , a member that prevents first worm  83 J or the like from coming into contact 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. 
     Sixth Embodiment 
     In a sixth embodiment, the fifth embodiment is changed such that the humanoid robot includes the hand including a hand breadth rotation finger in which the entire finger rotates in the hand breadth direction instead of the opposed finger.  FIG.  105    is a perspective view illustrating a left hand  9 B included in a humanoid robot according to the sixth embodiment when a hand breadth rotation finger  88  extends viewing from the backside of the hand.  FIG.  106    is a perspective view illustrating left hand  9 B when hand breadth rotation finger  88  is directed in the direction intersecting palm plate  82  viewing from the backside of the hand.  FIGS.  107 ,  108 ,  109 ,  110 , and  111    are a front view illustrating left hand  9 B, a side view illustrating left hand  9 B viewing from the side existing first finger  83 , a rear view, a side view illustrating left hand  9 B viewing from the side existing fourth finger  86 , and a side view illustrating left hand  9 B viewing from the fingertip side, respectively, when hand breadth rotation finger  88  extends.  FIGS.  112 ,  113 ,  114 ,  115 , and  116    are a front view illustrating left hand  9 B, a side view illustrating left hand  9 B viewing from the side existing first finger  83 , a rear view, a side view illustrating left hand  9 B viewing from the side existing fourth finger  86 , and a side view illustrating left hand  9 B viewing from the fingertip side, respectively, when hand breadth rotation finger  88  is directed in the direction intersecting palm plate  82 .  FIGS.  117  and  118    are enlarged perspective views of hand breadth rotation finger  88 .  FIG.  117    is a perspective view illustrating hand breadth rotation finger  88  when hand breadth rotation finger  88  extends.  FIG.  118    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.  105  to  118   , 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 fifth embodiment. The cover and the like omitted in  FIGS.  95  to  104    of the fifth embodiment are also illustrated in  FIGS.  105  to  118   . 
     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 in which a substantially rectangular plate material is bent into a U-shape. The substantially rectangular plate has 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 second worm wheel  83 N and components that exist in a portion not being sandwiched between two plates materials included in second dactylus  83 B, that are, partial gear  83 Q, idler gear  83 R, outer-idler gear  83 SA, and the like. 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 in 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 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 rotate 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 existing first finger attaching part  82 A 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 rotate 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 easily held 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. The side surface on the wrist side has a shorter side near the attaching surface to palm plate  82  in the trapezoidal shape 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 motion 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 a worm gear mechanism in which a worm and a worm wheel are used, so that strong 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 rotates 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. 
     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 X,  100 Y,  100 Z: humanoid robot 
               1 : trunk 
               2 : head (second member) 
               2 A: head base plate 
               3 : upper limb 
               4 ,  4 X: lower limb 
               5 : chest (first member, second member) 
               5 U: chest upper portion 
               5 D: chest lower portion 
               6 : waist (first member) 
               7 : upper arm 
               7 A: actuator holder 
               8 : forearm (first member, torsion axis) 
               9 ,  9 A,  9 B: hand (second member) 
               10 ,  10 X: 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 ,  11 X: lower leg 
               12 ,  12 Y: 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 
               14 : upper arm drive main actuator 
               14 L: upper arm drive main link 
               14 M: motor (power source) 
               15 : upper arm drive auxiliary actuator 
               15 L: upper arm drive auxiliary link 
               15 M: motor (power source) 
               16 : intrathoracic joint 
               17 : intrathoracic actuator 
               17 L: intrathoracic link 
               17 M: motor (power source) 
               18 : thoracolumbar joint 
               19 : thoracolumbar center actuator 
               19 A: screw rod 
               19 B: nut 
               19 C: cylinder 
               19 D: nut position fixing unit 
               19 E: nut rotation holding unit 
               19 F: nut gear 
               19 G: drive gear 
               19 L: thoracolumbar center link (variable length link) 
               19 Z: thoracolumbar center actuator 
               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) 
               20 : thoracolumbar right actuator 
               20 L: thoracolumbar right link (variable length link) 
               20 M: motor (power source) 
               21 : thoracolumbar left actuator 
               21 L: thoracolumbar left link (variable length link) 
               21 M: motor (power source) 
               22 : hip 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 
               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 
               32 : elbow drive outside link 
               33 : elbow drive inside Link 
               34 : upper arm outside actuator 
               34 A: screw rod 
               34 B: nut 
               34 C: rail 
               34 D: gripper 
               34 M: motor (power source) 
               35 : upper arm inside actuator 
               35 A: screw rod 
               35 B: nut 
               35 C: rail 
               35 D: gripper 
               35 M: motor (power source) 
               36 : wrist joint 
               37 : forearm front actuator 
               37 L: forearm front link (variable length link) 
               37 M: motor (power source) 
               37 N: link attachment 
               38 : forearm outside actuator 
               38 L: forearm outside link (variable length link) 
               38 M: motor (power source) 
               38 N: link attachment 
               39 : forearm inside actuator 
               39 L: forearm inside link (variable length link) 
               39 M: motor (power source) 
               39 N: link attachment 
               40 ,  40 X: knee joint 
               41 : ankle joint 
               41 A: front-back rotation yoke 
               41 B: right-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) 
               47 : toe drive actuator 
               47 L: toe drive link 
               47 M: motor (power source) 
               51 : shoulder frame 
               52 : thorax frame 
               53 : thorax front-back coupling frame 
               54 : chest center coupling frame 
               55 : intrathoracic joint frame 
               56 : backbone (torsion axis, coupling rod) 
               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 base) 
               82 B: second finger attaching part (finger base) 
               82 C: third finger attaching part (finger base) 
               82 D: fourth finger attaching part (finger base) 
               82 E: opposed finger attaching part (finger base) 
               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 base) 
               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 T: second gear head 
               83 V,  84 V,  85 V,  86 V: first motor fixing unit 
               88 W: hand breadth finger base 
               83 X,  84 X,  85 X,  86 X,  88 X: first dactylus cover 
               83 Y,  84 Y,  85 Y,  86 Y,  88 Y: second dactylus cover 
               83 Z,  84 Z,  85 Z,  86 Z,  88 Z: second worm cover 
               91 : 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 
               97 U: 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 K: 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 
             J 2 : chest-side auxiliary link 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 6 : chest right link attaching unit (second-member-side link attaching unit) 
             J 7 : chest left link attaching unit (second-member-side link attaching unit) 
             J 8 : waist right link attaching unit (first-member-side link attaching unit) 
             J 9 : waist left link attaching unit (first-member-side link attaching unit) 
             J 10 : waist center link attaching unit (first-member-side link 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 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 
             J 21 : main-link-side auxiliary link attaching unit (upper-arm-drive-main-link-side auxiliary link attaching unit) 
             J 22 : upper arm outside link attaching unit (upper-arm-side link attaching unit) 
             J 23 : upper arm inside link attaching unit (upper-arm-side link attaching unit) 
             J 24 : elbow drive inside link attaching unit (forearm-side main link attaching unit) 
             J 25 : elbow drive outside link attaching unit (elbow-drive-main-link-side auxiliary link attaching unit) 
             J 26 : forearm front link attaching unit (first-member-side link attaching unit) 
             J 27 : forearm outside link attaching unit (first-member-side link attaching unit) 
             J 28 : elbow drive inside link attaching unit (first-member-side link attaching unit) 
             J 29 : hand-side front link attaching unit (second-member-side link attaching unit) 
             J 30 : hand-side outside link attaching unit (second-member-side link attaching unit) 
             J 31 : hand-side inside link attaching unit (second-member-side link 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) 
             J 43 : foot-main-body-side link attaching unit 
             J 44 : toe-side link attaching unit 
             C 1 : chest bending unit 
             C 2 : body bending unit (three-rotational-degree-of-freedom connection mechanism) 
             C 3 : neck (three-rotational-degree-of-freedom connection mechanism) 
             C 4 : shoulder 
             C 5 : elbow 
             C 6 : wrist (three-rotational-degree-of-freedom connection mechanism) 
             C 7 : crotch (three-rotational-degree-of-freedom connection mechanism) 
             C 8 : knee 
             C 9 : ankle 
             C 10 : intra-foot bending unit 
             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