Abstract:
The anthropomorphic force-reflective master arm is a light, anthropomorphic, back-drivable, six degree of freedom (DOF) master arm designed to control the motion of a remote slave device having arbitrary structure. Three of the link members are rotationally coupled to each other to form a handle, such that axes of rotation of each of the handle link members intersects at the user&#39;s hand position. The kinematics of the master arm is simplified to two independent sub-systems, which are the hand position and hand orientation.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application is a continuation-in-part of U.S. patent application Ser. No. 12/289,792, filed Nov. 4, 2008. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    The present invention relates to robotic control systems, and particularly to an anthropomorphic force-reflective master arm that allows a human operator to map his hand motion to a remote slave tool in unstructured environments in which autonomous robots cannot be used. 
         [0004]    2. Description of the Related Art 
         [0005]    It is often necessary that a human operator manually control the motion of a remote tool being held by an arbitrary slave device, e.g., a robotic arm manipulating a device outside a satellite in space, an underwater robotic arm, etc. The remote slave device is sometimes located in a hostile or unstructured environment, which justifies the need to keep the human operator in a safe remote location. The interconnection between the human interface system and the slave device is arbitrary, and may use a dedicated or public network. The interface is designed to permit the operator hand-operated translation and rotation of the control, and to transmit such changes to the slave device so that the changes are superimposed to a current tool position and orientation. 
         [0006]    An improvement to this human interface would provide the capability to simultaneously measure all hand changes in position and orientation in order to minimize the number of iterations needed for tool set up in a desired configuration. Forces and torques exerted on the tool by a workpiece would be streamed from the slave device to reflect back on the operator&#39;s hand. The interface must provide force feedback to let the operator feel the forces displayed on its motors. An increased force feedback gain is desired to provide acceptable fidelity and sensitivity to small force/torque feedback magnitudes because the interface inertia felt at the operator hand must be very small. 
         [0007]    Thus, an anthropomorphic force-reflective master arm solving the aforementioned problems is desired. 
       SUMMARY OF THE INVENTION 
       [0008]    The anthropomorphic force-reflective master arm is a lightweight, backdrivable, six degree of freedom robotic arm that can serve as a master arm to control the motion of a remote slave arm. The master arm includes up to six serially connected rotary joints that extend from a grounded base to a handle that can be grasped and manipulated by an operator. The grounded base houses six motors. The position of operator hand origin depends only on the first three rotary joints (nearest to the base). The last three rotary joints (nearest to the handle) have concurrent rotation axes that intersect at the operator hand origin and are used for rendering the rotation of the operator&#39;s hand. 
         [0009]    A lightweight, balanced mechanism is used for the last three rotary joints, which are arranged to directly measure operator forearm rotation, operator horizontal elevation, and operator vertical elevation, respectively. The operator feels the same impedance in all rotational directions due to the balanced mechanism in the last three rotary joints, which improves force feedback fidelity. This arrangement uncouples hand translation from hand orientation. 
         [0010]    Since the motors are grounded at the base, a back drivable transmission uses pre-tensioned cable and lightweight pulleys to connect each motor to its corresponding joint. The fidelity and reversibility of the transmission mechanism facilitates the display of kinesthetic force feedback on the operator hand. The master arm provides a singularity-free mechanism to render the operator hand motion and map it to a remote tool while providing a high fidelity kinesthetic force display. The master arm weighs three kilograms, has more than one cubic meter of work envelope, and has better similarity to the human arm than previous designs. 
         [0011]    Sensors determine movement of the handle and transmit corresponding signals to a control computer. The control computer maps movement of the handle to a remote slave arm. Similarly, sensors at the remote slave arm determine reactive forces resulting from the mapped movement of the slave arm and transmit corresponding signals to the control unit. The control unit sends corresponding signals to activate the motors at the base of the master arm to reflect the forces encountered by the slave arm to the handle, so that the operator senses reaction of the workpiece to movement of the slave arm as though the operator were manipulating the slave arm directly. 
         [0012]    These and other features of the present invention will become readily apparent upon further review of the following specification and drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0013]      FIG. 1  is a perspective view of an anthropomorphic force-reflective master arm according to the present invention, the cables being omitted for clarity. 
           [0014]      FIG. 2  is a schematic view of the cable interlink transmission and motor configuration of the anthropomorphic force-reflective master arm according to the present invention. 
           [0015]      FIG. 3  is a perspective view of a cable guide system for degrees of freedom  4 ,  5  and  6  of an anthropomorphic force-reflective master arm according to the present invention. 
           [0016]      FIG. 4  is a perspective view of an alternative embodiment of an anthropomorphic force-reflective master arm according to the present invention. 
           [0017]      FIG. 5  is a schematic view of the cable interlink transmission and motor configuration of the anthropomorphic force-reflective master arm of  FIG. 4 . 
           [0018]      FIG. 6  is a partial schematic side view of a portion of the cable interlink transmission of  FIG. 5 . 
           [0019]      FIG. 7  diagrammatically illustrates joints, wheels, wire loops, and links of the anthropomorphic force-reflective master arm of  FIG. 4 . 
       
    
    
       [0020]    Similar reference characters denote corresponding features consistently throughout the attached drawings. 
       DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0021]    As shown in  FIG. 1 , the present invention relates to an anthropomorphic force-reflective robotic master arm (AFRMA)  10  that includes a plurality of links serially connected at rotary joints. The arm  10  extends from a base  12  to a handle  14  in a fashion similar to a human arm. A plurality of motors M 1  through M 6  are disposed on the base  12  by mounting blocks  206  to generate force/torque components according to feedback from a slave (remote) arm. Location of the motors M 1  through M 6  on the base  12  instead of at the rotational link joints improves the responsiveness of the arm  10 . 
         [0022]    In  FIG. 1 , a reducer pulley  202  is mounted on link L 1  and driven by motor M 1  using a flexible steel rope drive  203 . In the configuration shown, link L 1  has a hollow cylinder  230  extending axially between the link L 1  side arms. Ten cables extend through cylinder  230  to drive the five links L 2  through L 6 .  FIG. 4  shows a cable orientation schematic for an interlink transmission  1260  including the ten cables  2 ,  2 ′,  3 ,  3 ′,  4 ,  4 ′,  5 ,  5 ′ and  6 ,  6 ′, which are connected to threaded roller group A 2  through A 6  of  FIG. 4 . Each roller is mounted on a shaft of corresponding motor M 2  through M 6 , respectively. Further, cables  6 ,  6 ′ are associated with DOF 6  and connected to threaded wheel (pulley)  310 , which is shown in  FIG. 3 . A low-friction pulley mechanism is used to guide the cables  2  through  6 ′ from the motor rollers A 2 -A 6  to the interlink transmission and, more particularly, to small-diameter pulleys at each of the DOF 2 -DOF 6  rotational joints. A configuration similar to cylinder  1230  is provided for the cables to traverse the fourth link L 4  (of  FIG. 4 ). The pulley-drive orientation, which includes threaded wheels P 3  and P 4 , ensures the independence between the rotation of link L 1  and the subsequent five links L 2 -L 6 . 
         [0023]    The master arm  10  is sampled at regular time intervals by sensors connected to a control computer. Cartesian changes in operator hand position and orientation are transmitted to the control computer to map movement of a slave arm that may be kinematically different from the master arm  10 . All six rotatable joints are mechanically decoupled from each other and have no backlash due to the pre-tensioned transmission cables. A remote slave arm can respond by a motion that is a replica of operator hand motion driving the master arm  10 . 
         [0024]    The motors M 1 -M 6  of master arm  10  include threaded rollers  50  and are disposed on the fixed platform  12  to improve the dynamics of master arm  10 . Transmission cables interconnect motors M 1 -M 6  to pulleys at rotational joints DOF 1 -DOF 6 . To the extent practicable, the transmission cables associated with a first link having a specific rotational DOF extend near a rotation axis of a second, interconnected link in order to decouple rotation of the first link from rotation of the second, interconnected link. As shown in  FIG. 1 , the first L 1  and fourth L 4  links exemplify the aforementioned decoupled configuration. 
         [0025]    Each of the first transmission loops starts with a threaded roller mounted on the electric motor shaft. The transmission wire is freely wrapped three times around the roller along a machined deep thread. Embedding the wire in the thread will practically eliminate slippage. Both ends of the rope of the first transmission loops are wrapped around the driven threaded wheel at J 1 . Each wire is wrapped two times around the wheel to provide an acceptable range of motion (ROM) at the end link. In the final wrap, the rope is introduced through a specially designed inclined through-hole to be completely restrained from any slippage by a tightening screw device on the side of the wheel (not shown). 
         [0026]    Again referring to  FIG. 1 , a reducer pulley  202  is mounted on link L 1  and connected to motor M 1  using a flexible steel rope  203 . In the configuration shown, link L 1  has a hollow cylinder  230  extending axially between the link sidearms. Ten cables extend through cylinder  230  to drive the five links L 2  through L 6 .  FIG. 2  shows a cable orientation schematic for an interlink transmission  260  comprising the ten cables ( 2 ,  2 ′,  3 ,  3 ′,  4 ,  4 ′, and  5 ,  5 ′), which are connected to threaded roller group A 2  through A 6  of motor group  270 . Moreover cables  6 ,  6 ′ are associated with DOF 6  and connected to pulley  310 , which is shown in  FIG. 3 . A low friction pulley mechanism is used to guide the cables  2  through  5 ′ from the motor rollers A 4 -A 6  to the interlink transmission, more particularly, to small-dimensioned pulleys at each of the DOF 1 -DOF 6  rotational joints. A configuration similar to cylinder  230  is provided to traverse the fourth link L 4 . The pulley-drive orientation, which includes threaded wheels P 3  and P 4 , ensures the independence between the rotation of link L 1  and the subsequent five links L 2 -L 6 . 
         [0027]    The first link L 1  is driven by a single loop. The following links Li (i=2, 3, 4, 5, 6) are driven by a number (i−1) cable-threaded wheel (pulley) loop assemblies (CPLs). For example, link L 3  is driven by two independent CPLs; the first composed of wires  3 - 3 ′ starting at roller A 3  mounted on motor M 3  and ending at wheel P 3  in joint J 1 , and the second starting at wheel P 3 ′ (P 3 ′ is a smaller diameter wheel fixed to P 3 ) and ending on P 3 - 1  in J 2 . P 3 - 1  is fixed on link L 3  and drives it to execute DOF 3 . 
         [0028]    In this manner, the loops remain independent to reduce physical effort required to maintain the master arm  10  in a localized area, and to improve system reliability. The independence of the CPLs reduces the length of the wire limiting it to the distance between adjacent joints which will reduce wire elongation during operation of the arm. Pre-tensioning the wire is done independently for each loop. The independent pre-tensioned configuration of wires for each cable pulley loop CPL allows a high-speed, low (force) tension cable to be used for the first n−1 CPL&#39;s and, finally, a high (force) tension wire is used for the nth CPL connected to the corresponding link. 
         [0029]    The motor-link transmission  260  is based on a cable-pulley configuration that extends from a motor (one of M 2 -M 6 ) to a link (one of L 2 -L 6 ) through the hollow cylinders  230  and  240 , while uncoupling the transmitted motion from that of the traversed link. The motor-link transmission  260  is based on the cables  2  through  5 ′ being of a multiple, independent closed-loop variety. The connectivity between a motor (one of M 1 -M 6 ) and a link (one of L 1 -L 6 ) is achieved through multiple Cable Pulley Loop (CPL) mechanisms. Each CPL is an independent system. The transmission from motor to link is then achieved using an arbitrary subset of attached (pulley level) CPLs. The first loop L 1  transmits motion from the motor M 1  to the first link L 1  (DOF 1 ). In this and all other links, speed reduction is performed as close as possible to the intended driven link. 
         [0030]    Each loop starts with a threaded roller mounted on the electric motor shaft. The transmission wire is freely wrapped three times around the roller along a machined deep thread. The thread pitch and depth are selected according to the rope diameter. Embedding the wire in the thread will practically eliminate slippage. Both ends of the rope are wrapped around the driven threaded wheel. Each wire is wrapped two times around the wheel (pulley) to provide an acceptable range of motion (ROM) at the end link. In the final wrap, the rope is introduced through a specially designed inclined through-hole to be completely restrained from any slippage by a tightening screw device (not shown). 
         [0031]    The first link L 1  and the second link L 2  are driven by a single loop each. The following links (L 2  through L 6 ) are driven by L 1  cable pulley loop assemblies (CPLs). In this manner, the loops remain independent to reduce physical effort required to maintain the master arm  10  in a localized area, and to improve system reliability. Pre-tensioning the wire is done independently for each loop. The independent pre-tensioned configuration of wires for each loop (CPL) allows a high-speed, low (force) tension cable to be used for the first n−1 CPL&#39;s and, finally, a high (force) tension wire is used for the n th  CPL connected to the corresponding link. 
         [0032]    Due to the aforementioned configuration of drive motors M 1  through M 6  and transmission cables  203 ,  2 ,  2 ′,  3 ,  3 ′,  4 ,  4 ′,  5 ,  5 ′, and  6 , 6 ′, the master arm  10  has low friction, low inertia, and low mass. The motors M 1 -M 6  are disposed on the stable platform  12  to eliminate the potential of damaging the master arm  10  due to excess weight and inertia. Arm fidelity is improved to thereby more accurately transmit a reflected force feedback. Mounting all of the motors M 1  through M 6  on base  12  provides maximum possible force/torque dynamics, as well as enlarging the force transmission bandwidth. The force/torque vector exerted on a slaved tool is sensed by a force sensor, which is generally installed at the wrist of the slave arm. The sensed vector is used to compute the force/torque vector exerted on the slaved tool. The tool force/torque vector is sampled and transmitted at regular time intervals (streamed) to the master arm station, where it is converted into a motor torque vector that reproduces the tool force/torque vector at the operator hand center  14 . This allows the operator to feel the force/torque that is proportional to the one exerted on the remote tool. 
         [0033]    As most clearly shown in  FIG. 3 , the L 5  and L 6  link members have associated pulleys  305  and  310 , respectively. A user&#39;s hand grabs L 6 , which is a vertical member rotatably attached to and extending from L 5 . L 6  is responsive to a twist (yaw) motion of the hand, while pivotal bracket-shaped link L 5  is responsive to a pitch motion of the user&#39;s hand. Cable guides  300  are disposed on L 4  and are threaded onto threaded receivers  312 , making L 4  responsive to a rotation (roll) of the user&#39;s hand. 
         [0034]      FIGS. 4-7  illustrate an alternative embodiment of the anthropomorphic force-reflective robotic master arm (AFRMA)  100  that also includes a plurality of links serially connected at rotary joints. As in the previous embodiment, the arm  100  extends from a base  112  to a handle  114  in a fashion similar to a human arm. A plurality of motors M 101  through M 106  are disposed on the base  112  by mounting blocks  1206  to generate force/torque components according to feedback from a slave (remote) arm. Location of the motors M 101  through M 106  on the base  112  instead of at the rotational link joints improves the responsiveness of the arm  100 . 
         [0035]    In the alternative embodiment of  FIG. 4 , a motor rearrangement is utilized. The joints between links L 1  and L 2 , and links L 2  and L 3 , are identified as J 1  and J 2 , respectively. All the threaded wheels (pulleys) in joint J 1  are labeled as P 2  through P 6 . The cables are drawn from the threaded rollers mounted on shafts of motors M 2 -M 6  through the hollow cylinder  1230  to the intermediate and driven wheels in joint J 1 . 
         [0036]    The system of guiding wheels  1260  is identified in  FIG. 4  but is not shown for purposes of simplification. The details of guiding wheels  1260  are shown in  FIG. 5 . The cables are correlated with the motors in  FIG. 5  and attached to their outward pulleys in joint J 1 , making evident the first independent transmission cable loop. The system of pulleys  1260   FIG. 5  shows how the ropes are guided upon exiting the hollow cylinder  230  towards the threaded wheels of J 1 . 
         [0037]      FIG. 6  shows an example of the second transmission cable loop (multiple loops) driving DOF 3  at J 2  with the reduction performed at J 1 . Referring to  FIG. 7 , in joint J 1 , wheels P 3 , P 4 , P 5  and P 6  have corresponding wheels P 3 ′, P 4 ′, P 5 ′ and P 6 ′. Wheel P 2  has no P 2 ′, as it is directly attached to L 2 . J 1  has nine wheels (two for each of P 3 , P 4 , P 5 , and  6 ) and one for P 2 , which is attached to L 2 . J 2  has seven wheels (two for each of P 4 , P 5  and P 6 ) and one for P 3 , which is attached to L 3 . It should be noted that some wheels directly connect to their corresponding link; e.g., P 2  in J 1  and P 3  in J 2 . Two cable loops for DOF 5  and DOF 6  go through a set of guiding pulleys  1300  and end at the pulley set  1312 .  FIG. 7  also shows the details of  1312  and  1305  and their loop wiring to DOF 5  and DOF 6 . 
         [0038]    The master arm  100  is sampled at regular time intervals by sensors connected to a control computer. Cartesian changes in operator hand position and orientation are transmitted to the control computer to map movement of a slave arm that may be kinematically different from the master arm  100 . All six rotatable joints are mechanically decoupled from each other and have no backlash due to the pre-tensioned transmission cables. A remote slave arm can respond by a motion that is a replica of operator hand motion driving the master arm  100 . 
         [0039]    The motors M 011 -M 106  of master arm  100  include threaded rollers  150  and are disposed on the fixed platform  112  to improve the dynamics of master arm  100 . Transmission cables interconnect motors M 101 -M 106  to pulleys at rotational joints DOF 101 -DOF 106 . To the extent practicable, the transmission cables associated with a first link having a specific rotational DOF extend near a rotation axis of a second, interconnected link in order to decouple rotation of the first link from rotation of the second, interconnected link. As shown in  FIG. 4 , the first L 101  and fourth L 104  links exemplify the aforementioned decoupled configuration. 
         [0040]    Again referring to  FIG. 4 , a reducer pulley  1202  is mounted on link L 101  and connected to motor M 101  using a flexible steel rope  1203 . In the configuration shown, link L 101  has a hollow cylinder  1230  extending axially between the link sidearms. Ten cables extend through cylinder  1230  to drive the five links L 102  through L 106 .  FIGS. 5 and 6  show a cable orientation schematic for an interlink transmission  1260  comprising the ten cables ( 102 ,  102 ′,  103 ,  103 ′,  104 ,  104 ′, and  105 ,  105 ′), which are connected to threaded roller group A 102  through A 106  of motor group  1270 . Moreover cables  106 ,  106 ′ are associated with DOF 106  and connected to pulley  1310 , which is shown in  FIG. 7 . A low friction pulley mechanism is used to guide the cables  102  through  105 ′ from the motor rollers A 104 -A 106  to the interlink transmission, more particularly, to small-dimensioned pulleys at each of the DOF 101 -DOF 106  rotational joints. A configuration similar to cylinder  1230  is provided to traverse the fourth link L 104 . The pulley-drive orientation, which includes threaded wheels P 3  and P 4 , ensures the independence between the rotation of link L 101  and the subsequent five links L 102 -L 106 . 
         [0041]    The motor-link transmission  1260  is based on a cable-pulley configuration that extends from a motor (one of M 102 -M 106 ) to a link (one of L 102 -L 106 ) through the hollow cylinders  1230  and  1240 , while uncoupling the transmitted motion from that of the traversed link. The motor-link transmission  1260  is based on the cables  102  through  105 ′ being of a multiple, independent closed-loop variety. The connectivity between a motor (one of M 101 -M 106 ) and a link (one of L 101 -L 106 ) is achieved through multiple Cable Pulley Loop (CPL) mechanisms. Each CPL is an independent system. The transmission from motor to link is then achieved using an arbitrary subset of attached (pulley level) CPLs. The first loop L 101  transmits motion from the motor M 101  to the first link L 101  (DOF 101 ). In this and all other links, speed reduction is performed as close as possible to the intended driven link. 
         [0042]    Each loop starts with a threaded roller mounted on the electric motor shaft. The transmission wire is freely wrapped three times around the roller along a machined deep thread. The thread pitch and depth are selected according to the rope diameter. Embedding the wire in the thread will practically eliminate slippage. Both ends of the rope are wrapped around the driven threaded wheel. Each wire is wrapped two times around the wheel (pulley) to provide an acceptable range of motion (ROM) at the end link. In the final wrap, the rope is introduced through a specially designed inclined through-hole to be completely restrained from any slippage by a tightening screw device (not shown). 
         [0043]    The first link L 101  and the second link L 102  are driven by a single loop each. The following links (L 102  through L 106 ) are driven by L 101  cable pulley loop assemblies (CPLs). In this manner, the loops remain independent to reduce physical effort required to maintain the master arm  100  in a localized area, and to improve system reliability. Pre-tensioning the wire is done independently for each loop. The independent pre-tensioned configuration of wires for each loop (CPL) allows a high-speed, low (force) tension cable to be used for the first n−1 CPL&#39;s and, finally, a high (force) tension wire is used for the n th  CPL connected to the corresponding link. 
         [0044]    Due to the aforementioned configuration of drive motors M 101  through M 106  and transmission cables  1203 ,  102 ,  102 ′,  103 ,  103 ′,  104 ,  104 ′,  105 ,  105 ′, and  106 ,  106 ′, the master arm  100  has low friction, low inertia, and low mass. The motors M 101 -M 106  are disposed on the stable platform  112  to eliminate the potential of damaging the master arm  100  due to excess weight and inertia. Arm fidelity is improved to thereby more accurately transmit a reflected force feedback. Mounting all of the motors M 101  through M 106  on base  112  provides maximum possible force/torque dynamics, as well as enlarging the force transmission bandwidth. The force/torque vector exerted on a slaved tool is sensed by a force sensor, which is generally installed at the wrist of the slave arm. The sensed vector is used to compute the force/torque vector exerted on the slaved tool. The tool force/torque vector is sampled and transmitted at regular time intervals (streamed) to the master arm station, where it is converted into a motor torque vector that reproduces the tool force/torque vector at the operator hand center  114 . This allows the operator to feel the force/torque that is proportional to the one exerted on the remote tool. 
         [0045]    As most clearly shown in  FIG. 7 , the L 105  and L 106  link members have associated pulleys  1305  and  1310 , respectively. A user&#39;s hand grabs L 106 , which is a vertical member rotatably attached to and extending from L 105 . L 106  is responsive to a twist (yaw) motion of the hand, while pivotal bracket-shaped link L 105  is responsive to a pitch motion of the user&#39;s hand. Cable guides  1300  are disposed on L 4  and are threaded onto threaded receivers  1312 , making L 104  responsive to a rotation (roll) of the user&#39;s hand. 
         [0046]    The cable corresponding to DOF 106  goes through  1300  and ends at  1312 . The other wheel side of  1312  is cabled to upper wheel  1305  (which is formed as two wheels), which is also connected to  1310  through another cable loop. 
         [0047]    As shown in  FIGS. 4 and 7 , joint J 1  includes wheels P 3 , P 4 , P 5  and P 6  (which have corresponding wheels P 3 ′, P 4 ′, P 5 ′ and P 6 ′, as shown in  FIG. 7 , forming joint J 2 ). Wheel P 2  has no corresponding linkage wheel, as it is directly attached to L 102 . J 1  includes a total of nine wheels (two for each of P 3 , P 4 , P 5 , and P 6 ) and one for P 2 , which is attached to L 102 . J 2  has a total of seven wheels (two for each of P 4 ′, P 5 ′, and P 6 ′) and one for P 3 ′, which is attached to L 103 . It should be noted that some wheels directly connect to their corresponding link; e.g., P 2  in J 1  and P 3  in J 2 . 
         [0048]    In use, object orientation is uncoupled from object translation; i.e., where the object is held by a slave device controlled using Cartesian Coordinates by the master arm, the object changes its position accordingly when the operator only translates his or her hand in any direction without a change in object orientation. This has deep consequences on the quality of tele-operation, such as reducing the operator psychomotor effort. 
         [0049]    Further, the kinematics of the master arm are composed of two independent sub-systems: (1) the operator hand position (object position), which only depends on the first three master arm DOFs, and (2) the operator hand orientation (object orientation), which only depends on the last three DOFs of the master arm. 
         [0050]    Advantageously, the tele-operation targeting the setting of objects in a given geometric position and orientation requires a number of trials that is the minimum possible, as compared to any other master arm DOF arrangement having coupled positions and orientations. Further, in use, the operator feels the same mechanical impedance when rotating the hand grip in any direction of the last three rotary joints, which improves force feedback fidelity and the operator ability to identify the direction of a kinesthetic force which is displayed on the master arm. 
         [0051]    It should be noted that, in the above, the cable pulley loop (CPL) mechanism is formed by the transmission cable connections to the pulleys being multiple, independent, and closed loop. The motion of the links is achieved through multiple transmission loop mechanisms where the first link is driven by a single loop, and the subsequent links (Li) are driven by (i−1) independent loops. The independence of the loops is to minimize wire elongation during operation (increasing reliability) and reduce maintenance effort. 
         [0052]    It is to be understood that the present invention is not limited to the embodiment described above, but encompasses any and all embodiments within the scope of the following claims.