Changes between Version 3 and Version 4 of Rehab/KinematicsJointRangesConversionFactors


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Timestamp:
Nov 3, 2016, 9:09:16 PM (2 years ago)
Author:
aj
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  • Rehab/KinematicsJointRangesConversionFactors

    v3 v4  
    44A good introduction to coordinate frames, transformations and kinematics is beyond the scope of this document. There are several good introductory robotics books available. We recommend Spong, M.; Hutchinson, S.; Vidyasagar, M. Robot Modeling and Control; 2006 John Wiley & Sons as we use the variant of the Denavit-Hartenberg (D-H)  method that is from this book to establish the coordinate frames.
    55
    6 Figure 1 below shows the Proficio in its zero position. A positive joint motion is based on the right hand rule for each axis.
     6D-H frames are defined roughly as shown in Figure 1 when the robot is in its zero position (NOT the robot’s home position). Note that the joint range of Joint 3 (Table 2) prevents the Proficio from actually reaching this position. Frames 0 and 1 are located at the intersection of the J1 and J2 axes. Frame 2 is coincident to the J3 axis. The frame 3 origin is coincident to the center of the haptic ball when it points straight up. The D-H parameters do not change between left- and right-handed configurations. However, the configuration files do contain separate world-to-base transforms for each configuration. These transforms define the origin of the world frame to be at the user’s sternum, 540 mm from the X1-Z1 plane along Z0. The diagram shows the locations of the world origin in left-handed and right-handed robot configurations. A positive joint motion is based on the right hand rule for each axis.
    77
    88{{{
     
    1212'''Figure 1: Proficio D-H frames'''
    1313}}}
    14 
    1514
    1615Equation 1 below gives the transform between two adjacent D-H coordinate frames. The D-H parameters that were derived from this equation are located in Table 1 below. Note that c and s stand for cos and sin respectively.
     
    7069}}}
    7170
    72 '''Forward Kinematics for the 4-DOF WAM'''
     71'''Forward Kinematics for the Proficio'''
    7372
    74 The forward kinematics of the 4-DOF WAM system is used to determine the end tip location and orientation. These transformations are generated using the parameters in Table 1 and the matrix in Equation 1.
     73The forward kinematics of the Proficio are used to determine the end tip location and orientation. These transformations are generated using the parameters in Table 1 and the matrix in Equation 1.
     74
     75The forward kinematics are determined for any frame on the robot by mulitplying all of the transforms up to and including the final frame. To determine the endpoint location and orientation use the following equation:
    7576
    7677{{{
     
    7879{{{
    7980#!latex
    80 $^{4}T_{tool}=\left[\begin{array}{cccc}
    81 u_{x} & v_{x} & w_{x} & P_{x}\\
    82 u_{y} & v_{y} & w_{y} & P_{y}\\
    83 u_{z} & v_{z} & w_{z} & P_{z}\\
    84 0 & 0 & 0 & 1\end{array}\right]$
     81$^{0}T_{3}=^{0}T_{1}^{1}T_{2}^{2}T_{3}^{3}$
    8582}}}
    8683 
    87 '''Equation 3: Tool frame matrix'''
    88 }}}
    89 
    90 You define the   frame for your specific end-effector. The forward kinematics are determined for any frame on the robot by mulitplying all of the transforms up to and including the final frame. To determine the tool end tip location and orientation use the following equation:
    91 
    92 {{{
    93 #!div class="center" align="center"
    94 {{{
    95 #!latex
    96 $^{0}T_{Tool}=^{0}T_{1}^{1}T_{2}^{2}T_{3}^{3}T_{4}^{4}T_{Tool}$
    97 }}}
    98  
    99 '''Equation 4: Tool end tip position and orientation equation for the 4-DOF WAM'''
    100 }}}
    101 
    102 '''Forward Kinematics for the 7-DOF WAM'''
    103 
    104 As with the previous example, you define the   frame for your specific end-effector. The forward kinematics are determined for any frame on the robot by mulitplying all of the transforms up to and including the final frame. To determine the end tip location and orientation use the following equation:
    105 
    106 {{{
    107 #!div class="center" align="center"
    108 {{{
    109 #!latex
    110 $^{0}T_{Tool}=^{0}T_{1}^{1}T_{2}^{2}T_{3}^{3}T_{4}^{4}T_{5}^{5}T_{6}^{6}T_{7}^{7}T_{Tool}$
    111 }}}
    112  
    113 '''Equation 5: Tool end tip position and orientation equation for the 7-DOF WAM'''
     84'''Equation 3: Tool end tip position and orientation equation for the Proficio'''
    11485}}}
    11586
     
    213184}}}
    214185
    215 == Joint Resolution ==
    216 {{{
    217 #!div class="center" align="center"
    218 '''Table 9: Joint resolution'''
    219 || ||'''Motor Encoder[[BR]](ME) Cts/Rev'''||'''Motor/Joint[[BR]]Ratio'''||'''ME Cts/[[BR]]Joint Rev'''||'''Joint Encoder[[BR]](JE) Cts/Rev'''||'''Meters/[[BR]]Joint Rev'''||'''ME Position[[BR]]Resolution (m)'''||'''ME Orientation[[BR]]Resolution (rad)'''||'''JE Position[[BR]]Resolution (m)'''||'''JE Orientation[[BR]]Resolution (rad)'''||
    220 || '''J1''' || 4096|| 42|| 172,032|| 1,578,399|| 6.28|| 36.5E-6|| 36.5E-6|| 4.0E-6|| 4.0E-6||
    221 || '''J2''' || 4096|| 28.25|| 115,712|| 655,360|| 6.28|| 54E-6|| 54E-6|| 9.6E-6|| 9.6E-6||
    222 || '''J3''' || 4096|| 16.8|| 68,812|| 655,360|| 3.14|| 45E-6|| 91E-6|| 4.8E-6|| 9.6E-6||
    223 || '''J4''' || 4096|| 18|| 73,728|| 327,680|| 3.14|| 42.6E-6|| 85.2E-6|| 9.6E-6|| 19.2E-6||
    224 || '''J5''' || 4096|| 9.48|| 38,830|| N/A|| 376.8E-3|| 9.7E-6|| 161.7E-6|| N/A|| N/A||
    225 || '''J6''' || 4096|| 9.48|| 38,830|| N/A|| 376.8E-3|| 9.7E-6|| 161.7E-6|| N/A|| N/A||
    226 || '''J7''' || 4096|| 14.93|| 61,153|| N/A|| 0|| N/A|| (backlash) 17.5E-3|| N/A|| N/A||
    227 }}}