Changes between Version 2 and Version 3 of Burt-Research/KinematicsJointRangesConversionFactors


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Timestamp:
Dec 29, 2016, 9:38:27 PM (8 years ago)
Author:
aj
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  • Burt-Research/KinematicsJointRangesConversionFactors

    v2 v3  
    33A 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.
    44
    5 D-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.
     5D-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 BURT 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.
    66
    77{{{
    … …  
    99[[Image(htdocs:therapy/DHFramesSm.PNG)]]
    1010
    11 '''Figure 1: Proficio D-H frames'''
     11'''Figure 1: BURT D-H frames'''
    1212}}}
    1313
    … …  
    2727'''Equation 1: D-H generalized transform matrix'''
    2828
    29 '''Table 1: Proficio frame parameters'''
     29'''Table 1: BURT frame parameters'''
    3030||i||a,,i,,||α,,i,,||d,,i,,||θ,,i,,||
    3131||1||0||π/2||0||θ,,1,,||
    … …  
    6868}}}
    6969
    70 '''Forward Kinematics for the Proficio'''
     70'''Forward Kinematics for BURT'''
    7171
    72 The 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.
     72The forward kinematics of BURT 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.
    7373
    7474The 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:
    … …  
    8181}}}
    8282 
    83 '''Equation 3: Tool end tip position and orientation equation for the Proficio'''
     83'''Equation 3: Tool end tip position and orientation equation for BURT'''
    8484}}}
    8585