Lie Group Representation of Kinematics and Dynamics of Manipulators
The D-H parameter method has found extensive application in the analysis of manipulator motion.However,it primarily describes motions along the x and z axes,neglecting the y-axis motion.To address this limitation,the screw theory method was emploied to represent the manipulator's position and orientation as a screw,conducting an in-depth analysis of its kinematics and dynamics.In con-trast to the traditional D-H approach for forward kinematics,screw theory offers a holistic depiction of the robot arm's motion,eliminating the necessity for an intermediate reference system with explicit geometric significance.To tackle the inverse kinematic problem of the el-bow robotic arm,the Paden-Kahan subproblem was applied,resulting in the computation of an inverse kinematics solution.Leveraging screw theory and Lie group-Lie algebra,the Newton-Euler approach was employed to construct an efficient recursive dynamic model.Ulti-mately,the manipulator's inverse kinematic solution derived through the screw theory was subjected to simulation and verification,with its workspace calculation revealing that the screw theory method offers a more concise,accurate,and effective approach.
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