Simplified Jacobian Analysis for Parallel Robots with Regular Limbs

doi:10.3901/JME.2016.09.036

Abstract

Abstract: Jacobian is significant to the analysis of kinematics, precision and stiffness of parallel manipulators. Usually the wrench, which is reciprocal to all the twists in a limb except the twist of the actuated joint, is needed for Jacobian analysis. The procedure to calculate this wrench, however, is quite complex. Hence, for the particular limb structures commonly used in parallel robots, a novel concept about the regular limbs is presented, and the limb structural characteristics are summarized. The actuating wrenches of the revolute and prismatic joints are studied, and the approach to simplify the Jacobian analysis of parallel robots is proposed based on the actuating wrenches, which overcomes the complex procedure in existing methods to calculate the limb constraint wrench produced by the actuated joint. The partial Jacobian matrix can be obtained without the calculation of the limb constraint wrenches, and the overall Jacobian matrix can be derived with these limb constraint wrenches to perform the kinematic and static bijection between actuated joints and the moving platform. The proposed method can not only apply to the common 6 DOF parallel robots, but also apply to the lower mobility parallel robots with regular limbs.

Key words: actuating wrenches, Jacobian, parallel manipulators, screw theory, twists

CLC Number:

TH112

BU Wanghui, ZHENG Yuxin, ZHANG Pan, HUA Binbin. Simplified Jacobian Analysis for Parallel Robots with Regular Limbs[J]. Journal of Mechanical Engineering, 2016, 52(9): 36-41.

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