Type Synthesis of Parallel Mechanisms With a Constant Jacobian Matrix

Author:

Zhao Yanzhi1,Cao Yachao2,Kong Xianwen3,Zhao Tieshi1

Affiliation:

1. Parallel Robot and Mechatronic System Laboratory, Key Laboratory of Advanced Forging and Stamping Technology, Science of Ministry of National Education, Yanshan University, Qinhuangdao 066004, Hebei, China e-mail:

2. Parallel Robot and Mechatronic System Laboratory, Yanshan University, Qinhuangdao 066004, Hebei, China; School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510640, Guangdong, China e-mail:

3. School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK e-mail:

Abstract

Jacobian matrix plays a key role in the analysis, design, and control of robots. For example, it can be used for the performance analysis and evaluation of parallel mechanisms (PMs). However, the Jacobian matrix of a PM generally varies with the poses of the moving platform in the workspace. This leads to a nonconstant performance index of the PM. PMs with a constant Jacobian matrix have simple kinematics and are easy to design and control. This paper proposes a method for obtaining PMs with a constant Jacobian matrix. First, the criteria for detecting invariance of a Jacobian matrix are obtained based on the screw theory. An approach to the synthesis of PMs with a constant Jacobian matrix is then proposed. Using this approach, PMs with a constant Jacobian matrix are synthesized in two steps: the limb design and the combination of the limbs. Several PMs with a constant Jacobian matrix are obtained. In addition to the translational parallel mechanisms (TPMs) with a constant Jacobian matrix in the literature, the mixed-motion PMs whose moving platform can both translate and rotate with a constant Jacobian matrix are newly identified. The input/output velocity analysis of several PMs is presented to verify that Jacobian matrix of these PMs is constant.

Publisher

ASME International

Subject

Mechanical Engineering

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