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RESEARCH PAPERS

Forward/Reverse Velocity and Acceleration Analysis for a Class of Lower-Mobility Parallel Mechanisms

[+] Author and Article Information
Si J. Zhu

Robotics Research Center, Mechanical Engineering College, Yanshan University, Qinhuangdao City, Hebei 066004, P.R. Chinazhusj@ysu.edu.cn

Zhen Huang1

Robotics Research Center, Mechanical Engineering College, Yanshan University, Qinhuangdao City, Hebei 066004, P.R. Chinahuangz@ysu.edu.cn

Hua F. Ding

Robotics Research Center, Mechanical Engineering College, Yanshan University, Qinhuangdao City, Hebei 066004, P.R. Chinadhf@ysu.edu.cn

1

Corresponding author.

J. Mech. Des 129(4), 390-396 (Apr 11, 2006) (7 pages) doi:10.1115/1.2429698 History: Received June 08, 2005; Revised April 11, 2006

This paper proposes a novel kinematic analysis method for a class of lower-mobility mechanisms whose degree-of-freedom (DoF) equal the number of single-DoF kinematic pairs in each kinematic limb if all multi-DoF kinematic pairs are substituted by the single one. For such an N-DoF (N<6) mechanism, this method can build a square (N×N) Jacobian matrix and cubic (N×N×N) Hessian matrix. The formulas in this method for different parallel mechanisms have unified forms and consequently the method is convenient for programming. The more complicated the mechanism is (for instance, the mechanism has more kinematic limbs or pairs), the more effective the method is. In the rear part of the paper, mechanisms 5-DoF 3-R(CRR) and 5-DoF 3-(RRR)(RR) are analyzed as examples.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Hessian for a 5-DoF mechanism

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Figure 2

Sketch of mechanism 3-R(CRR)

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Figure 3

Simulation of movable platform motion

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Figure 4

Angular kinematics simulation

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Figure 5

Linear kinematics simulation: (a) parallel mechanism 3-(RRR)(RR); (b) one (RRR)(RR) limb at a general configuration

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Figure 6

Sketch of 3-(RRR)(RR)

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