Mobility of Overconstrained Parallel Mechanisms

[+] Author and Article Information
Jian S. Dai

Department of Mechanical Engineering, School of Physical Sciences and Engineering, King’s College London, University of London, Strand, London, WC2R 2LS, United KingdomJian.Dai@KCL.ac.uk

Zhen Huang

Department of Mechanical Engineering, Yanshan University, PR Chinahuangz@ysu.edu.cn

Harvey Lipkin

Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405harvey.lipkin@me.gatech.edu

J. Mech. Des 128(1), 220-229 (Oct 14, 2004) (10 pages) doi:10.1115/1.1901708 History: Received June 17, 2004; Revised October 14, 2004

The Kutzbach–Grübler mobility criterion calculates the degrees of freedom of a general mechanism. However, the criterion can break down for mechanisms with special geometries, and in particular, the class of so-called overconstrained parallel mechanisms. The problem is that the criterion treats all constraints as active, even redundant constraints, which do not affect the mechanism degrees of freedom. In this paper we reveal a number of screw systems of a parallel mechanism, explore their inter-relationship and develop an original theoretical framework to relate these screw systems to motion and constraints of a parallel mechanism to identify the platform constraints, mechanism constraints and redundant constraints. The screw system characteristics and relationships are investigated for physical properties and a new approach to mobility analysis is proposed based on decompositions of motion and constraint screw systems. New versions of the mobility criterion are thus presented to eliminate the redundant constraints and accurately predict the platform degrees of freedom. Several examples of overconstrained mechanisms from the literature illustrate the results.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

The four basic screw subspaces in reciprocal pairs.

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Figure 4

4-UPU parallel mechanism

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Figure 5

3-RRRH parallel mechanism

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Figure 6

4-RPUR parallel mechanism

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Figure 7

3-RPS parallel mechanism

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Figure 3

3-RR(RRR) parallel mechanism



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