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Research Papers: Mechanisms and Robotics

Disturbed Configuration Bifurcation Characteristics of Gough–Stewart Parallel Manipulators at Singular Points

[+] Author and Article Information
Yu-Xin Wang1

College of Machine and Energy, Zhejiang University, Hangzhou 310027, P.R. Chinastratẖtj@hotmail.com

Yu-Tong Li

College of Machine and Energy, Zhejiang University, Hangzhou 310027, P.R. China

1

Corresponding author.

J. Mech. Des 130(2), 022304 (Dec 27, 2007) (9 pages) doi:10.1115/1.2813784 History: Received August 17, 2006; Revised April 16, 2007; Published December 27, 2007

In this paper, the disturbed configuration bifurcation characteristics of Gough–Stewart parallel manipulators at singular points are investigated. At first, the expended equation corresponding with the kinematics equation of the manipulator is introduced for eliminating the rank reduction and obtaining all of the theoretical singular points. Then, the assembly configurations at the singular points and the configuration bifurcation characteristics near them have been studied. It is found that the configuration bifurcation characteristics at the singular points belong to the turning point type through the Golubitsky–Schaeffer normal form identification. Next, utilizing the universal unfolding approach, the configuration bifurcation characteristics under the perturbation parameters applied to the extendable legs are analyzed. The investigation reveals that all configuration branches converged in the same singular point in the unperturbed system will be separated in the disturbed system. Based on this discovery, a novel approach for the parallel manipulator to pass through the singular points with a desired configuration is presented. The method presented in this paper can be utilized as the singularity avoidance approach for the parallel manipulators with strict trace and exact orientation control requirements, such as virtual parallel machine tools.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

A 6-SPS Gough–Stewart manipulator

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Figure 2

Assembly configuration at different singular points. (a) Assembly configuration at the singular point M1. (b) Assembly configuration at the singular point M2. (c) Assembly configuration at the singular point M3. (d) Assembly configuration at the singular point M4.

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Figure 3

Configuration bifurcation characteristics at M1 and M4

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Figure 4

Configuration bifurcation characteristics at the singular point M1(x10={0.2228,−0.4422,0.1272,−73.0075deg,35.9255deg,2.3552deg}T,μ10={1.146,2,2,2,2,2}T)

Grahic Jump Location
Figure 5

Perturbed configuration bifurcation characteristics at the singular point M1(l10=1.1460536, l20=1.99996, l30=2.000109, l40=2.0005, l50=2.0005, l60=1.9999)

Grahic Jump Location
Figure 6

A possible perturbed method to avoid turning point singularity

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