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Research Papers

A New Approach for Singularity Analysis and Closeness Measurement to Singularities of Parallel Manipulators

[+] Author and Article Information
Xin-Jun Liu1

The State Key Laboratory of Tribology and Institute of Manufacturing Engineering, Department of Precision Instruments and Mechanology,  Tsinghua University, Beijing 100084, Chinaxinjunliu@mail.tsinghua.edu.cn

Chao Wu, Jinsong Wang

The State Key Laboratory of Tribology and Institute of Manufacturing Engineering, Department of Precision Instruments and Mechanology,  Tsinghua University, Beijing 100084, China

1

Corresponding author.

J. Mechanisms Robotics 4(4), 041001 (Aug 10, 2012) (10 pages) doi:10.1115/1.4007004 History: Received November 24, 2010; Accepted April 20, 2012; Published August 10, 2012; Online August 10, 2012

Singularity analysis is one of the most important issues in the field of parallel manipulators. An approach for singularity analysis should be able to not only identify all possible singularities but also explain their physical meanings. Since a parallel manipulator is always out of control at a singularity and its neighborhood, it should work far from singular configurations. However, how to measure the closeness between a pose and a singular configuration is still a challenging problem. This paper presents a new approach for singularity analysis of parallel manipulators by taking into account motion/force transmissibility. Several performance indices are introduced to measure the closeness to singularities. By using these indices, a uniform “metric” can be found to represent the closeness to singularities for different types of nonredundant parallel manipulators.

FIGURES IN THIS ARTICLE
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Copyright © 2012 by American Society of Mechanical Engineers
Topics: Manipulators
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References

Figures

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Figure 1

Process of singularity analysis of an n-DOF parallel manipulator

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Figure 2

A 3-R UU parallel manipulator (a) kinematic structure and (b) an R UU leg

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Figure 3

A singular configuration of the 3-R UU manipulator

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Figure 4

An input transmission singular configuration of the 3-R UU manipulator

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Figure 5

An planar 3-R RR parallel manipulator

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Figure 6

Distributions of index values in the constant-orientation workspace of the planar 3-R RR manipulator with ϕ=0: (a) ITI; (b) OTI; and (c) LSI

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Figure 7

Relationships between angle ϕ and the value of OTI by fixing xO′=yO′=0

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Figure 8

A 3-axis articulated tool head (a) kinematic structure and (b) kinematic scheme

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Figure 9

Distributions of index values in the orientation workspace of the 3-P RS manipulator: (a) ITI; (b) OTI; (c) CTI; and (d) LSI

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Figure 10

Relationships between tilt angle (θ) and the values of ITI, OTI, and CTI by fixing ϕ=0 deg

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