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Research Papers

Motion/Force Constrainability Analysis of Lower-Mobility Parallel Manipulators

[+] Author and Article Information
Xin-Jun Liu

The State Key Laboratory of Tribology and
Institute of Manufacturing Engineering,
Department of Mechanical Engineering,
Tsinghua University,
Beijing 100084, China
Beijing Key Lab of Precision/Ultra-Precision
Manufacturing Equipments and Control,
Tsinghua University,
Beijing 100084, China
e-mail: xinjunliu@mail.tsinghua.edu.cn

Xiang Chen

The State Key Laboratory of Tribology and
Institute of Manufacturing Engineering,
Department of Mechanical Engineering,
Tsinghua University,
Beijing 100084, China
Beijing Key Lab of Precision/Ultra-Precision
Manufacturing Equipments and Control,
Tsinghua University,
Beijing 100084, China

Meyer Nahon

Department of Mechanical Engineering and
Centre for Intelligent Machines,
McGill University,
Montreal, QC H3A 2K6, Canada

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received October 11, 2013; final manuscript received December 27, 2013; published online April 3, 2014. Assoc. Editor: Yuefa Fang.

J. Mechanisms Robotics 6(3), 031006 (Apr 03, 2014) (9 pages) Paper No: JMR-13-1205; doi: 10.1115/1.4026632 History: Received October 11, 2013; Revised December 27, 2013

The constraint performance analysis in the limited kinetostatic subspace of parallel manipulators is a significant but ignored issue. The motion/force constrainability analysis, with focus on lower-mobility parallel manipulators, is the subject of this study. Via the theory of screws, three generalized frame-invariant constraint indices are proposed based on the concept of the power coefficient. The introduced indices can not only identify the singularity and the fully constrained property but also measure the closeness between a particular pose and an unconstrained configuration (or fully constrained configuration). In order to demonstrate the feasibility and the validity of the analysis methods and indices, the detailed evaluation of two typical industrial parallel manipulators are presented, the Sprint Z3 head and the Tricept mechanism.

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References

Figures

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Fig. 1

The twist screw and wrench screw of a rigid body

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Fig. 2

Method to determine the elements of the twists/wrenches systems

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Fig. 6

(a) A prototype of Sprint Z3 head [7] and (b) a scheme of 3-PRS mechanism

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Fig. 7

The performance distribution map of the ICI of the 3-PRS PM within the orientation workspace

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Fig. 8

The performance distribution map of the OCI within the orientation workspace of the 3-PRS PM

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Fig. 9

The performance distribution map of the TCI within the orientation workspace of the 3-PRS PM

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Fig. 10

The relationships between the values of the proposed indices (ICI, OCI, and TCI) and the varying tilt angle, θ([0 deg, 180 deg]), by fixing the azimuth angle, ϕ = 0 deg

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Fig. 11

(a) A prototype of Tricept [30] and (b) a scheme of 3-UPS&1-UP mechanism

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Fig. 12

The performance distribution map of the OCI within the x–y workspace by fixing the z-value of the moving platform as z = 40 mm

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Fig. 13

The performance distribution map of the TCI within the x–y workspace by fixing the z-value of the moving platform as z = 40 mm

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Fig. 14

The variation of the TCI and the z-value when fixing the x- and y-values at A ((x, y) = (0, 0)), and B ((x, y) = (15, 0))

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