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Technical Brief

A Dual Space Approach for Force/Motion Transmissibility Analysis of Lower Mobility Parallel Manipulators

[+] Author and Article Information
Haitao Liu

Key Laboratory of Mechanism Theory
and Equipment Design of The Ministry of Education,
Tianjin University,
Tianjin 300072, China
e-mail: liuht@tju.edu.cn

Manxin Wang

Key Laboratory of Mechanism Theory
and Equipment Design of The Ministry of Education,
Tianjin University,
Tianjin 300072, China
e-mail: wangmxtju@aliyun.com

Tian Huang

Key Laboratory of Mechanism Theory
and Equipment Design of The Ministry of Education,
Tianjin University, Tianjin 300072, China
School of Engineering,
The University of Warwick,
Coventry CV4 7AL, UK
e-mail: tianhuang@tju.edu.cn; tian.huang@warwick.ac.uk

Derek G. Chetwynd

School of Engineering,
The University of Warwick,
Coventry CV4 7AL, UK
e-mail: d.g.chetwynd@warwick.ac.uk

Andrés Kecskeméthy

Chair of Mechanics and Robotics,
University of Duisburg-Essen,
Duisburg 47057, Germany
e-mail: andres.kecskemethy@uni-due.de

Manuscript received May 3, 2014; final manuscript received April 3, 2015; published online June 10, 2015. Assoc. Editor: J. M. Selig.

J. Mechanisms Robotics 7(3), 034504 (Aug 01, 2015) (7 pages) Paper No: JMR-14-1101; doi: 10.1115/1.4030371 History: Received May 03, 2014; Revised April 03, 2015; Online June 10, 2015

By drawing on the duality of twist space and wrench space, this paper presents a general and systematic approach for force/motion transmissibility analysis of lower mobility nonredundant and nonoverconstrained parallel manipulators. This leads to the formulation of a complete and justifiable model that enables the force/motion transmissibility analysis to be integrated into a unified framework under the umbrella of a homogenous and decoupled linear transformation that maps the coordinates of the platform wrench/twist in the joint space to its natural coordinates in the operation space. Utilizing the penalty method to avoid the indeterminate form “0/0” when the local maximum of a virtual coefficient approaches zero, a set of dimensionally homogeneous transmission indices is proposed which can be employed for precisely representing the closeness to different types of singularities defined in twist space as well as for dimensional optimization. An example is given to illustrate the effectiveness of this approach.

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References

Figures

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Fig. 1

A framework for force/motion transmissibility analysis of the nonredundant and nonoverconstrained lower mobility parallel manipulators

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Fig. 2

Schematic diagram of a 3-PRS parallel manipulator

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Fig. 3

Distributions: (a) ηS, (b) ηPP, (c) ηPR, and (d) ηO of the 3-PRS parallel manipulator

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Fig. 4

Variations of: (a) 1: σmin(Wa), 2: σmin(Wc), and 3: σmin(W); (b) 1: σmin(Ta*), 2: σmin(Tc*); and 3: σmin(T*); (c) 1: ηPP, 2: ηPR, and 3:ηP versus θ

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Fig. 5

Distribution of the basis elements of Wc and Tc* given ψ=180 deg and θ=0 deg to 69.7 deg

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Fig. 6

Variations of 1: OTI and 2: CTI versus θ

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