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Research Papers

An Approach to Determining the Unknown Twist/Wrench Subspaces of Lower Mobility Serial Kinematic Chains

[+] Author and Article Information
Tian Huang

Professor
Key Laboratory of Mechanism Theory and
Equipment Design of Ministry of Education,
Tianjin University,
Tianjin 300072, China
e-mail: tianhuang@tju.edu.cn;
tian.huang@warwick.ac.uk

Shuofei Yang

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

Manxin Wang

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

Tao Sun

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

Derek G. Chetwynd

School of Engineering,
The University of Warwick,
Coventry CV4 7AL, UK
e-mail: D.G.Chetwynd@warwick.ac.uk

1Corresponding author.

Manuscript received March 5, 2013; final manuscript received August 27, 2014; published online December 4, 2014. Assoc. Editor: Xilun Ding.

J. Mechanisms Robotics 7(3), 031003 (Aug 01, 2015) (9 pages) Paper No: JMR-13-1048; doi: 10.1115/1.4028622 History: Received March 05, 2013; Revised August 27, 2014; Online December 04, 2014

Mainly drawing on screw theory and linear algebra, this paper presents an approach to determining the bases of three unknown twist and wrench subspaces of lower mobility serial kinematic chains, an essential step for kinematic and dynamic modeling of both serial and parallel manipulators. By taking the reciprocal product of a wrench on a twist as a linear functional, the underlying relationships among their subspaces are reviewed by means of the dual space and dual basis. Given the basis of a twist subspace of permissions, the causes of nonuniqueness in the bases of the other three subspaces are discussed in some depth. Driven by needs from engineering design, criteria, and a procedure are proposed that enable pragmatic, consistent bases of these subspaces to be determined in a meaningful, visualizable, and effective manner. Three typical examples are given to illustrate the entire process. Then, formulas are presented for the bases of the twist/wrench subspaces of a number of commonly used serial kinematic chains, which can readily be employed for the formulation of the generalized Jacobian of a variety of lower mobility parallel manipulators.

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Figures

Grahic Jump Location
Fig. 1

Illustration of a twist and a wrench

Grahic Jump Location
Fig. 2

A fixed axis rotation

Grahic Jump Location
Fig. 3

A RPS kinematic chain

Grahic Jump Location
Fig. 4

Schematic diagram of SPR kinematic chain

Grahic Jump Location
Fig. 5

Schematic diagram of UPR kinematic chain

Grahic Jump Location
Fig. 6

Schematic diagram of PU kinematic chain

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