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Technical Brief

Identification of Canonical Basis of Screw Systems Using General-Special Decomposition

[+] Author and Article Information
Genliang Chen

State Key Laboratory of Mechanical System and Vibration,
Shanghai Key Laboratory of Digital Manufacture for
Thin-walled Structures,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: leungchan@sjtu.edu.cn

Hao Wang

State Key Laboratory of Mechanical System and Vibration,
Shanghai Key Laboratory of Digital Manufacture for
Thin-walled Structures,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: wanghao@sjtu.edu.cn

Zhongqin Lin

State Key Laboratory of Mechanical System and Vibration,
Shanghai Key Laboratory of Digital Manufacture for
Thin-walled Structures,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: zqlin@sjtu.edu.cn

Xinmin Lai

State Key Laboratory of Mechanical System and Vibration,
Shanghai Key Laboratory of Digital Manufacture for
Thin-walled Structures,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: xmlai@sjtu.edu.cn

Manuscript received July 9, 2015; final manuscript received June 27, 2017; published online April 5, 2018. Assoc. Editor: Jian S. Dai.

J. Mechanisms Robotics 10(3), 034501 (Apr 05, 2018) (8 pages) Paper No: JMR-15-1194; doi: 10.1115/1.4039218 History: Received July 09, 2015; Revised June 27, 2017

The theory of screws plays a fundamental role in the field of mechanisms and robotics. Based on the rank-one decomposition of positive semidefinite (PSD) matrices, this paper presents a new algorithm to identify the canonical basis of high-order screw systems. Using the proposed approach, a screw system can be decomposed into the direct sum of two subsystems, which are referred to as the general and special subsystems, respectively. By a particular choice of the general subsystem, the canonical basis of the original system can be obtained by the direct combination of the subsystems' principal elements. In the proposed decomposition, not only the canonical form of the screw system but also the corresponding distribution of all those possible base elements can be determined in a straightforward manner.

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Copyright © 2018 by ASME
Topics: Screws
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Figures

Grahic Jump Location
Fig. 1

Construction of the principal frames for the subsystems

Grahic Jump Location
Fig. 2

Influences of L1 on the structure of the associated G1

Grahic Jump Location
Fig. 3

Flowchart of the general-special decomposition

Grahic Jump Location
Fig. 4

Canonical basis of the systems belonging to G2⊕L2

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