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Research Papers

Type Synthesis of Parallel Mechanisms With a Constant Jacobian Matrix

[+] Author and Article Information
Yanzhi Zhao

Parallel Robot and Mechatronic System
Laboratory,
Key Laboratory of Advanced Forging and
Stamping Technology,
Science of Ministry of National Education,
Yanshan University,
Qinhuangdao 066004, Hebei, China
e-mail: yzzhao@ysu.edu.cn

Yachao Cao

Parallel Robot and Mechatronic System Laboratory,
Yanshan University,
Qinhuangdao 066004, Hebei, China;
School of Mechanical
and Automotive Engineering,
South China University of Technology,
Guangzhou 510640, Guangdong, China
e-mail: yccaoryan@stumail.ysu.edu.cn

Xianwen Kong

School of Engineering and Physical Sciences,
Heriot-Watt University,
Edinburgh EH14 4AS, UK
e-mail: X.Kong@hw.ac.uk

Tieshi Zhao

Parallel Robot and Mechatronic System
Laboratory,
Key Laboratory of Advanced Forging and
Stamping Technology,
Science of Ministry of National Education,
Yanshan University,
Qinhuangdao 066004, Hebei, China
e-mail: tszhao@ysu.edu.cn

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received December 11, 2017; final manuscript received July 10, 2018; published online September 25, 2018. Assoc. Editor: Andreas Mueller.

J. Mechanisms Robotics 10(6), 061011 (Sep 25, 2018) (10 pages) Paper No: JMR-17-1411; doi: 10.1115/1.4040962 History: Received December 11, 2017; Revised July 10, 2018

Jacobian matrix plays a key role in the analysis, design, and control of robots. For example, it can be used for the performance analysis and evaluation of parallel mechanisms (PMs). However, the Jacobian matrix of a PM generally varies with the poses of the moving platform in the workspace. This leads to a nonconstant performance index of the PM. PMs with a constant Jacobian matrix have simple kinematics and are easy to design and control. This paper proposes a method for obtaining PMs with a constant Jacobian matrix. First, the criteria for detecting invariance of a Jacobian matrix are obtained based on the screw theory. An approach to the synthesis of PMs with a constant Jacobian matrix is then proposed. Using this approach, PMs with a constant Jacobian matrix are synthesized in two steps: the limb design and the combination of the limbs. Several PMs with a constant Jacobian matrix are obtained. In addition to the translational parallel mechanisms (TPMs) with a constant Jacobian matrix in the literature, the mixed-motion PMs whose moving platform can both translate and rotate with a constant Jacobian matrix are newly identified. The input/output velocity analysis of several PMs is presented to verify that Jacobian matrix of these PMs is constant.

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Figures

Grahic Jump Location
Fig. 1

Process of type synthesis of PMs with a constant Jacobian matrix3

Grahic Jump Location
Fig. 2

The 3DoF quintessential symmetric TPMs with a constant Jacobian: (a) 3-CRU, (b) 3-CPR, (c) 3-PPRR, and (d) 3-PRPU

Grahic Jump Location
Fig. 3

The 3DoF quintessential asymmetric TPMs with a constant Jacobian: (a) CRU-PRPU-PPRU, (b) CPU-CRU-PPRR, (c) PRPR-PPRU-CRU, and (d) PRRR-PPRR-PRPR

Grahic Jump Location
Fig. 4

The sketch of PPRR-CRR-CPR TPM

Grahic Jump Location
Fig. 5

Distribution of the input velocity when the corresponding joints are actuated

Grahic Jump Location
Fig. 6

Distribution of the output velocity of the moving platform

Grahic Jump Location
Fig. 7

The sketch of PR-C mixed-motion PM

Grahic Jump Location
Fig. 8

Distribution of the input velocity when the corresponding joints are actuated

Grahic Jump Location
Fig. 9

Distribution of the output velocity of the moving platform

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