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Research Papers

Accuracy Analysis of Redundantly Actuated and Overconstrained Parallel Mechanisms With Actuation Errors

[+] Author and Article Information
Jianzhong Ding

School of Mechanical
Engineering and Automation,
Beihang University,
Beijing 100191, China
e-mail: jianzhongd@buaa.edu.cn

Chunjie Wang

School of Mechanical
Engineering and Automation,
Beihang University,
Beijing 100191, China
e-mail: wangcj@buaa.edu.cn

Hongyu Wu

School of Mechanical
Engineering and Automation,
Beihang University,
Beijing 100191, China
e-mail: hongyu@buaa.edu.cn

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received March 20, 2017; final manuscript received August 9, 2018; published online September 25, 2018. Assoc. Editor: Raffaele Di Gregorio.

J. Mechanisms Robotics 10(6), 061010 (Sep 25, 2018) (7 pages) Paper No: JMR-17-1070; doi: 10.1115/1.4041212 History: Received March 20, 2017; Revised August 09, 2018

A general accuracy analysis method of redundantly actuated and overconstrained parallel mechanisms is proposed. Coupled effects of actuation errors and internal elastic forces arose from the elastic deformation are both considered. The accuracy analysis approach is based on the Lie-group theory and screw theory, and it includes three steps. First, stiffness matrices of serial legs are obtained. Second, the movement of each leg is modeled based on group theory and the elastic forces arose from the deformation are represented using the stiffness matrices, following which the multiclosed-loop structure constraint and self-balanced force constraint are modeled. Finally, the error pose is estimated. The proposed method is illustrated by the accuracy study of a redundantly actuated and overconstrained Stewart platform. The error modeling is easy as the use of stiffness matrix can model the passive joint motions and deformation together. Moreover, the proposed method is computationally cheap as all computations are linear.

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Figures

Grahic Jump Location
Fig. 1

Euler–Bernoulli beam

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Fig. 2

Parallel mechanism with n legs

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Fig. 5

Schematic diagrams of Stewart mechanism: (a) general and (b) active overconstrained

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Fig. 6

Elastic model of the overconstrained Stewart mechanism

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Fig. 3

Manipulator pose actuated independently by the leg 1

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Fig. 7

Elastic model of the leg 1

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Fig. 8

Elastic model of the nominal leg 2

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Fig. 9

Constraint space of the leg 7

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Fig. 10

Closed-loop constraint and the error pose

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