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Research Papers

A Method for Compliance Modeling of Five Degree-of-Freedom Overconstrained Parallel Robotic Mechanisms With 3T2R Output Motion

[+] Author and Article Information
Wen-ao Cao

School of Mechanical Engineering and
Electronic Information,
China University of Geosciences (Wuhan),
Wuhan 430074, China
e-mail: cwao1986@163.com

Huafeng Ding

School of Mechanical Engineering and
Electronic Information,
China University of Geosciences (Wuhan),
Wuhan 430074, China
e-mail: dhf@ysu.edu.cn

Donghao Yang

School of Mechanical Engineering and
Electronic Information,
China University of Geosciences (Wuhan),
Wuhan 430074, China
e-mail: yangdh9311@163.com

1Corresponding author.

Manuscript received June 24, 2016; final manuscript received November 9, 2016; published online December 22, 2016. Assoc. Editor: Raffaele Di Gregorio.

J. Mechanisms Robotics 9(1), 011011 (Dec 22, 2016) (11 pages) Paper No: JMR-16-1184; doi: 10.1115/1.4035270 History: Received June 24, 2016; Revised November 09, 2016

This paper presents an approach to compliance modeling of three-translation and two-rotation (3T2R) overconstrained parallel manipulators, especially for those with multilink and multijoint limbs. The expressions of applied wrenches (forces/torques) exerted on joints are solved with few static equilibrium equations based on screw theory. A systematic method is proposed for deriving the stiffness model of a limb with considering the couplings between the stiffness along the constrained wrench and the one along the actuated wrench based on strain energy analysis. The compliance model of a 3T2R overconstrained parallel mechanism is established based on stiffness models of limbs and the static equilibrium equation of the moving platform. Comparisons show that the compliance matrix obtained from the method is close to the one obtained from a finite-element analysis (FEA) model. The proposed method has the characteristics of involving low computational efforts and considering stiffness couplings of each limb.

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Figures

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Fig. 1

Typical 3T2R overconstrained parallel mechanisms: (a) structure type, (b) 5-RRUR mechanism, (c)5-PRUR mechanism, and (d) 5-RPRRR mechanism

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Fig. 3

Limb i of 5-RRUR parallel mechanism

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Fig. 4

Three substructures of limb i

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Fig. 5

Local frame of substructure ij

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Fig. 6

Deformations of 5-RRUR parallel mechanism under an external unit couple along x-direction: (a) x-direction linear deformation, (b) y-direction linear deformation, (c) z-direction linear deformation, (d) x-direction angular deformation, (e) y-direction angular deformation, and (f) z-direction angular deformation

Grahic Jump Location
Fig. 7

Deformations of 5-PRUR parallel mechanism under an external unit force along z-direction: (a) x-direction linear deformation, (b) y-direction linear deformation, (c) z-direction linear deformation, (d) x-direction angular deformation, (e) y-direction angular deformation, and (f) z-direction angular deformation

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