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Research Papers: Mechanisms and Robotics

Analysis of Stiffness and Elastic Deformation for Some 3–5-DOF PKMs With SP R or RP S-type legs

Yi Lu and Bo Hu
[+] Author and Article Information
Yi Lu

Robotics Research Center, College of Mechanical Engineering, Yanshan University, Qinhuangdao, Hebei 066004 P.R. Chinaluyi@ysu.edu.cn

Bo Hu

Robotics Research Center, College of Mechanical Engineering, Yanshan University, Qinhuangdao, Hebei 066004 P.R. China

J. Mech. Des 130(10), 102307 (Sep 11, 2008) (8 pages) doi:10.1115/1.2918918 History: Received August 05, 2007; Revised December 12, 2007; Published September 11, 2008

This paper proposes an equivalent mechanism approach for establishing the stiffness matrices of some 3–5DOF (degree of freedom) parallel kinematic machines (PKMs) with SP̱R- or RP̱S-type legs and solving their elastic deformations. First, the geometric constraints of constrained wrench of these PKMs are analyzed, and the poses of the active/constrained forces are determined. Second, based on the principle of virtue work and the determined active/constrained forces, the formulas are derived for solving the 6×6 Jacobian matrices of these PKMs and the stiffness matrices of SP̱R or RP̱S-type active legs. Third, based on the elastic deformations of the SP̱R or RP̱S active legs, the equivalent 6-DOF rigid PKMs of these elastic PKMs are constructed, and their 6×6 Jacobian matrices are derived. Finally, the formulas are derived for solving the total stiffness matrices and the elastic deformation of the 3DOF 3SP̱R, 3DOF 3RP̱S, 4DOF 2SP̱S+2SP̱R, and 5DOF 4SP̱S+SP̱R PKMs.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

The 3SP̱R PKM and its force situation

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Figure 2

The elastic deformations of the SP̱R-type leg ri under Fai (a) and under Fci (b)

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Figure 3

An elastic 3SP̱R PKM and its equivalent rigid PKM

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Figure 4

The 2SP̱S+2SP̱R PKM and its equivalent rigid 6-DOF 2SP̱S+2SPP̱R PKM

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Figure 5

The 4SP̱S+SP̱R PKM and its equivalent rigid 6-DOF 4SP̱S+SPP̱R PKM

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Figure 6

The analytic solved results of the 3SP̱R PKM

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Figure 7

The analytic solved results of the total stiffness matrix for the 3-SP̱R PKM

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