This paper proposes an equivalent mechanism approach for establishing the stiffness matrices of some 3–5DOF (degree of freedom) parallel kinematic machines (PKMs) with - or -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 Jacobian matrices of these PKMs and the stiffness matrices of or -type active legs. Third, based on the elastic deformations of the or active legs, the equivalent 6-DOF rigid PKMs of these elastic PKMs are constructed, and their Jacobian matrices are derived. Finally, the formulas are derived for solving the total stiffness matrices and the elastic deformation of the 3DOF , 3DOF , 4DOF , and 5DOF PKMs.
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October 2008
Research Papers
Analysis of Stiffness and Elastic Deformation for Some 3–5-DOF PKMs With SPR or RPS-type legs
Yi Lu,
Yi Lu
Robotics Research Center, College of Mechanical Engineering,
e-mail: luyi@ysu.edu.cn
Yanshan University
, Qinhuangdao, Hebei 066004 P.R. China
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Bo Hu
Bo Hu
Robotics Research Center, College of Mechanical Engineering,
Yanshan University
, Qinhuangdao, Hebei 066004 P.R. China
Search for other works by this author on:
Yi Lu
Robotics Research Center, College of Mechanical Engineering,
Yanshan University
, Qinhuangdao, Hebei 066004 P.R. Chinae-mail: luyi@ysu.edu.cn
Bo Hu
Robotics Research Center, College of Mechanical Engineering,
Yanshan University
, Qinhuangdao, Hebei 066004 P.R. ChinaJ. Mech. Des. Oct 2008, 130(10): 102307 (8 pages)
Published Online: September 11, 2008
Article history
Received:
August 5, 2007
Revised:
December 12, 2007
Published:
September 11, 2008
Citation
Lu, Y., and Hu, B. (September 11, 2008). "Analysis of Stiffness and Elastic Deformation for Some 3–5-DOF PKMs With SPR or RPS-type legs." ASME. J. Mech. Des. October 2008; 130(10): 102307. https://doi.org/10.1115/1.2918918
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