A simple yet general method determines the stiffness matrix for parallel manipulators with serially connected legs. Link and actuator flexibilities for each leg are modeled by flexibility matrices that are additive. The effect of passive joints is implicitly included using reciprocal screws to yield a leg stiffness matrix that is generally singular. Since the legs act in parallel the leg stiffnesses are additive and yield the manipulator stiffness. The method is applicable to overconstrained, exactly constrained, and underconstrained robots in generic or singular configurations. It is illustrated using the Tricept robot containing a passive constraint leg and an overconstrained translating manipulator. Numerical results are confirmed using commercial structural analysis software.
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August 2014
Research-Article
Stiffness of Parallel Manipulators With Serially Connected Legs
Han Sung Kim,
Han Sung Kim
Department of Mechanical Engineering,
e-mail: hkim@kyungnam.ac.kr
Kyungnam University
,Changwon 631-701, South Korea
e-mail: hkim@kyungnam.ac.kr
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Harvey Lipkin
Harvey Lipkin
School of Mechanical Engineering,
e-mail: harvey.lipkin@me.gatech.edu
Georgia Institute of Technology
,Atlanta, GA 30332
e-mail: harvey.lipkin@me.gatech.edu
Search for other works by this author on:
Han Sung Kim
Department of Mechanical Engineering,
e-mail: hkim@kyungnam.ac.kr
Kyungnam University
,Changwon 631-701, South Korea
e-mail: hkim@kyungnam.ac.kr
Harvey Lipkin
School of Mechanical Engineering,
e-mail: harvey.lipkin@me.gatech.edu
Georgia Institute of Technology
,Atlanta, GA 30332
e-mail: harvey.lipkin@me.gatech.edu
Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received July 10, 2012; final manuscript received November 15, 2013; published online April 3, 2014. Assoc. Editor: Yuefa Fang.
J. Mechanisms Robotics. Aug 2014, 6(3): 031001 (9 pages)
Published Online: April 3, 2014
Article history
Received:
July 10, 2012
Revision Received:
November 15, 2013
Citation
Sung Kim, H., and Lipkin, H. (April 3, 2014). "Stiffness of Parallel Manipulators With Serially Connected Legs." ASME. J. Mechanisms Robotics. August 2014; 6(3): 031001. https://doi.org/10.1115/1.4026333
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