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Research Papers

Stiffness of Parallel Manipulators With Serially Connected Legs

[+] Author and Article Information
Han Sung Kim

Department of Mechanical Engineering,
Kyungnam University,
Changwon 631-701, South Korea
e-mail: hkim@kyungnam.ac.kr

Harvey Lipkin

School of Mechanical Engineering,
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 6(3), 031001 (Apr 03, 2014) (9 pages) Paper No: JMR-12-1095; doi: 10.1115/1.4026333 History: Received July 10, 2012; Revised November 15, 2013

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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Figures

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Fig. 1

Kinematic model of the Tricept parallel platform

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Fig. 2

Joints and elastic elements connected in series by rigid bodies model singular stiffness

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Fig. 3

Elastic model of link ki

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Fig. 6

Line spring model of a Tricept manipulator

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Fig. 7

Linear and rotational stiffness along the y-axis

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Fig. 8

Geometry of a Cartesian parallel manipulator

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Fig. 10

Line spring model of a Cartesian parallel manipulator

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