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Research Papers

Udwadia-Kalaba Approach for Parallel Manipulator Dynamics

[+] Author and Article Information
Jin Huang

The State Key Laboratory of Advanced
Design and Manufacturing for Vehicle Body,
Hunan University,
Changsha, Hunan 410082, China
e-mail: huangjin0107@gmail.com

Y. H. Chen

Professor
The George W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: yehwa.chen@me.gatech.edu

Zhihua Zhong

Professor
The State Key Laboratory of Advanced
Design and Manufacturing for Vehicle Body,
College of Mechanical and Vehicle Engineering,
Hunan University,
Changsha, Hunan 410082, China

1Present address: George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332.

2Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received March 8, 2011; final manuscript received March 2, 2013; published online August 23, 2013. Assoc. Editor: Eugenio Schuster.

J. Dyn. Sys., Meas., Control 135(6), 061003 (Aug 23, 2013) (11 pages) Paper No: DS-11-1070; doi: 10.1115/1.4024600 History: Received March 08, 2011; Revised March 02, 2013

A novel Udwadia-Kalaba approach for parallel manipulator dynamics analysis is presented. The approach segments a parallel manipulator system into several leg-subsystems and the platform subsystem, which are connected by kinematic constraints. The Udwadia-Kalaba equation is then used to calculate the constraint forces due to the constraints. Based on this, the equation of motion, which is an explicit (i.e., closed) form, can be formulated. The method allows a systematic procedure to generate the dynamic model for both direct dynamics and inverse dynamics without invoking additional variables (such as multipliers or quasi-variables), nor does it require projection. A classical parallel Stewart-Gough platform is chosen to demonstrate the feasibility and advantages of this approach.

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Figures

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Fig. 1

A parallel mechanism

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Fig. 3

An UPS Stewart-Gough Platform

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Fig. 4

The segmentation of the UPS Stewart-Gough platform

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Fig. 5

A leg subsystem of the Stewart-Gough platform

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Fig. 6

Distribution of the points Pi in frame {P}

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Fig. 7

Distribution of the points Bi in frame {B}

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Fig. 8

The desired translational displacement of the platform

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Fig. 9

The desired angular displacement of the platform

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Fig. 10

The desired translational velocity of the platform

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Fig. 11

The desired angular velocity of the platform

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Fig. 12

The desired translational acceleration of the platform

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Fig. 13

The desired angular acceleration of the platform

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Fig. 14

The actuator force

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