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Determination of singularities of some 4-DOF parallel manipulators by translational/rotational Jacobian matrices

Published online by Cambridge University Press:  21 September 2009

Yi Lu ,
Yan Shi  and
Jianping Yu
Yi Lu*
Affiliation:
Robotics Research Center, College of Mechanical Engineering, Yanshan University, Qinhuangdao, Hebei 066004, P.R. China
Yan Shi
Affiliation:
Robotics Research Center, College of Mechanical Engineering, Yanshan University, Qinhuangdao, Hebei 066004, P.R. China
Jianping Yu
Affiliation:
College of Foreign Studies, Yanshan University, Qinhuangdao, Hebei 066004, P.R. China
*
*Corresponding author. E-mail: [email protected]
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Summary

A novel analytic approach is proposed for determining the singularities of some four degree of freedom (DOF) parallel manipulators (PMs). First, the constraint and displacement of a general 4-DOF PM are analyzed. Second, a common 3 × 4 translational Jacobian matrix Jν and a common 3 × 4 rotational Jacobian matrix Jω are derived, and a 4 × 4 general Jacobian matrix J of the 4-DOF PMs is derived from Jν and Jω. Since a complicated process to determine singularities from the 4 × 6 Jacobian matrix is transformed into a simple process to determine singularity from J, the singularities of the some 4-DOF PMs with 3 translations and 1 rotation, or with 3 rotations and 1 translation, or with combined translation–rotations are analyzed and determined easily by this approach.

Keywords

Parallel manipulatorSingularityJacobian matrix
Type
Article
Information
Robotica , Volume 28 , Issue 6 , October 2010 , pp. 811 - 819
Copyright
Copyright © Cambridge University Press 2009

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