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Kinematic analysis of limited-dof parallel manipulators based on translational/rotational Jacobian and Hessian matrices

Published online by Cambridge University Press:  27 February 2009

Yi Lu ,
Yan Shi  and
Jianping Yu
Yi Lu*
Affiliation:
College of Mechanical Engineering, Yanshan University, Qinhuangdao, Hebei 066004, P. R. China
Yan Shi
Affiliation:
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: luyi@ysu.edu.cn
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Summary

This paper proposes an approach for solving the velocity and acceleration of the limited-dof (dof n < 6) parallel kinematic machines with linear active legs by means of translational/rotational Jacobian and Hessian matrices. First, based on the established or derived constraint and displacement equations, the translational/rotational Jacobian and Hessian matrices are derived. Second, the formulae for solving inverse/forward velocities and accelerations are derived from translational and rotational Jacobian/Hessian matrices. Third, a 2SPR + UPU PKM and a 2SPS + RPRR PKM are illustrated for explaining how to use this method. This approach is simple because it needs neither to eliminate 6-n rows of an n × 6 Jacobian matrix nor to determine the screw or pose of the constrained wrench.

Keywords

parallel manipulatorkinematicstranslational Jacobianrotational Jacobian
Type
Article
Information
Robotica , Volume 27 , Issue 7 , December 2009 , pp. 971 - 980
Copyright
Copyright © Cambridge University Press 2009

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