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Robotica (2009), 27:259-268 Cambridge University Press
Copyright © Cambridge University Press 2008


Inverse dynamics of the 6-dof out-parallel manipulator by means of the principle of virtual work

Yongjie Zhaoa1 c1 and Feng Gaoa1

a1 State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, P.R. China.
Article author query
zhao y [Google Scholar]
gao f [Google Scholar]


In this paper, the inverse dynamics of the 6-dof out-parallel manipulator is formulated by means of the principle of virtual work and the concept of link Jacobian matrices. The dynamical equations of motion include the rotation inertia of motor–coupler–screw and the term caused by the external force and moment exerted at the moving platform. The approach described here leads to efficient algorithms since the constraint forces and moments of the robot system have been eliminated from the equations of motion and there is no differential equation for the whole procedure. Numerical simulation for the inverse dynamics of a 6-dof out-parallel manipulator is illustrated. The whole actuating torques and the torques caused by gravity, velocity, acceleration, moving platform, strut, carriage, and the rotation inertia of the lead screw, motor rotor and coupler have been computed.

(Received April 17 2008)

(Online publication May 23 2008)

KEYWORDS:Out-parallel manipulator; Robot dynamics; Inverse dynamics; Principle of virtual work; Link Jacobian matrices


c1 Corresponding author. E-mail: