A Lagrange-Euler Formulation for the Dynamics of a Planar 3-DOF Parallel Manipulator

by

V. P. Revathi, Bhaskar Dasgupta and T. S. Mruthyunjaya

Abstract:

This paper deals with the dynamic formulation for a 8-link 3-dof planar parallel manipulator with prismatic actuations. The Lagrange-Euler approach has been employed with the output variables and the input variables as the generalized coordinates. This selection of generalized coordinates has been shown to result in a system of equations in a very simplified form, from which the Lagrange multipliers can be completely eliminated resulting in a system of ordinary differential equations with the constraints incorporated implicitly.

The formulation has been implemented for the inverse dynamic computation for trajectories planned in both task-space and joint-space. Results for a test manipulator for tracking a trajectory in each case has been presented.

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