A Canonical Formulation of the Direct Position Kinematics Problem for a General 6-6 Stewart Platform

by

Bhaskar Dasgupta and T. S. Mruthyunjaya

Abstract:

This paper deals with the direct position kinematics problem of a general 6-6 Stewart platform, the complete solution of which is not reported in the literature till now and even establishing the number of possible solutions for the general case has remained an unsolved problem for a long period. Here a canonical formulation of the direct position kinematics problem for a general 6-6 Stewart platform is presented. The kinematic equations are expressed as a system of six quadratic and three linear equations in nine unknowns, which has a maximum of 64 solutions. Thus, it is established that the mechanism, in general, can have upto 64 closures. Further reduction of the system is shown arriving at a set of three quartic equations in three unknowns, the solution of which will yield the assembly configurations of the general Stewart platform with far less computational effort compared to earlier models.

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