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.