A closed-form forward kinematics solution for the 6-6(p) Stewart platform

This paper studies the forward kinematics of a special 6-6 Stewart platform , in which both the base and the mobile platforms are similar hexagons. A c oncise closed-form solution to the forward kinematics of the Stewart platfo rm is obtained by introducing a quaternion to represent the transformation matrix. It is very interesting to find that the eight possible solutions ha ve a very simple inner symmetry relationship. So, the solutions obtained fr om the approach presented in this paper are concise, represented as the squ ares of the four quaternion components. Besides, unnecessary complex roots are avoided automatically. Finally, only univariate quadratic equations are required to solve in this approach.