A closed-form forward kinematics solution for the 6-6/sup p/ Stewart platform

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