Forward kinematic analysis of a 6-3 type Stewart platform mechanism

Abstract

The Stewart platform mechanism is one example of a fully parallel, six-degrees-of-freedom manipulator. Its forward kinematic analysis, i.e. finding the position and orientation of the top platform when a set of link lengths is given, has been extensively studied in the past. Study results have shown that if the closed-form solving procedure is performed, then this analysis could finally lead to a 16th-order polynomial equation in one unknown from which 16 different positions and orientations of the top platform can be determined. However, obtaining the solutions from such a high-order polynomial equation is quite an arduous task which is both computationally complex and time consuming. Relative to the closed-form solving procedure, the purpose of this paper is to propose an alternative numerical algorithm based upon the Newton-Raphson method in order to work out the forward kinematic analysis of a 6-3 type Stewart platform mechanism. The numerical results show that the present solutions could be obtained within a few iteration steps and are in excellent agreement with the published literature.