Guaranteed solution of direct kinematic problems for general configurations of parallel manipulators

Finding all possible positions of a Stewart platform from the knowledge of the lengths of its limbs amounts to solving a set of nonlinear equations, the number of real solutions of which is, in the general case, unknown a priori. This paper shows how Hansen's algorithm (1992), based upon interval analysis, can be used to get all solutions in an approximate but guaranteed way even when the platform is nonplanar and the equations are nonpolynomial and with real coefficients. Computation is simple enough to be performed on a personal computer.