THE STEWART PLATFORM OF GENERAL GEOMETRY HAS 40 CONFIGURATIONS

The Stewart platform is a six-degree-of-freedom, in-parallel linkage. It is used in automotive and flight simulators, positioning tables for assembly and robotic applications, and various other applications req uiring linkages with high structural stiffness. It consists of a base link, a coupler link, and six adjustable-length legs supporting the co upler link. Each leg consists of a prismatic joint with ball-joint con nections to the base and coupler, respectively. The forward kinematics problem for the Stewart platform may be stated as follows:given the v alues of the six prismatic joint displacement inputs to the linkage, c ompute the position and orientation of the coupler link. This problem may be set up as a system of nonlinear multivariate polynomial equatio ns. We solve this problem using a numerical technique known as polynom ial continuation. We show that for Stewart platforms of general geomet ry (i.e., platforms in which the linkage parameters are arbitrary comp lex numbers) this problem has 40 distinct solutions.