Method and apparatus for controlling geometrically simple parallel

Abstract

A system, method and apparatus for controlling, via a closed-form forward displacement computation, the position and orientation of a movable platform of a parallel mechanism. A movable platform is supported above a base platform by a plurality of parallel support legs such as linear actuators. The dimensions of the base platform and the movable platform, as well the lengths of the support legs, are provided to a control system. The control system is operative to compute at least one closed-form forward displacement solution of the geometry of a polyhedron (an octahedron for the disclosed embodiments) formed by the movable platform, the base platform, and the support legs. The control system determines a final position and orientation of the movable platform by eliminating imaginary roots of the closed-form solutions and roots which would result in discontinuous paths of travel for the movable platform. A novel special 6-6 parallel mechanism is also disclosed. The control system is suitable for controlling known 3-3 or 6-3 Stewart platforms in a novel manner, as well as controlling the novel special 6-6 parallel mechanism. The special 6-6 parallel mechanism is distinguished from a general 6-6 by the fact that it is geometrically reducible to an octahedron, and therefore it has a simple geometry, even though its legs possess distinct connections. Also disclosed is a method for reducing the novel special 6-6 parallel mechanism to a Stewart platform equivalent, which is then controlled by the disclosed closed-form forward displacement control system.