Kinematics of a nine-legged in-parallel manipulator with configurable platform

Configurable platforms bring a research field to expand the attributes of parallel manipulators. This work is devoted to investigate the kinematics of a nine-degrees-of-freedom parallel manipulator whose active kinematic pairs are located near to the fixed platform, and it is equipped with a 6-R configurable platform. The mobility of the proposed 9-UPUR{6R} configurable parallel manipulator is such that it is possible to manipulate the kinematics of a grasping triangle associated to the configurable platform. The theory of screws is systematically applied to solve the direct and inverse infinitesimal kinematics of the manipulator. As an intermediate step, the displacement analysis is approached by means of algebraic geometry. The contribution is complemented with numerical examples to illustrate the versatility of the method of kinematic analysis.