Kinematic Analysis of the Spherically Actuated Platform Manipulator

New methods for the inverse and forward kinematic analysis of the novel six degrees of freedom (6DOF) parallel manipulator which has only two legs are presented. The actuation of the new mechanism is through two base-mounted spherical actuators. In the inverse pose kinematic, active joint variables are directly calculated with no need for the evaluation of passive joint variables. In the forward pose kinematic, closed form solution adopting a new approach is presented. It is shown that the inverse and forward pose kinematic have sixteen and four different solutions, respectively. Moreover, closed form equations for the rate kinematic analysis are proposed. Finally, two different categories of the singularity points for the new mechanism with their geometrical interpretation are introduced. In one category the mechanism loses one or more DOF while in the other one it gains one or more DOF.