Inverse kinematics of variable geometry parallel manipulator

The variable geometry parallel manipulator (VGPM) is a kind of manipulator that is suitable to change the spatial distribution of a variable geometry body (VGB). In the VGPM, the Stewart platform is utilized as a driving mechanism, and a number of spatial RSRR kinematic chains, which connect with the base frame and the top platform through revolute pairs, respectively, guide the rigid plates with spatially shaped inner surfaces to form the envelope of the VGB. The inverse kinematics problem of the VGPM is to determine every actuator displacement of the Stewart platform for given the outlet area and deflection angle of the VGB. In this paper, we present a method to solve this kind of inverse kinematics problem. At first, we present an assumption of the double semi-ellipses approximate distribution model of the VGB to determine the approximate position and orientation of the top platform. Through analysis of the deviations between the approximate distribution model and the given distribution parameters of the VGB, after making the compensation of the deviations, we obtain the corrected inverse kinematic solution of the VGPM with acceptable tolerance.