Impedance control of a redundantly actuated 3-DOF planar parallel link mechanism using direct drive linear motors

The impedance control of a 3-degree-of-freedom (DOF) xyθ planar parallel link mechanism (PLM) with four redundant actuators, i.e., a 3D4M PLM, is proposed. The impedance control requires forward kinematics, which gives the position and orientation of the end effector of the PLM. The notable link arrangement of the 3D4M PLM makes it easy to derive the forward kinematics, which have been difficult to derive for conventional parallel links. In addition, the relations of static forces, including the internal force through redundant actuation, are derived. Using the forward kinematics, formulas of the impedance control that take into consideration the internal force of the 3D4M PLM are derived. Based on the design of decoupled dynamics, an experimental system of the 3D4M PLM is developed. A PLM is constructed on linear motors in which four moving parts are individually driven on one stator part. Workspace impedance control achieved by force command is implemented in the experimental system using a digital signal processor (DSP) based real time controller. Experimental responses of free damped vibrations to impedance control are compared with corresponding theoretical responses.