Kinematics and Optimization of a Spatial 3-UPU Parallel Manipulator

Abstract

The structural characteristics associated with parallel manipulators are investigated. Using these characteristics a class of 3 degree-of-freedom parallel manipulators are enumerated. Several parallel manipulators with only translational degrees of freedom are identified and the 3-UPU parallel manipulator is chosen for design analysis and optimization. The kinematics of this 3-UPU parallel manipulator is studied. Two geometric conditions that lead to pure translational motion of the moving platform are described. Due to the simple kinematic structure, the inverse kinematics yields two equal and opposite limb lengths whereas the direct kinematics produces two possible manipulator postures with one being the mirror image of the other. The Jacobian matrix is derived and several singular conditions are discussed. Furthermore the conditions for existence of an isotropic point within the workspace are discussed and equations to compute the isotropic configurations of a 3-UPU manipulator are derived. Finally, we undertake architecture optimization and show that certain values of design variables maximize the global condition index of the 3-UPU manipulator. [S1050-0472(00)01404-5]