Research on the Conditions and Optimization of 3-UPU Parallel Manipulators That Naturally Realize Three Translational Degrees of Freedom

The characteristics of the degrees of freedom (DOFs) of the 3-UPU parallel mechanisms (PMs) are closely related to the orientations of the ending R joints fixed connected with the platforms. The orientations of the ending revolute (R) joints in the Tsai 3-UPU PM cannot naturally realize three translational DOFs. First, this paper gives and proves the geometric conditions of the ending R joint fixed to the platforms that can naturally ensure three translational DOFs of the 3-UPU PMs. Second, based on the common motion/force index and good transmission workspace volume of the 3-UPU translational PMs, the performance map of the PMs is drawn, and the corresponding optimization design area of the PMs is obtained. Finally, combined with the obtained optimization design area, in view of the differences in the constraint and stiffness performance of the 3-UPU translational PMs, the multi-objective optimization is carried out using the game theory algorithm, and the orientations of the ending R joints for the 3-UPU translational PMs with good constraint and stiffness performance are obtained.