Workspace analysis of 3-CPS parallel micro-manipulator for mirror active adjusting platform

Abstract

In order to adjust telescope mirrors with high precision, a 3 cylindrical-prismatic-spherical (CPS) parallel micro-manipulator with 6 degrees-of-freedom (DOF) and partial decoupling is proposed. Structure characteristics of the micro-manipulator were analyzed and the kinematic equations were derived based on Euler method. To avoid tedious derivation, Jacobian matrix with screw theory representing the input and output relation of micro-manipulator is established by using velocity influence coefficient method. Combining topological structure characteristics of the 3-CPS parallel micro-manipulator, the solving procedures of workspace are obtained. Moreover, the position workspace with a given orientation and the orientation workspace with a given translation position are constructed by numerical simulations. The workspace range is chosen as the optimization goal of structure parameters, and the circumcircle radius ratio of base and moving platform and the lengths of each sub-link are optimized. The maximum condition number and the minimum singular value are chosen as the precision indexes to analyze the precision performance of the workspace. Then, the properties of the position workspaces with various orientations and the orientation workspaces with various positions are simulated numerically, and the simulation results prove that the 3-CPS parallel micro-manipulator has an ability to achieve high precision operations. This research provides a workspace modeling and optimization method for the practical application in telescope mirror adjustment or other fields requiring high precision.