Stiffness Analysis of a Low-DOF Parallel Manipulator using the Theory of Reciprocal Screws

역나선 이론을 이용한 저자유도 평행구조 기구의 강성해석

This paper presents a methodology for the stiffness analysis of a low-DOF parallel manipulator. A low-DOF parallel manipulator is a spatial parallel manipulator which has less than six degrees of freedom. The reciprocal screws of actuations and constraints in each leg can be determined by making use of the theory of reciprocal screws, which provide information about reaction forces due to actuations and constraints. When pure force is applied to a leg, the leg stiffness is modeled as a linear spring along the line. For pure couple, it is modeled as a rotational spring about the axis. It is shown that the stiffness model of an F-DOF parallel manipulator consists of F springs related to actuations and 6-F springs related to constraints connected from the moving platform to the base in parallel. The $6{\times}6$ Cartesian stiffness matrix is obtained, which is the sum of the Cartesian stiffness matrices of actuations and constraints. Finally, a 3-UPU parallel manipulator is used as an example to demonstrate the methodology.