Stiffness And Its Characteristic Analysis Of A Class Of Lower Mobility Parallel Manipulators

This paper is focous on analysising the stiffness and characteristic of stiffness of a class of lower-mobility parallel manipulators(PMs). This class of lower-mobility PMs is the manipulator with liner active legs. The number of degree of freedom(DOF) of this class of lower-mobility PMs is equal to or more than three which have kinematic coupling characteristic. The realization conditions of diagonalization and the exestience conditions of compliant center and compliant axes are analyzed. This research provides important theoretical support for designing, optimizing and applying of this class mechanisms. The analysis results for this class of lower-mobility PMs provide important practical significance in engineering application. The main research of this paper is as fllows:The stiffness models of planar 3RPS and series-parallel n(3RPS)are established based on the unified stiffness model considering both active and constrained wrenches for lower-mobility PMs with linear active legs.The unified finite element(FE) model of the three-DOF PM is esatiblished with linear active legs. The correctness and generality of the FE model is verified by comparisoning the symmetrical and antisymmertical 3RPS PMs, planar 3RPS PM and series-parallel n(3RPS) PM based on the theoretical and FE models.By introducing the eigenscrws decomposition and principal axes decomposition, the coupling index is introduced to estimate the decomposition stiffness matrix wether it can be composed by six simple springs based on principal axes decomposition.The diagnalization position and pose conditions of symmetrical 3RPS and planar 3RPS PMs are analyzed based on eigenscrews decomposition and principal axes decomposition.The relation between eigenscrews decomposition, principal axes decomposition and compliant axes are analyzed based on the elastic theory. The existence conditions of compliant axis obtained by principal axes decomposition are analyzed. The relation between the existence condition of compliant axis and diagnalization of stiffness matrix are analyzed. The compliant axes of symmetrical and antisymmetrical 3RPS and planar 3RPS PMs are analyzed under normal and special positions.The stiffness model of four-DOF 2RPS-2UPS PM is established. The characteristic stiffness of this PM is analyzed based on the eigenscrew decomposition and principal axes decomposition under a normal postion. The maximum and minimum stiffness surfaces are given to estimate the stiffness performance. This example indicatied that the stiffness matrix decomposition and elastic theory are appropriate for any other lower-mobility PMs analyse.