A modified elasto-dynamic model based static stiffness evaluation for a 3-PRS PKM

Abstract

This paper proposes a modified elasto-dynamic model for a three-prismatic revolute spherical parallel kinematic machine, in which the flexibility of the prismatic revolute spherical limb structures are accounted in and modeled as a hollowed spatial beam with nonuniform cross section. The governing equations are derived through substructure synthesis and finite element formulation. The stiffness matrix of the platform is then extracted from global stiffness matrix and its characteristics at typical configurations are calculated to reveal complicated coupling effects of diagonal and nondiagonal elements of the stiffness matrix. The concept of principle stiffness and coupled stiffness are proposed and their distributions over the workspace are predicted with numerical simulations in a quick manner. Then the stiffness of the platform is physically interpreted as a kinematically unconstrained rigid body suspended by six screw springs with equivalent spring constants and pitches through eigenscrew decomposition. The distributions of screw spring constants over the workspace are then plotted to demonstrate a duality property. At last, the effects of some design variables such as structural and dimensional parameters on system rigidity performance are investigated with the purpose of providing useful information for the structural design and performance enhancement of the parallel kinematic machine.