Nonlinear kinetostatic modeling and analysis of a large range 3-PPR planar compliant parallel mechanism

Abstract

Kinetostatic modeling is critical in the design of large range multi-degree-of-freedom compliant parallel mechanisms. However, geometric nonlinearities and coupling effects between kinematic chains create difficulties to the modeling. This paper presents a nonlinear method of kinetostatic modeling for these mechanisms. Geometric nonlinearities are considered by applying the beam constraint model, and load equilibrium conditions and geometric compatibility equations are combined to formulate the coupling effects between kinematic chains. Based on the proposed method, an iterative nonlinear kinetostatic model is developed for a 3-prismatic–prismatic–revolute large range compliant parallel mechanism. Approximate analytical models for three flexure joints are adopted to avoid the nested iteration algorithm, thereby increasing the computational efficiency. Compared with the linear kinetostatic model, the actuation forces are almost identical, and the open-loop position errors decrease by 68% to a value of 32.5 μm for a circular trajectory with a radius of 2.5 mm using finite element analyses. Furthermore, the computational efficiency increases significantly compared with the nested iterative model. In addition, the kinetostatic characteristics of the mechanism are analyzed, and the main reasons for geometric nonlinearities are investigated. Finally, experiments are conducted to validate the developed iterative nonlinear kinetostatic model.