A nonlinear analysis of spatial compliant parallel modules: Multi-beam modules

This paper presents normalized, nonlinear and analytical models of spatial compliant parallel modules—multi-beam modules with a large range of motion. The models address the non-linearity of load-equilibrium equations, applied in the deformed configuration, under small deflection hypothesis. First, spatial nonlinear load-displacement equations of the tip of a beam, conditions of geometry compatibility and load-equilibrium conditions for a spatial three-beam module are derived. The nonlinear and analytical load-displacement equations for the three-beam module are then solved using three methods: approximate analytical method, improved analytical method and numerical method. The nonlinear–analytical solutions, linear solutions and large-deflection FEA solutions are further analyzed and compared. FEA verifies that the accuracy of the proposed nonlinear–analytical model is acceptable. Moreover, a class of multi-beam modules with four or more beams is proposed, and their general nonlinear load-displacement equations are obtained based on the approximate load-displacement equations of the three-beam module. The proposed multi-beam modules and their nonlinear models have potential applications in the compliant mechanism design. Especially, the multi-beam modules can be regarded as building blocks of novel compliant parallel mechanisms.