Two PRBMs of Euler spiral segments and their chained models for analyzing general curved beams in compliant mechanisms

Abstract

Utilizing general curved beams can significantly enhance the mechanical properties of compliant mechanisms. However, the large-deflection analysis of general curved beams is still a challenging task. As one of the corresponding analysis methods for curved beams, chained pseudo-rigid-body model (CPRBM) is easy to implement, but requires a fine discretization to guarantee its analysis accuracy. To solve this problem, this paper proposes a new method for constructing coarse-discretization CPRBMs. The proposed method discretizes a curved beam into several segments, and regards each segment as an Euler spiral beam that can be modeled by PRBM. For this purpose, this paper derives the large-deflection equations of the Euler spiral beams with non-zero initial curvature. A 2R PRBM and a 3R PRBM are proposed for this kind of Euler spiral beams. The relationship between PRBM parameters and the initial shape of Euler spiral beams is established. Analysis cases and experiment are used to verify the chained models based on 2R/3R PRBMs. The results show that the coarse-discretization CPRBMs have higher computational efficiency and accuracy than the traditional CPRBM.