Design of Bistable Pinned-Pinned Arches with Torsion Springs by Determining Critical Points

摘要

This paper describes a simplified method to analyze and design a bistable pinned-pinned arch with torsion springs at the pin (revolute) joints. Finite, but not zero, values of torsion spring constants offer the dual advantage of being amenable to monolithic compliant bistable arches wherein torsion springs are realized with equivalent revolute flexures; and giving enhanced range of travel between the stable states and reduced switching forces. However, the equilibrium equations become intractable for analytical solution unlike the extreme cases of fixed-fixed and pinned-pinned arches. Therefore, a new method for analyzing and designing novel bistable arches is presented here by determining critical points in the force-displacement curve. First, the equilibrium equations for post-buckling analysis are derived by writing the deflected profile as a linear combination of the buckling mode shapes of the corresponding straight beam with torsion springs at the pinned ends. These equations are then used to find the critical points with maximum, minimum, and zero forces. The critical points not only provide an approximate view of the bistable force-displacement curve but also enable synthesis of arches with desired behaviour. By using this semi-analytical method, we present an example of an arch with reduced switching force, large switch-back force, and enhanced travel between the two stable states.