Potential Energy as Design Criterion in Planar Multistable Mechanisms

Toggle mechanisms are used throughout engineering to accomplish various tasks, for example residential electrical switching. The design of toggle mechanisms can be broken into three categories: determination of a topology, geometric parameterization, and optimization. While topological determination and optimization have well established processes for use in design, geometric parameterization which includes defining link lengths and spring stiffness has largely been left to engineering judgement. This paper presents a design methodology using potential energy graphs which informs the engineering decisions made in choosing mechanism parameters, giving designers higher confidence in the design. A kinematic analysis coupled with Lagrange’s equation determines the relationship between the mechanism parameters and the potential energy curve. Plotting the potential energy with respect to the generalized coordinate yields a graph with a slope that is the generalized force or moment. The relationships between parameters and their effects on the mechanism are difficult to observe in the equations of motion, but potential energy plots readily provide information pertinent to the design of toggle mechanisms and decouple their effects. The plots also allow design by position rather than time which makes the design process faster. The design process is applied to three examples: a simple toggle mechanism, a compliant mechanism, and a reconfigurable mechanism to show the nuances of the approach.