Pseudo-Reflection: A Graphical Method to Predict Stable Positions in Four-Bar and Five-Bar Bistable Linkages

Abstract

Abstract. This work introduces Pseudo-Reflection, a graphical method for predicting candidate stable positions in bistable linkages and compliant mechanisms. Compared to computational methods that are typically used to model the energy landscape and determine stability, graphical methods can offer intuitive advantages, particularly in early-stage design. In particular, Pseudo-Reflection enables designers to rapidly visualize a linkage’s stable positions relative to a base geometry, making stable positions a controllable design input rather than a byproduct. This work shows how to use Pseudo-Reflection to predict the second stable position of bistable four-bar, slider–crank, and slider–rocker linkages with one dominant spring, and bistable five-bar linkages with two dominant springs. Each of these can be created as compliant mechanisms. Furthermore, this method integrates with existing graphical synthesis techniques and is compatible with modern computer-aided design tools, enabling designers to rapidly and intuitively predict stable positions.