Design of Multi-Degree-of-Freedom Planar Morphing Mechanisms With Single-Degree-of-Freedom Sub-Chains

Abstract

This paper deals with the synthesis of multi-degree-of-freedom planar mechanisms by breaking the problem into the synthesis of multiple single-degree-of-freedom planar mechanisms. Specifically, this paper investigates synthesizing shape-changing mechanisms capable of matching multiple closed profiles with significant changes in shape. These mechanisms can be used for applications such as morphing wings or morphing dies for polymer extrusion. Well established synthesis techniques for single-degree-of-freedom planar mechanisms are used and reviewed for completeness. The paper then compares multiple forms of two optimization techniques used to find suitable mechanisms. The problems investigated herein are highly nonlinear and highly constrained; therefore, advanced optimization strategies are needed. This paper uses both gradient-based optimization and a genetic algorithm (GA) to find mechanisms capable of matching the design profiles. It also looks at additions to the GA that leverage the presence of the single-degree-of-freedom subchains. The gradient-based optimization and GA with additions were able to find mechanisms with better matching error than the blind GA. However, the improvement was modest and not always present, indicating that it is likely best to start with the blind GA and introduce gradient-based optimization, additions to the GA, and changes in the setting as needed to improve results.