Kinematic Synthesis of Planar, Shape-Changing Mechanisms

This work presents a systematic framework to synthesize planar mechanisms capable of approximating a shape change defined by a set of morphing curves in different positions. The framework starts with a procedure to design rigid-body shape-changing mechanisms, which is an extension of the existing synthesis approach that includes the segmentation and mechanization processes. The mechanization process is reformulated so that a group of single degree-of-freedom solution mechanisms that trade off minimizing matching error with maximizing mechanical advantage can be found efficiently from a genetic algorithm (GA) optimization. This rigid-body synthesis procedure can be extended to generate partially compliant shape-changing mechanisms by including two Pseudo-Rigid-Body (PRB) models: flexural pivots and flexible beams. Since the simplified PRB beam model is not accurate, an independent optimization loop is established to redefine flexible beams of the partially compliant solution mechanism using a finite link beam model.

Partially compliant mechanisms can only generate relatively small-scale shape change due to stress concentrations. To achieve larger ranges of motion, fully distributed compliant mechanisms are synthesized using the structural optimization approach. For a shape-change problem, the rigid-body solution's base topology is utilized to provide new insight into the topological complexity required for the structural optimization. The base topology is either directly evaluated via dimensional synthesis or else used to define an initial mesh network for an optimization to find topologies and dimensions simultaneously. Simple but viable distributed compliant shape-changing designs can be obtained, which shows that a thorough search within the preselected design space defined by the base topology typically leads to a superior local minimum. This same idea is also applied to the design of path generating compliant mechanisms whose complete output paths are examined within a two-objective GA.