Determining the Number of Distinct Solutions in Planar Mechanism Design

Abstract

This work investigates two novel approaches to sorting solutions to planar-mechanism-synthesis problems. The examples contained herein are specific to planar morphing mechanisms, but the procedure is general and can easily be extended to any planar-mechanism-synthesis problem. The results indicate that the two approaches, namely self-organizing map (SOM) neural network and modal assurance criterion (MAC), can be used to sort a set of solution mechanisms into a reduced set of distinct solution groups. Additionally two sorting approaches (inclusive and exclusive) were investigated. This process can be used to take the initial set of solution mechanisms, often numbering in the hundreds, and pare it down to a significantly smaller set of substantially different designs. For the two case studies presented herein, one set was reduced by a factor of ten and the other by a factor of five. This means that a designer has fewer mechanisms to look through and that the differences in these mechanisms are clearer so that considerations such as size and joint locations may more easily be considered. It was found that the MAC method with inclusive sorting is generally a better starting point because it runs quickly and gives a more compact set of distinct solution mechanisms. The paper concludes with some recommendations for best practices for sorting solutions for a general mechanism-design problem.