Application of Spatial and Fourier Transforms to the Synthesis of Path Generation Mechanisms

Abstract

Abstract This work presents an approach for the invariant characterization, storage and search of planar path generation mechanisms. Spatial transformations and Fourier descriptors are used to characterize the path of four-bar planar mechanisms. The invariant characteristic information is then stored in a database. The resulting characteristic information for the path is invariant under rigid transformations — translation, rotation and scaling. Solution comparison and matching techniques are discussed and implemented to evaluate the deviation of a desired path to candidate paths stored in a database. A description of each method and the relative performance of file development and search methods are generated for four-bar mechanisms. Each method may be applied to any path generation planar mechanisms since the output path is characterized and stored in a database for solution comparison. The specific type of mechanism that generates the path is not necessarily required for identification of candidate solutions. A database of 7,845 candidate path solutions is developed to evaluate each method. The database of path solutions and related mechanism definitions are based on crank-rocker, four bar mechanism solutions developed by Hrones and Nelson (1951).