Informed latent space exploration for image-based path synthesis of linkages

This paper brings together rigid body kinematics and machine learning to create a novel approach to path synthesis of linkage mechanisms under practical constraints, such as location of pivots. We model the coupler curve and constraints as probability distributions of image pixels and employ a Convolutional Neural Network (CNN) based Variational AutoEncoder (VAE) architecture to capture and predict the features of the mechanism. Plausible solutions are found by performing informed latent space exploration so as to minimize the changes to the input coupler curve while seeking to find user-defined pivot locations. Traditionally, kinematic synthesis problems are solved using precision point approach, wherein the input path is represented as a set of points and a set of equations in terms of design parameters are formulated. Generally, this problem is solved via optimization, wherein a measure of error between the given path and the coupler curve is minimized. A limitation of this approach is that the existing formulations depend on the type of mechanism, do not admit practical constraints in a unified way, and provide a limited number of solutions. However, in the machine design pipeline, kinematic synthesis problems are concept generation problems, where designers care more about a large number of plausible and practical solutions rather than the precision of input or the solutions. The image-based approach proposed in this paper alleviates the difficulty associated with inherently uncertain inputs and constraints.