A Machine Learning Approach to Kinematic Synthesis of Defect-Free Planar Four-Bar Linkages

The past forty years of research in mechanism synthesis has witnessed an unprecedented volume of work in formulating and solving planar four-bar linkage synthesis problems. However, finding practical and useful mechanisms for the motion synthesis problem has proven to be elusive, as a large majority of mechanisms turn out to be defective with respect to their assembly modes. Most methods formulate the problem as a discrete precision position problem, which inherently ignores the continuity information in the input, resulting in linkages with branch-, circuit- and order-defects. In this paper, we bring together diverse fields of pattern recognition, machine learning, artificial neural network, and computational kinematics to present a novel approach that solves this problem both efficiently and effectively. At the heart of this approach lies an objective function that compares the motion as a whole thereby capturing designer’s intent. In contrast to widely used structural error or loop-closure equation based error functions which convolute the optimization by considering shape, size, position, and orientation simultaneously, this objective function computes motion difference in a form, which is invariant to similarity transformations. We employ auto-encoder neural networks to create a compact and clustered database of invariant motions of known linkages. The query is raised in the database for nearest neighbors, which are either solutions or good initial conditions for fast local optimization techniques. In spite of highly non-linear parameters space, our approach discovers a wide pool of defect-free solutions very quickly. We show that by employing proven machine learning techniques, this work could have far-reaching consequences to creating a multitude of useful and creative conceptual design solutions for mechanism synthesis problems, which go beyond planar four-bar linkages.