Generative Design of Planar Four-Bar Motions

Abstract

Abstract. This article introduces a novel deep generative approach to the approximate motion synthesis of planar four-bar mechanisms. Existing motion synthesis approaches for synthesizing four-bar mechanisms have generally focused on representing the motion as five or less discrete poses while not providing any guarantees on the practicality of the solutions, such as ones without circuit-, branch-, and order defects. This article presents a conditional variational autoencoder (C-VAE)-based approach for synthesizing practical mechanisms that can capture the overall motion requirement while generating a continuous motion approximately. The mathematical machinery in our work uses quaternions and kinematic mapping to represent the geometric constraints of dyads of four-bar mechanism as algebraic constraint manifolds in a three-dimensional projective space. The parameters describing the manifolds encode information about the type and dimensions of constituent dyads of four-bar mechanisms. These parameters are used as input to a C-VAE that uses an arbitrarily large number of input poses approximating a motion as the condition. A procedure is presented for normalizing input motions such that they are invariant with respect to rotation, scale, translation, and reflection. The trained model can generate several pairs of constraint manifolds from which four-bar mechanisms with different parameters can be retrieved. These mechanisms’ coupler poses approximate the input’s coupler poses to varying degrees of error. A method for filtering mechanisms by the quality of match of their output motion to the input motion is also proposed. Different metrics for quantifying the similarity of an output mechanism’s motion with the input motion are presented for path and orientation separately.