Data-Driven Dimensional Synthesis of Diverse Planar Four-bar Function Generation Mechanisms via Direct Parameterization

Planar four-bar mechanisms are widely used in mechanical systems due to their simplicity and versatility. In designing a mechanism to achieve a desired task, accurately calculating its dimensions--a process known as dimensional synthesis--is essential. However, even for four-bar mechanisms, this synthesis presents considerable challenges. Unlike kinematic analysis, which determines output motion from given dimensions, dimensional synthesis is an inverse problem: given a desired output motion, typically expressed as precision points, the objective is to determine the corresponding mechanism dimensions. Extensive research has been conducted on dimensional synthesis since Freudenstein [1] introduced his foundational analytical approach for four-bar mechanisms. Contemporary studies in this field follow two major approaches: exact synthesis, also known as the precision point approach, which aims to find mechanism dimensions that satisfy desired characteristics exactly only at a finite number of discrete precision points, and the approximate approach, which focuses on obtaining solutions that minimize structural error over the entire range of motion. In this study, a novel data-driven approach is proposed to solve the dimensional synthesis problem of multi-type four-bar function generation mechanisms, leveraging machine learning to bypass the need to solve complex systems of equations and conduct optimization tasks. A supervised learning framework consisting of three key components is proposed: 1) a large synthetic dataset, 2) a deep neural network model, and 3) effective training methods.