A Matrix-Based Approach to Unified Synthesis of Planar Four-Bar Mechanisms for Motion Generation

This paper presents a novel approach based on matrices for the synthesis of planar four-bar mechanisms that unifies the type and dimensional synthesis while addressing the motion generation problem. While kinematics mapping and quaternions are commonly used in kinematic synthesis, we demonstrate that they are not essential in formulating unified design equations. The proposed approach utilizes matrices and mechanism parameters directly to produce design equations that incorporate information about the type and dimensions of planar four-bar mechanisms. It also integrates the constraints of a pose with other practical constraints, such as the location of fixed and moving pivots, into a single constraint system. This method simplifies the interpretation of mechanism parameters and their computation, as demonstrated by examples of five-pose synthesis and four-pose synthesis with one extra condition.