Function-generation synthesis of planar four-bar linkage through kinematic modeling and hybrid hierarchical optimization

To address the optimization challenges posed by higher-order nonlinear equations in the function generation of four-bar linkage (FBL), this paper presents a novel approach for the function-generation synthesis of planar FBL. Specifically, the auxiliary angle formula from trigonometric identity transformation is employed to derive an explicit analytical expression for the input-output angular relationship in FBL, simplifying the complexity of the derivation process in kinematic modeling. Additionally, a new form of constructing an error objective function based on the input-output dials is proposed, and the mapping model between the prescribed function and the input-output (I/O) function of the function generation is established. Furthermore, a hybrid hierarchical optimization algorithm is proposed to combine the gradient descent interior point method with a meta-heuristic algorithm for FBL parameter optimization. A simulated logarithmic function generator was produced, and the generated results were analyzed. It was found that the maximum error between the values produced by the generator and the true values of the logarithmic function is 0.0015, which is within the acceptable range.