Low-dimensional trajectory synthesis for four-bar mechanisms via clustering-guided SVD-PCA registration and adaptive annealing hummingbird optimization

That the traditional trajectory synthesis model for the four-bar mechanism encounters significant challenges is evident in its high-dimensional design variables, its tendency to become trapped in local optima during optimization, and its substantial computational overhead. To address these issues, a low-dimensional shape calibration framework is presented in this paper, which integrates the Clustering-guided SVD-PCA (Singular Value Decomposition-Principal Component Analysis) Two-stage Registration Trajectory Error Function with the Adaptive Annealing Hummingbird Algorithm (AAHA). By setting the positioning variables to zero initially, only six design variables—namely, the link lengths, the coupler link length, and the initial angle—are retained, significantly reducing the search space complexity. What follows is a process where source points are selected through k -means clustering, preliminarily registered using Singular Value Decomposition (SVD), and then finely calibrated with Principal Component Analysis (PCA) to select reference points, achieving high-precision rigid registration. Enhanced with dynamic flight mode weighting, post-migration weight reinitialization, and the simulated annealing criterion, the AAHA algorithm effectively balances global exploration and local convergence. To demonstrate this approach’s effectiveness, comparative experiments involving teardrop-shaped and cross-shaped trajectories were conducted. That the proposed method outperforms Simulated Annealing (SA), Particle Swarm Optimization (PSO), Teaching-Learning-Based Optimization (TLBO), and the original Artificial Hummingbird Algorithm (AHA) is reflected in its superior optimal fitness value, convergence rate, and robustness. Thus, an efficient solution for trajectory synthesis in four-bar mechanisms is provided, offering significant value for designing algorithms to tackle high-dimensional mechanical optimization problems.