The kinematics analysis and improvement of the 3T1R 4-PUU parallel mechanism using the whale optimization algorithm

Abstract. This paper focuses on the 4-PUU parallel mechanism with Schönflies motion, investigating its kinematic analysis and utilizing intelligent algorithms to solve its forward kinematics equations. Using screw theory as the mathematical framework, the number and nature of the degrees of freedom of the 4-PUU parallel mechanism are analyzed, proving that the mechanism can achieve 3T1R motion. The forward and inverse position kinematics equations are established with link lengths as constraints, and the velocity and acceleration equations of the mechanism are derived using the vector method. The forward kinematics equations of the mechanism are transformed into an unconstrained optimization problem, which is solved using an improved beluga whale optimization (BWO). To enhance the uniformity of the initial population distribution, a chaotic-opposition-based learning initialization strategy is introduced. Additionally, an elite strategy and a golden-sine-based position update mechanism are incorporated to improve the optimization capability of BWO. The integration of these strategies results in an enhanced optimization algorithm with superior global search ability. Given the mechanism's dimensional parameters, theoretical and motion simulations are conducted using MATLAB and Adams. The results indicate that the motion simulation curves from Adams closely match the numerical simulation curves from MATLAB, validating the theoretical derivation. Building on this, the improved beluga whale optimization (IBWO) algorithm, along with comparison algorithms (DEb1, ABC, PSO), is applied to solve the forward kinematics equations for interpolation points along the simulated trajectory. Numerical experiments demonstrate that IBWO outperforms the other comparison algorithms in solving the problem efficiently and accurately.