Analysis and validation of Degrees of Freedom and Kinematics of the 2-RPU&2-RPR Parallel Mechanism

For a novel 2-RPU&2-RPR parallel mechanism, we first describe its structural composition and working principle, confirming that the mechanism has one translational and one rotational degree of freedom. Then, using the modified G-K formula in mechanism theory, we analyze and conclude that the mechanism has two degrees of freedom. Next, we analyze the constraints on the mechanism’s motion, based on the geometric method and spatial position vector method, and establish the closed-loop equations for each chain. We derive the forward and inverse kinematic models of the mechanism. Finally, we build a platform for model validation in Matlab Simulink to numerically verify the results of forward and inverse kinematics, where the forward solution matches the inverse solution. Using Simscape Multibody, we create a virtual prototype of the mechanism and perform simulations under the same conditions, which can verify the correctness of the kinematic model.