Closed-Form Dynamic Analysis of a Novel Planar TTR Manipulator Based on Virtual Work and Hamiltonian Mechanics

This study presents the modeling, analysis, and control of a novel planar three-degrees-of-freedom TTR (Translational–Translational–Rotational) mechanism. A comprehensive kinematic and dynamic formulation is developed, with the governing equations derived analytically using the principles of virtual work and Hamiltonian mechanics. Due to the nonlinear nature of the inverse kinematics, a numerical solution based on the modified Newton–Raphson method is employed to compute joint trajectories. To ensure robust trajectory tracking in the presence of modeling uncertainties and external disturbances, a sliding-mode control strategy is designed and implemented. The proposed approach is evaluated through numerical simulations and experiments conducted on a custom-built prototype. Quantitative performance metrics, including mean squared error, are used to assess tracking accuracy and to compare simulation and experimental results. The consistency between analytical modeling, numerical solutions, and experimental observations demonstrates the feasibility of the proposed framework for planar robotic motion control applications.