Geometric Design, Mathematical Modeling, and Motion Analysis of a Novel 2T1R Planar Manipulator Based on Nested Circular Plates

This paper presents a novel TTR mechanism, also known as a 2T1R (2-Translation-1-Rotation) three-degree-of-freedom planar mechanism, achieved through the arrangement of three nested circular plates. With its ample workspace and high stiffness, this mechanism is well-suited for a variety of industrial applications. The study begins with an exploration of the mechanism’s degree of freedom using screw theory, followed by mathematical modelling of its direct and inverse kinematics for optimal movement between points. Employing an algorithm to eliminate redundant responses, programming and analysis are conducted in LabVIEW. To ensure precise motion of the end effector through designated points, cubic spline interpolation is utilized, with coding implemented in LabVIEW following mathematical analysis of spline equations. Additionally, two distinct motion paths are considered. This examination reveals the mechanism’s ability to traverse linear and circular paths with minimal error. The mechanism demonstrates acceptable accuracy in executing circular trajectories, as confirmed through experimental validation. Verification of the real path’s conformity to the simulated path involves detecting the end effector’s motion using linear and circular sensors, with results recorded and compared to the simulated trajectory. The findings demonstrate consistency between the experimental and simulated results.