Kinematic jerk analysis of the Jansen mechanism via screw theory

This work presents a comprehensive study of the instantaneous kinematics of the Jansen mechanism, extending up to the third-order derivative. As a preliminary step, displacement analysis is conducted using geometric algebra, which yields concise closed-form solutions. Subsequently, screw theory is applied to investigate the instantaneous kinematics of the mechanism, including a detailed jerk analysis. A key aspect of the approach involves the elimination of passive joint rates through the application of the Klein form. This enables the systematic derivation of input-output equations for the instantaneous kinematics of the parallel manipulator, expressed in a compact matrix format. To validate the proposed methodology, numerical examples are provided, demonstrating the robustness and reliability of the kinematic analysis. To the best of the author’s knowledge, this is the first study to apply screw theory to the jerk analysis of the Jansen mechanism. This contribution is particularly relevant given the mechanism’s intended function: to replicate the leg motion of certain biological systems, which inherently involves controlled acceleration peaks.