GEOMETRIC JACOBIANS DERIVATION AND KINEMATIC SINGULARITY ANALYSIS FOR 6-DOF ROBOTIC MANIPULATOR

This article investigates the kinematic singularities and geometric Jacobians of a 6-DOF robotic manipulator, incorporating a prismatic joint, from the perspective of singularity theory. The study begins by deriving the forward kinematics using the Denavit-Hartenberg (D-H) convention and examines the Jacobian matrices to identify configurations where the Jacobian matrix becomes rank-deficient, signaling the presence of kinematic singularities. These singularities pose critical challenges, such as restricting end-effector mobility and leading to infinite solutions in inverse kinematics. The determinant of the Jacobian matrix is employed to detect singular configurations, and the implications for motion control and trajectory planning are discussed. Through a detailed analysis and MATLAB simulations, the article highlights the importance of singularity avoidance and provides a deeper understanding of the manipulator's kinematic behavior. The findings emphasize the need for strategic design and motion planning to ensure optimal performance and stability in robotic manipulation tasks