Closed-Form Geometric Inverse Kinematics of 6-DOF Robot Arm Using Four Active Joints

Abstract

Abstract— This paper proposes a closed-form geometric inverse kinematics method for a tabletop-mounted six-degree-of-freedom (6-DOF) robot manipulator with four active joints. Although the robot consists of six mechanical joints, only the base, shoulder, elbow, and wrist pitch are included in the inverse kinematics computation, while wrist roll and gripper joints are fixed. The method focuses on end-effector position control without considering orientation to reduce computational complexity. The robot is implemented using an ESP32-based controller with link lengths of 12 cm, 12 cm, and 12,5 cm. Experimental evaluation under various workspace configurations shows a global average positioning error of 7,1 cm, with a maximum error of 12,04 cm. For selected workspace regions, a lower mean error of 3,04 cm is achieved with 100% inverse kinematics solvability. The proposed approach provides reliable performance for non-precision manipulation tasks and embedded real-time implementation.