General approach for inverse kinematics of nR robots

Usually finding the method to use to solve the inverse kinematics of a nR robot is a difficult problem as no effective analytic method has been identified so far. This article uses a semi-analytic method and a general method to solve the spatial nR robot inverse kinematics problem. It overcomes the numerical method's limitations related to accuracy with a real-time aspect. Initially, conformal geometric space theory was used to establish general kinematic equations. Based on that, the weighted space vector projection method was used to analyze the relationship between the robot spatial rotation angles and the value of the space vector projection. The weighted value of every joint's projection on the end-effector vector was treated as the basis for changing the robot end's orientation. By determining the weighted value of every joint's projection on the end-effector vector, it was possible to achieve the semi-analytic inverse kinematic solution. Finally, to prove the validity and feasibility of the theory it was tested with a special 6R robot.