Geometric technique for the kinematic modeling of a 5 DOF redundant manipulator

This paper describes a geometrical method for solving the inverse kinematic (IK) problem of a 5 Degrees of Freedom (DOF) redundant manipulator. A geometric inverse kinematics solution is desirable as it provides complete and simple solutions to the problem and determines efficiently the relationship between the joints and the end-effector without iterative process. Using a geometric method, if a solution exists, we provide all feasible solutions to the IK problem and from these solutions an optimal solution can be selected using a performance criterion such as stability of the platform, collision avoidance, joint limits, manipulability or singularity avoidance. The method is computationally inexpensive and can be useful in planning with redundant manipulators and in sensor based environments.