Freeing the serial mechanism designer from inverse kinematic solvability constraints

This paper presents a fast numerical solution for the inverse kinematics of a serial manipulator. The method is implemented on the C-arm, a manipulator designed for use in robotic surgery. The inverse kinematics solution provides all possible solutions for any six degree-of-freedom serial manipulator, assuming that the forward kinematics are known and that it is possible to solve for the remaining joint angles if one joint angle's value is known. With a fast numerical method and the current levels of computing power, designing a manipulator with closed-form inverse kinematics is no longer necessary. When designing the C-arm, we therefore chose to weigh other factors, such as actuator size and patient safety, more heavily than the ability to find a closed-form inverse kinematics solution.