A computer-aided geometric approach to inverse kinematics

Abstract

This paper presents a geometric approach to solving the inverse kinematics for three-joint placeable robotic manipulators. The distinct feature of this approach is that it uses geometric variables such as length, area ratio, and Pythagoras difference to find the closed form solutions. It is proved here that for any three-joint placeable manipulator there exists a geometric variable that keeps constant during the evolution of the manipulator. With this invariant, a characteristic equation of the manipulator can be derived and can be transformed into a polynomial equation with degree up to four. Therefore the closed form solution of the three-joint placeable manipulator can be obtained. A characteristic equation of the three-revolute-joint manipulator produced by this approach with the assistance of Maple is listed in the Appendix. The possible application of this geometric approach to a six-joint manipulator is also discussed in the paper. © 1998 John Wiley & Sons, Inc. 15: 131–143, 1998