A COMPUTER-AIDED GEOMETRIC APPROACH TO INVERSE KINEMATICS

This paper presents a geometric approach to solving the inverse kinema tics for three-joint placeable robotic manipulators. The distinct feat ure of this approach is that it uses geometric variables such as lengt h, area ratio, and Pythagoras difference to find the closed form solut ions. It is proved here that for any three-joint placeable manipulator there exists a geometric variable that keeps constant during the evol ution of the manipulator. With this invariant, a characteristic equati on of the manipulator can be derived and can be transformed into a pol ynomial equation with degree up to four. Therefore the closed form sol ution of the three-joint placeable manipulator can be obtained. A char acteristic equation of the three-revolute-joint manipulator produced b y this approach with the assistance of Maple is listed in the Appendix . The possible application of this geometric approach to a six-joint m anipulator is also discussed in the paper. (C) 1998 John Wiley & Sons, Inc.