Dual Numbers, Lie Algebra and 6R Inverse Kinematics

Abstract

The ordinary Euler angles and Briant angles for describing rotations are well known and often used in robotics. However it is sometimes necessary to analyze the product of three general rotations R 1 R 2 R 3. We point out some dual invariants which are independent of the articular parameters and can be calculated, so all the quantities of the form {X { RY} can be determined for X and Y in the Lie algebra D;. Using these results, the 6R inverse kinematics problem can be solved.