On the computational aspect of the matrix exponentials and their use in robot kinematics

The exponential matrix representation in describing rotations has a geometric appeal in studying the kinematics of mechanisms and in characterizing their singularities. Here, we show its potential computational appeal using the classical Cayley-Hamilton theorem. In so doing, a connection between the geometric and computational aspects is clearly underlined. Then for the purpose of a demonstration, we perform explicit calculations to obtain the kinematics relations of the Stanford manipulator.