Homogenous transformation matrices

Abstract

In the introductory chapter we have seen that robots have either translational or rotational joints. We therefore need a unified mathematical description of translational and rotational displacements. The translational displacement d, given by the vector

$$\textbf{d} = a\textbf{i} + b\textbf{j} + c\textbf{k},$$

(2.1)

can be described also by the following homogenous transformation matrix H

$$\textbf{H} = Trans(a,b,c) = \left[\begin{array}{llll} 1 & 0 & 0 & a\\ 0 & 1 & 0 & b\\ 0 & 0 & 1 & c\\ 0 & 0 & 0 & 1 \end{array}\right].$$

(2.2)