Homogenous Transformation Matrices

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)