Question

What is g1*g2?

Answer 1

Probably the easiest way to see the answer is by using the matrix representation of transformations.\[g1*g2=\left[\begin{matrix}R_1 & d_1 \\ 0 & 1\end{matrix}\right]*\left[\begin{matrix}R_2 & d_2 \\ 0 & 1\end{matrix}\right]=\left[\begin{matrix}R_1*R_3 & R_1*d_2+d_1 \\ 0 & 1\end{matrix}\right]\]Thus \[R = R_1*R_2\]and \[d = R_1*d_2+d_1\]