Exercise $2$: $3$ DOF spherical manipulator

$1.$Calculate the iacobian and end$-$effector velocities.

Reminder:

The $i^{th}$ column of $J_v$ is given by:

$J_{v_i}=\{\begin{array}{ccc}{z}_{i-1}(0_n-0_{i-1})& \text{f}\text{o}\text{r}\text{i}\text{r}\text{e}\text{v}\text{o}\text{l}\text{u}\text{t}\text{e}& \\ z_{i-1}& \text{f}\text{o}\text{r}\text{i}\text{p}\text{r}\text{i}\text{s}\text{m}\text{a}\text{t}\text{i}\text{c}& \end{array}$

The $i^{th}$ column of $J_{}$ is given by:

$J_m=\{\begin{array}{ccc}{z}_{i-1}& \text{f}\text{o}\text{r}\text{i}\text{r}\text{e}\text{v}\text{o}\text{l}\text{u}\text{t}\text{e}& \\ 0& \text{f}\text{o}\text{r}\text{i}\text{p}\text{r}\text{i}\text{s}\text{m}\text{a}\text{t}\text{i}\text{c}& \end{array}$