Question

In a 2-DOF (RP) manipulator, the joint link parameters are given asLink i	ai	$\alpha_i$	di	$\theta_i$
1	0	$90\degree$	0	$\theta_1$
2	0	0	d2	0
The final transformation matrix for this manipulator is S

• A. $\begin{bmatrix} C_1 & 0 & S_1 & 0\\\ S_1 & 0 & -C_1 & 0\\\ 0 & 1 & 0 & 0\\\ 0 &0 & 0 & 1 \end{bmatrix}$
• B. $\begin{bmatrix} 1 & 0 & 0 & 0\\\ 0 & 1 & 0 & 0\\\ 0 & 0 & 1 & d_2\\\ 0 &0 & 0 & 1 \end{bmatrix}$
• C. $\begin{bmatrix} C_1 & 0 & S_1 & 0\\\ S_1 & 0 & -C_1 & 0\\\ 0 & 1 & 0 & d_2\\\ 0 &0 & 0 & 1 \end{bmatrix}$
• D. $\begin{bmatrix} C_1 & 0 & S_1 & d_2S_1\\\ S_1 & 0 & -C_1 & -d_2C_1\\\ 0 & 1 & 0 & 0\\\ 0 &0 & 0 & 1 \end{bmatrix}$

Answer 1

Answer: (D)

$\begin{bmatrix} C_1 & 0 & S_1 & d_2S_1\\\ S_1 & 0 & -C_1 & -d_2C_1\\\ 0 & 1 & 0 & 0\\\ 0 &0 & 0 & 1 \end{bmatrix}$

Answer 2

The correct option is (D): $\begin{bmatrix} C_1 & 0 & S_1 & d_2S_1\\\ S_1 & 0 & -C_1 & -d_2C_1\\\ 0 & 1 & 0 & 0\\\ 0 &0 & 0 & 1 \end{bmatrix}$