A simple 2 DOF planar robot is shown. Prepare a D H parameter table and perform forward kinematics to find the location and orientation of end effector B.[Figure: base joint O on a fixed support. Link OA, 3 m long, makes 110° measured anticlockwise f…

Joint angles: \(\theta_1 = 110^\circ\); \(\theta_2 = -65^\circ\) (measured clockwise from the extension of link 1). Link 2 absolute angle \(= \theta_1 + \theta_2 = 45^\circ\).

\(^{i-1}T_i = \begin{bmatrix}\cos\theta_i & -\sin\theta_i & 0 & a_i\cos\theta_i\\ \sin\theta_i & \cos\theta_i & 0 & a_i\sin\theta_i\\ 0&0&1&0\\0&0&0&1\end{bmatrix}\)

\(^0T_1 = \begin{bmatrix}-0.342 & -0.940 & 0 & -1.026\\ 0.940 & -0.342 & 0 & 2.819\\ 0&0&1&0\\0&0&0&1\end{bmatrix}\), \(^1T_2 = \begin{bmatrix}0.423 & 0.906 & 0 & 0.845\\ -0.906 & 0.423 & 0 & -1.813\\ 0&0&1&0\\0&0&0&1\end{bmatrix}\)

\(^0T_2 = {}^0T_1\,{}^1T_2 = \begin{bmatrix}\cos45^\circ & -\sin45^\circ & 0 & 3\cos110^\circ + 2\cos45^\circ\\ \sin45^\circ & \cos45^\circ & 0 & 3\sin110^\circ + 2\sin45^\circ\\ 0&0&1&0\\0&0&0&1\end{bmatrix} = \begin{bmatrix}0.707 & -0.707 & 0 & 0.388\\ 0.707 & 0.707 & 0 & 4.233\\ 0&0&1&0\\0&0&0&1\end{bmatrix}\)

\(x_B = -1.026 + 1.414 = 0.388\) m, \(y_B = 2.819 + 1.414 = 4.233\) m

Answer: end effector B is at (0.388 m, 4.233 m) from O, with orientation 45° anticlockwise from the x-axis.