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How can I determine the DH parameters of the robot shown in the figure ? As i know, the z axis should show the rotation axis for rotary joints and direction of extension for prismatic joints, so the x0 axis and z1 axis overlap. When I try to obtain a robot model with DH parameters I obtain the following model on MATLAB. I don't know how can I obtain model where the prismatic joint extends on the x0 axis.
Using the DH convention in Robot Modeling and Control by Spong, the DH table is
$$ T_2^0 = \begin{bmatrix} c_{\theta_1} & 0 & -s_{\theta_1} & 0 \\ s_{\theta_1} & 0 & c_{\theta_1} & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1+d_1 \\ 0 & 0 & 0 & 1 \end{bmatrix} $$
