# Find the kinematic parameters using DH by Craig convention

I am trying to find the kinametic parameters using the J. Craig of the DH parameters for the following 2-DOF robotic manipulator.

where $$\ x,y$$ are the axes of the reference frame and $$\ q_1 , q_2$$ are the parameters of the revolute and prosmatic joint correspondingly. Until now, I have come up with the following solution:

My problem is that I am not at all sure if the term $$\ θ_1 - 90$$ is correct and if I have correctly placed the frames for the joints and the end effector. Axes $$\ x_0 , y_0 , z_0$$ are the axes of the reference frame, axes $$\ x_1 , z_1$$ are for the revolute joint, axes $$\ x_2,z_2$$ are for the prismatic joint and axes $$\ x_e,z_e$$ are for the end effector. I have intentionally left out the $$\ y$$ axes of the joints and the end effector since they are derived from the right hand rule.