There are 2 main rules in assigning frames following DH convention: source: Robot Modeling and Control, Spong et. al $x_i \perp z_{i-1}$ $x_i$ intersects $z_{i-1}$ In your attempts, Your first attempt is incorrect as your $z_2$ axis is not in the direction of actuation of the prismatic joint. I'm not clear on your second attempt as $x_1$ appears to be ...


Kinematics is based on geometry and joint constraints, so no change there at all. Dynamic motion results from the sum of forces, so the only change to a dynamic analysis is that you don't include gravity, but all other forces would remain.


Seems that the book has an error. You are right, they should correct that. In the drawing it can be seen that those two z-axis are indeed parallel. I recommend that you considered them parallel and try to draw them to see that it fits with the image.

Only top voted, non community-wiki answers of a minimum length are eligible