I'm working on a robot gimbal where there are 4 revolute joints (4th axis for gimbal lock, reducing inertia etc). The robot is nodal such that all axes have the same nodal point and rotating any axes keeps does not change the position of the end effector, only changes its look direction.
Normally for kinematics I define my robots just with trig. This time I'm trying to learn how to define the robot with DH parameters as it seems like every article I've read about 4 axis gimbals has used DH to define the model so I need to understand it.
Below is my kinematics diagram of the robot in its home position and what I'd like to check is that I've correctly defined my frames. I've been a bit confused with finding the common normal as the Xi distance to Zi-1 is zero so I found it hard to visualize that. I think I finally got it correct though.
The grayed out part of this model is just a support bearing. I added it for my own clarity as that's how the actual robot looks.
This is then the DH parameter table I came up with. I think the only length value that matters is L1. Since the robot is nodal, the length of the links 2 and 3 could be anything and it wouldn't affect it so I put them as zero, but the distance from the base to the robots nodal point does matter.
Did I define my model frames/DH parameters correctly?