Can anyone share their DH parameters for a simple PRP manipulator. I have some confusion in setting up the axes and obtaining a solution.
In some cases, as are you two cases in the upper part of the image, you might need additional "dummy" coordinate system to end up in the correct orientation. These are just additional lines in the DH table, with most of the coordinates set to 0.
In the upper left solution you might need an additional dummy coordinate system to transform from the 2nd coordinate system to the third one. Just add a dummy coordinate system with a pi/2 z rotation and the x rotation should be pi instead of pi/2 in the transformation which follows (now the 2nd line in the table).
the upper right one needs a dummy transformation with a pi/2 z rotation between system 2 and 3.
The lower left side solution is ok and so is the lower right side one.
Kinematic frames are different from the physical structure and the working drawings we create can lead us astray. Frames don't necessarily sit on the physical structure. In the frames sketch below frame 1 and 2 overlap. A close mechanical analog with a shift on the x axis between 1 and 2 is shown. However the only requirement is that the z axis match the direction of motion. Also I find it helpful to add my q parameters to the DH table entries so that the offset (the DH constant) is clear.