# Confusion in fixing DH frames

I am analyzing a concept of a surgical robot with 4 revolute joints and one sliding joint. I am not able to fix the coordinate frame for last prismatic joint. Following are the schematics of robot and DH frames I have fixed

As X4 axis and X5 axis are intersecting each other, I am not able to capture joint distance variable(di) for the slider. How can I fix this?

Following are the parameters for rest of the frames

Updated Frames:

• +1 for excellent penmanship! – uhoh Sep 26 '17 at 6:16

The updated image solves the problem. You did not consider the end-effector coordinate frame earlier. Also, the crosses (going into) in the diagrams should be replaced by dots(coming out), because the crosses don't hold the right hand rule in case you are using a right hand coordinate system.

Add a coordinate system that matches the previous coordinate system exactly. The last rotary joint will be the parameter for the next-to-last coordinate system, and the link length will be the parameter for the prismatic joint.

Note: a simpler approach is possible, but this gets the job done easily.

• I have added one more coordinate frame as shown in question. Is that what you suggested? Thanks – Siddhesh Sep 21 '17 at 15:39

In the first drawing the resulting D-H would results in the last line of you r D-H table to contain both $\theta_4$ and $d_1$ as parameters, provided you choose the frame in a proper way.

The second drawing solves your issue, at the coast of adding and extra frame, but makes it clearer from a parameters points of view. Although as noted @aniket-sharma the frame you draw are not direct which can lead to confusion/errors.

In general the D-H parametrization of an manipulator is not unique ! Because textbooks are listing to sets of rules, omitting to present the others. In general an open question while doing a D-H parametrization is the choice of orientation and location of both the first (base) and last (end-effector) frame.

For clarity they can be chose in a way that is not minimizing the total number of frames. Think for example as a manipulator mounted on a mobile base, for clarity some people consider as base frame a frame aligned with the one of the mobile center of mass, and then fix the first frame based on D-H convention. As for the location of the frame, for a rotational joint the origin should be located on the axis of rotation and for a prismatic joint on the direction of translation. For design where those two lines do not intersect in the 3D space or when they coinciding the location of the origin is a matter of convenience (and can be optimized for readability/simplicity or for computational efficiency).

The latter being the one at hand here, where you can have a compact form as first proposed or an easier to understand as the second proposed.