# DH Parameters with offset base

I'm looking at a pan tilt (RR) system. I want to define the kinematics between a world frame and the end effector. Every example I've seen looks at the world frame as being at the first joint (the zero frame). Can DH parameters be used with an offset base? My initial thought is yes, and that you define your world frame, your base frame, and your joint frames.Then there is an extra T matrix, but that one doesn't change since the transformation between your world frame and the fixed base frame is fixed. Thanks

You are correct in the sense that you just need an extra transformation from your world frame to the first frame (fixed) in you D-H parametrization. This transformation might be fixed or time varying (if you consider a mobile base robot for instance), but is not part of the D-H parametrization.

In other words, your D-H parametrization describes the kinematic of a joint collection in a generic way, then you have a transformation from world frame to the first joint which is not part of the D-H parametrization and should more be considered as on off-set.

• "our D-H parametrization describes the kinematic of a joint collection in a generic way, then you have a transformation from world frame to the first joint which is not part of the D-H parametrization and should more be considered as on off-set." This is the 'missing' piece of info I needed to help make it fully click. Thanks. – MechanicalMan Mar 5 at 0:15

You're correct-ish, but technically the DH parameters should go from actuated axis to actuated axis, so you would leave the (unactuated) base frame out completely and just go world coordinate to the first actuated axis.

You could of course just treat the base as a joint that you just never actuate ($\theta =0$).

Yes, you can just set up an additional transformation matrix from the global coordinate system to the first system at the base of the robot. These terms will all be constants. As @Chuck mentions, this is probably not technically D-H notation but the math works and it is simple to do.