Rack Pinion Mobilizer

[MarvinSt]

Rack Pinion Mobilizer

[sherm1]

A rack and pinion (and other geared systems) can be expressed by modeling the joints as mobilizers and the gear with a coupler constraint. Even that is a simplification since, although it models the motion correctly, it does not accurately capture the reaction forces at the gear contact (which produce measurable reactions elsewhere). It is not obvious to me how the entire mechanism could be replaced by a mobilizer. Recall from the paper that a mobilizer is a relationship between two bodies, defined by a transform function and related hinge matrix. Although not clear from the illustration above, a rack and pinion is a relation among three bodies -- the shaft, the rack, and the case (the shaft rotates wrt the case; the rack translates wrt the case. So to me that looks like two mobilizers plus a constraint.

In contrast a screw joint is a relation between only two bodies and is easily modeled as a mobilizer.

Do you see a way to model the rack & pinion as a single mobilizer?

[MarvinSt]

Yes, you are correct. A rack-pinion system will require a support body to weld the revolute joint to. I see that this is not required for the screw mobilizer.

I solved it now as follows, not sure if there is a better / more convenient way:

auto steering_rack = MobilizedBody::Slider(chassis_body, Transform(FromDirectionVector(steering_rack_dir, XAxis), PosWorldToBody(chassis_body, steering_rack_pos)), steeringRackInfo, Transform(Vec3(0)));

auto steering_shaft = MobilizedBody::Revolute(chassis_body, TransformWorldToBody(chassis_body, pinion_center_at_rack, steering_shaft_dir, ZAxis), steeringShaftInfo, Transform(Vec3(0.0, 0.0, -steering_shaft_len / 2.0)));

Constraint::NoSlip1D(chassis_body, PosWorldToBody(chassis_body, pinion_virtual_contact_pos), UnitVec3(steering_rack_dir), steering_rack, steering_shaft);

Better illustration below, the rack mount and pinion mount are attached to the same casing:

I think we can close this issue, as I misunderstood the concept of the mobilizers.

[sherm1]

That's a nice solution -- better than using a Coupler constraint since it properly places the reaction force at the contact point. One thing to note is that it NoSlip1d is a non-holonomic (velocity) constraint so doesn't specify the relation between the rotational and translational position coordinates. That's not necessarily a problem, just means you should take care to initialize those coordinates as you want them at start of simulation.

BTW, you may want to consider adopting "monogram" notation as a way to keep all the frames straight. Simbody uses that in its documentation, but we have refined it and documented it better in Drake here.