Users specify joints by giving a frame on the parent link (Jp) and a frame on the child link (Jc), plus joint-specific info. Joints are implemented with mobilizers that use an inboard frame F and outboard frame M in the multibody tree. Currently we use Jp and Jc for F and M. This is not always the optimal choice, in which case we would be better off making up new F and M's for computation, transforming back to Jp and Jc only when needed.

Examples are:

• Weld joints should enforce that F and M are always coincident, so that we do not have to compose X_FM during kinematics. Currently they enforce an arbitrary X_FM matching X_JpJc. A better choice of F (e.g. coincident with Jc) would make X_FM identity.
• Pin, prismatic, and screw joints specify an axis in addition to Jp and Jc. The underlying mobilizers would be much more efficient if the axis was aligned with one of the F and M coordinate axes. In that case the axis has only one non-zero element (a 1!) and the R_FM rotation matrix has a special 2d structure where only 4 elements change.

The victory condition for this issue is that we can create and bookkeep new frames, with appropriate conversions back to Jp and Jc as necessary, with a single example implemented (say Weld), without necessarily taking advantage yet of the potential speedups.

Separate issues will be filed for special-casing more mobilizers and taking advantage of the simplifications.

This is part of the Multibody performance epic #18442