OK, that would be mote a math/geometry problem than a AutoCAD technics (Jig) problem.
For example, you may want the moving entity rotates while moving, similar like the Moom moves around the Earth: while moving, it also rotates so that it alway with one side facing the Earth.
Assume you have an arc, which is a quarter of cricle. When move the antity from the arc's start to the end, the entity would also need to rotate 90 degree. Therefore, you can use the silimalr technics shown in my article and then get rotate angle (90 degree when moved a quarter of circle). It would be easy to calculate what the roate angle of the entity should be while moving long a circle (or arc). Once you get the rotation angle figured out, you just apply a rotation transform to the moving entity in the Jig's sampling code.