Kempe Universality

Created Donnerstag 25 Juli 2024

With one or more joints of a Planar linkage pinned to the plane, the motion of any particular free joint J is constrained by the structure of the linkage. A specific question here is this:

Let S be an arbitrary algebraic curve in the plane. Is there some linkage so that the motion of some free joint J traces out precisely S?

Yes. The original idea and a flawed proof for the construction of a linkage to trace a given curve is due to Alfred B. Kempe from 1876. The proof was repaired 2002.

Still open question: Whether there is a linkage to follow any algebraic curve that does not self-intersect during motion.

Backlinks: Design Problems