A question about angles in the Euclidean plane

Question

It has long been known that an arbitrary angle (in the Euclidean plane) cannot be trisected using only ruler and compass, but that this can be done using a mechanical linkage. Given any positive integer $n$ greater than 1, does there always exist a mechanical linkage (as defined by Kempe) that can divide an arbitrary angle (in the plane) into $n$ equal parts?

Answer 1

The linkage by J.J. Sylvester called "A Lady's Fan" here can readily be generalized to arbitrary $n$.