# Rolling Cycloidal Curves

Rolling Cycloidal Curves

An -cusped epicycloid can roll inside an -cusped epicycloid with the same generating circle radius and if . The same holds for hypocycloids. A cycloidal gear is effectively an alternating sequence of epicycloidal- and hypocycloidal arcs. An -lobed cycloidal gear can roll inside an -lobed cycloidal gear with the same generating circle radius if .

m

n

m<n

m

n

m<n