# Generalized polygonal Wankel engines

## Abstract

The trigonal Wankel engine is kinematically based on the motion
where a circle *p _{m}* of radius 3

*d*, as the moving pole curve, rolles on the circle

*p*of radius 2

_{s}*d*, as the standing pole curve in the interior. Then the regular trigonal rotor with circumcircle of radius

*ρ > 3d*, fixed concentrically to the moving pole circle, describes its orbit curve

*c*. This orbit curve

_{ρ}*c*is crutial in forming the engine space. Answering a question of István Revutzky, we prove (and animate by computer) that

_{ρ}*c*is a convex curve iff

_{ρ}*\rho*bigger or equal to 9

*d*. The parallel curve

*c*with distance

_{ρ+r}*r*will be the solution to the engine space if the triangle rotor touches

*c*with small roller circles of radius

_{ρ+r }*r*centred in the vertices of the triangle. All these concepts will be generalized - with animation - to a k-gonal rotor (2 < k natural number) in a unified way.