Generalized polygonal Wankel engines

Abstract

The trigonal Wankel engine is kinematically based on the motion where a circle p_m of radius 3d, as the moving pole curve, rolles on the circle p_s of radius 2d, 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_ρ . This orbit curve c_ρ is crutial in forming the engine space. Answering a question of István Revutzky, we prove (and animate by computer) that c_ρ is a convex curve iff \rho bigger or equal to 9d. The parallel curve c_ρ+r with distance r will be the solution to the engine space if the triangle rotor touches c_ρ+r with small roller circles of radius 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.