Department of Geometry, Institute
Budapest University of Technology
The trigonal Wankel engine is kinematically based on the motion where a circle of radius 3d, as the moving pool curve, rolles on the circle of radius 2d, as the standing pole curve in the interior. Then the regular trigonal rotor with outcircle of radius r>3d, fixed concentrically the moving pole circle, describes its orbit curve . This orbit curve is crutial in forming the engine space.
Answering a question of István Revuczky we prove and animate by computer that is a convex curve iff . The parallel curve with distance r will be the solution to the engine space if the triangle rotor touches 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 (, natural numbers) in a natural way.
The moving and the standing pole curves
[k=3-t], The moving
pole curve rolles
ont he standing pole curve . The moving pole
curve is a circle of the critical
radius kd, The standing pole curve is of radius (k-1)d ( here k=3, d=1, r=6).
Animation: [k=4-t], The moving pole curve rolles ont he standing pole curve . The moving pole curve is a circle of the critical radius kd, The standing pole curve is of radius (k-1)d ( here k=4, d=1, r=7).
non-konvex motor spaces
Anaimations for the parameters: [k=3], [k=4], [k=5], [k=8].
the file „Elliptor
zip” with the
animations to a directory on your
hard drive. The animations have been created with Maple 7.