**Generalized**** Polygonal
Wankel Engines**

Emil
Molnár and
Jenő Szirmai

Department of Geometry, Institute
of Mathematics

Budapest University of Technology
and Economics

The trigonal
Wankel engine is kinematically based on the motion
where a circle of
radius 3*d*, as the moving
pool curve, rolles on the
circle of radius
2*d*, as the standing pole curve in the
interior. Then the regular trigonal
rotor with outcircle of radius r>3*d*, 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__

Animation:
[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).

__Konvex and
non-konvex motor spaces__

Anaimations for the parameters: [k=3], [k=4], [k=5], [k=8].

*You*** can
download
the file „Elliptor
zip” with the
animations to a directory on your
hard drive. The animations have been created with Maple 7**.