The gerotor is a planar mechanism consisting of two surfaces whose rel
ative motion can be described by the kinematics of orbiting pitch circ
les. Typically, gerotor surfaces are prismatic with the axes of rotati
on parallel to the ruled surfaces. For a given position, the generated
cross section of the mechanism in the plane of motion is independent
of the location of the section along the axis of rotation. In this wor
k, a mathematical derivation for producing gerotors with non-prismatic
surfaces is presented. The implementation results in two types of ger
otors, mechanisms with conical surfaces relative to the rotor axis, an
d mechanisms with helical surfaces. These are relatively new invention
s and this is the first publication of the mathematical model describi
ng these mechanisms. The derivations of the mathematics associated wit
h each mechanism are presented. Comparisons of the mechanisms are pres
ented based on the displacement, compression ratio and surface area to
volume ratio. (C) 1997 Elsevier Science Ltd.