The application of the characteristics of cycloidal curves for the fou
r-stroke rotary internal combustion engine mechanism is introduced. Th
e major components of the cycloidal engine mechanism include a flywhee
l, a stationary sun gear, planetary gears, rotary bars, and rotary pis
tons. The rotary pistons are fixed to bars driven by pins of the plane
tary gears, and these pins follow a common trajectory of epicyloidal o
r hypocycloidal curve. Several combustion chambers are created by the
rotary pistons. As the flywheel makes a complete revolution, the relat
ive motion between rotary pistons and the specially positioned intake
ports, exhaust ports, and fuel injector generate four-stoke cycles wit
hin each of the combustion chambers. The constraint and classification
of the application of different cycloidal curves for the rotary engin
e mechanism are then presented. Further, the mathematical modeling is
developed. The position, velocity, and acceleration analyses of the ro
tary pistons of the cycloidal engine mechanisms are presented.