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

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