A triangular rotary engine includes several main components such as an eccentric shaft, a sun gear, a triangular rotor, a chamber, and apex seals. This study constructs the mathematical models for the chamber and triangular rotor profiles in a rotary engine, as well as for the kinematics and contact force of its apex seals by using the epitrochoid and envelope principles. The chamber profile is represented by design parameter, trochoid ratio, whose limitations are investigated together with the volume ratio. To simplify the calculation, the dynamics analysis model ignores the effects of combustion and thermal conditions in rotary engines. Gas force effect is taken into account by first constructing a fluid analysis model that measures the gas fluid moment on the triangular rotor. Then, based on the mathematical models of chamber and rotor, a systematic dynamics analysis model for a rotary engine is built. It allows analyzing the kinematics and the stress variations in all components of the engine. The dynamics model considers both output shaft torsion and fluid moment. The dynamics analysis then uses three cases of trochoid ratio to illustrate the effects of chamber profile design on the system dynamics properties of rotary engines. The results not only show the dynamic properties and differences in various mechanism designs but also indicate the stability and stress level in the components. In conclusion, the higher trochoid ratio with a larger variation in the chamber profile curvature reduces system stability and increases vibrations, stress fluctuations, and large stress peaks risk.

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