A rotary engine has a cycloid rotor and a sealing grid including a face seal that rotates with the rotor, and including other seals that do not rotate with the rotor. As the rotor rotates within a housing, the rotor, housing and seal grid form at least one working chamber between them, the chamber undergoing a change from initial volume V1 to V2, which is less than V1, thus compressing a working medium, and subsequently expanding to volume V3, which may be larger than V1, such that the chamber volume is a smooth and continuous function of rotor's rotational angle.