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A rotary engine includes a housing having a working cavity, a shaft, the shaft having an eccentric portion, a rotor having a first axial face, and a second axial face opposite the first axial face, the rotor disposed on the eccentric portion and within the working cavity, the rotor comprising a firs

A rotary engine includes a housing having a working cavity, a shaft, the shaft having an eccentric portion, a rotor having a first axial face, and a second axial face opposite the first axial face, the rotor disposed on the eccentric portion and within the working cavity, the rotor comprising a first cam on the first axial face, the first came having an eccentricity corresponding to the eccentricity of the eccentric portion of the shaft, and a cover integral with, or fixedly attached to, the housing, the cover comprising a plurality or rollers, each roller engaged with the cam, wherein the cam guides the rotation of the rotor as the rotor rotates within the working cavity and orbits around the shaft.

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1. A rotary engine comprising: a housing having a working cavity;a shaft having an eccentric portion;a rotor having a first axial face, and a second axial face opposite the first axial face, the rotor disposed on the eccentric portion and within the working cavity, the rotor comprising a first cam o

1. A rotary engine comprising: a housing having a working cavity;a shaft having an eccentric portion;a rotor having a first axial face, and a second axial face opposite the first axial face, the rotor disposed on the eccentric portion and within the working cavity, the rotor comprising a first cam on the first axial face, the first cam having an eccentricity corresponding to the eccentricity of the eccentric portion of the shaft; anda cover integral with, or fixedly attached to, the housing, the cover comprising a plurality of rollers, each roller engaged with the first cam, wherein the first cam guides the rotation of the rotor as the rotor rotates within the working cavity and orbits around the shaft. 2. The rotary engine of claim 1, further comprising a second cam on the second axial face of the rotor. 3. A rotary engine comprising: a housing having a working cavity;a shaft having an eccentric portion;a rotor having a first axial face, and a second axial face opposite the first axial face, the rotor disposed on the eccentric portion and within the working cavity;a first cam rigidly attached to the rotor;a cover integral with, or fixedly attached to, the housing; anda plurality of cam followers rigidly attached to the cover, each cam follower engaged with the first cam,wherein the first cam guides the rotation of the rotor as the rotor rotates within the working cavity and orbits around the shaft. 4. The rotary engine of claim 3, further comprising a second cam on the second axial face of the rotor. 5. The rotary engine of claim 3, wherein the plurality of cam followers comprise rollers. 6. The rotary engine of claim 3, wherein the rotor comprises N lobes, and the housing comprises N+1 lobe-receiving regions for successively receiving the lobes as the rotor rotates about an axis relative to the housing so as to form a working chamber of variable volume with the housing, the housing having (i) a peak disposed between each pair of adjacent lobe-receiving regions, and (ii) an intake port and an exhaust port, and the rotary engine further comprises: a plurality of peak seals, at least one of the plurality of peak seals disposed on each peak and configured to maintain contact with the rotor throughout a period of rotation of the rotor, each peak seal being radially biased against the rotor throughout the rotation of the rotor;a first passageway defined in the rotor to communicate cyclically between the intake port and the working chamber, the first passageway configured to allow air to enter from a radial face of the rotor into the working chamber, the working chamber defined as a volume lying between two peak seals, the housing and the rotor;a second passageway, distinct from the first passageway, defined in the rotor to communicate cyclically between the exhaust port and the working chamber, the second passageway configured to allow exhaust gas to exit from the working chamber through the radial face of the rotor. 7. The rotary engine of claim 6, wherein, at a first angle of the rotor within the housing, the working chamber forms a compression chamber having a maximum compression chamber volume, and at a second angle of the rotor within the housing the working chamber forms an expansion chamber having a maximum expansion chamber volume, the maximum expansion chamber volume being at greater than or equal to 1.0 times the maximum compression chamber volume. 8. The engine according to claim 7, wherein the maximum expansion chamber volume is at least 3 times the maximum compression chamber volume. 9. A cycloid engine including: a rotor having N lobes and a first cam rigidly attached to the rotor;a housing having a corresponding set of N+1 lobe-receiving regions for successively receiving the lobes as the rotor rotates about an axis relative to the housing, the housing having:(i) a first cover and a second cover axially disposed on first and second sides of the rotor, respectively, and a plurality of cam followers rigidly attached to the first cover or the second cover, each cam follower engaged with the first cam, wherein the first cam guides the rotation of the rotor as the rotor rotates within the housing;(ii) a peak disposed between each pair of adjacent lobe-receiving regions, and(iii) an intake port and an exhaust port;a plurality of peak seals, at least one of the plurality of peak seals disposed on each peak and configured to maintain contact with the rotor throughout a period of rotation of the rotor, each peak seal being radially biased against the rotor throughout the rotation of the rotor, on account of a cycloidal geometry of the rotor and the lobe-receiving portions;a first passageway defined in the rotor to communicate cyclically between the intake port and a working chamber, the first passageway configured to allow air to enter from a radial face of the rotor into the working chamber, the working chamber defined as a volume lying between two peak seals, the housing and the rotor; anda second passageway, distinct from the first passageway, defined in the rotor to communicate cyclically between the exhaust port and the working chamber, the second passageway configured to allow exhaust gas to exit from the working chamber through the radial face of the rotor. 10. The engine according to claim 9, further comprising: a first face seal, disposed between the first cover of the housing and the rotor, configured to seal the working chamber; anda second face seal, disposed between the second cover of the housing and the rotor, configured to seal the working chamber;wherein the first face seal is disposed near an outer edge of the rotor, the outer edge defined by an intersection of an axial face of the rotor with the radial face of the rotor, wherein the passageways and the face seals are configured to cause each face seal to maintain contact with both the rotor and one of the covers of the housing through all angular positions of the rotor while avoiding communication with either of the ports. 11. The engine according to claim 10, wherein the second face seal is disposed near a second outer edge of the rotor, the second outer edge defined by an intersection of a second axial face of the rotor with the radial face of the rotor. 12. The engine according to claim 10, wherein the first face seal is disposed on the axial face of the rotor, and the axial face includes a landing at the outer edge, wherein the landing is between the outer edge and the first face seal, the engine further comprising a button seal disposed so as to contact the rotor and the first face seal at the landing. 13. The engine according to claim 10, further comprising a lubricant channel in the first cover or the second cover, the lubricant channel disposed so as to continuously deliver lubricant to a corresponding one of the face seals. 14. The engine according to claim 9, wherein, at a first angle of the rotor within the housing, the working chamber forms a compression chamber having a maximum compression chamber volume, and at a second angle of the rotor within the housing the working chamber forms an expansion chamber having a maximum expansion chamber volume, the maximum expansion chamber volume being greater than or equal to 1.0 times the maximum compression chamber volume. 15. The engine according to claim 14, wherein the maximum expansion chamber volume is at least 3 times the maximum compression chamber volume. 16. The engine according to claim 9, further comprising a plurality of lubricant channels in the first cover or the second cover, each of the plurality of the lubricant channels disposed so as to deliver lubricant to a corresponding one of the plurality of peak seals. 17. The engine according to claim 9, wherein each peak seal has a contact region with the rotor, and the contact region is curved with a radius of curvature equal to a radius of curvature of a theoretical roller, which theoretical roller is uniquely defined by the geometry of the rotor and the geometry of the lobe-receiving regions.