A quadrilateral with four invariable lengths of sides has the characteristic of transforming the variation of the diagonal length to the variation of its interior angle. Thus, the combination of two quadrilaterals with a cam forms the differential velocity drive mechanism (DVDM) of a novel twin-rotor piston engine (TRPE). The DVDM restricts the two coaxial rotors to rotate with periodical but nonuniform velocity, and the volume of working chambers created by the adjacent vane pistons of the two rotors alternately expands and then contracts. The volumetric change of working chambers is used to generate the four-stroke engine cycle. The kinematic model and the detailed position, velocity, and acceleration analysis results of the TRPE are presented. The results show that this novel engine, associated with the advantages of higher uniformity of torque and power density due to multiple power strokes per revolution of the output shaft, has a compact and totally balanced design.