This study investigates the incorporation of an “enhanced” hypocycloid gear mechanism (HGM) in the design and development of internal combustion engine applications. The design incorporates a uniquely geared drive that provides the means for the piston–rod assembly to transverse on a straight-line, while delivering sinusoidal profiles for piston velocity and acceleration. A further feature of this mechanism is that the pinion shafts allow for a variable leverage point between the planetary carrier assembly and the output. This characteristic provided a nonlinear rate of piston movement because of the elliptical path of the pivot around the axis of the output shaft, which by slowing down the piston movement at the top dead center (TDC) allows the truly constant-volume combustion to take place and leads to higher efficiency and higher work produced. The simulation results of the study showed that the hypocycloid gear engine produced higher in-cylinder pressure at TDC compared to the conventional slider–crank engine of the same size.