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In this paper an approach is presented for the system parameterization and synthesis of a Rand-Cam® Engine configuration based on an axial-cylindrical cam driven mechanism. This engine consists of a stationary axial-cylindrical cam on which axially moving pistons (vanes) sweep around the cam as they are driven by the rotor, providing the volume displacement as the rotor delivers the rotary output torque directly to the shaft. It has been documented that this engine configuration has some unique features that make it particularly suitable for high power to weight ratio applications. The modeling strategy makes use of higher order curve and surface modeling techniques and object modeling approaches based on profile extruding, blending operations and constructive solid geometry. Some of the resulting models are further used for finite element engineering analysis through a programmatic logic built into the parameterized general model.