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The Rand-Cam engine is a positive displacement machine, operating on a four stroke cycle, which consists of a rotor with multiple axial vanes forming combustion chambers as the rotor and vanes rotate in a cam shaped housing. The cam housing, consisting of two “half-housings” or stators, contains a toroidal trough of varying depth machined into each stator. The two stators are phased so that the shallowest point on one trough corresponds to the deepest on the other. A set of six vanes, able to move axially through machined holes in the rotor, traverses the troughs creating six captured zones per side. These zones vary in volume with rotor rotation. Since each trough has two deep sections and two shallow sections with ramps in between, full four stroke operation is obtained between each pair of vanes in each trough, corresponding to twelve power “strokes” per revolution.