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The volumetric displacement of a Wankel rotary engine is a function of the trochoid ratio and the pin size ratio, assuming the engine has a unit depth and the number of lobes is specified. The mathematical expression which defines the displacement contains a function which can be evaluated directly and a normal elliptic integral of the second type which does not have an explicit solution. This paper focuses on the contribution of the elliptic integral to the total displacement of the engine. The influence of the elliptic integral is shown to account for as much as 20% of the total displacement, depending on the trochoid ratio and the pin size ratio. Two numerical integration techniques are compared in the paper, namely, the trapezoidal rule and Simpson's 1/3 rule. The bounds on the error, associated with each numerical method, are analyzed.

A new type of variable-stroke engine, or compressor, is presented in this paper. The stroke is adjusted by changing the length of the ground link using an auxiliary mechanism. Adjusting the ground link, changes the rotation angle and the effective length of the connecting rod, which in turn controls the pumping volume of the engine. The pumping action is caused by the motion of the piston which oscillates relative to the frame as the input crank rotates through a complete cycle. The motion of the piston induces a transverse force and a bending moment in the connecting rod but no axial force or static buckling load. Since swirl combustion is known to improve thermal efficiency, this variable-stroke engine was designed to induce high swirl rates. It is believed that this type of variable-stroke engine has not previously appeared in the literature and so a complete kinematic and dynamic force analysis is included in the paper.