Epitrochoidal curves modified by constant difference increments and their associated inner and outer envelopes may be defined in terms of four parametric equations in Cartesian coordinates. Four basic constants are required to specify a given epitrochoid and its envelope; use is made of a digital computer program to plot examples. Curves which are useful as profiles for rotary expanders and pumps are discussed, together with the limits of the constant difference modification that can be applied. Some apparently unrelated machine profiles may be defined in terms of the basic constants discussed using the parametric equations. Examples of such machines are illustrated.

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