This paper deals with the kinematic synthesis of volumetric rotary machines, which are generated by the planetary motion of regular curve-polygons.

In particular, the synthesis of both outer and inner conjugate profiles has been formulated as envelope of the polycentric profiles of a generating regular curve-polygon with any number of lobes, different radii of the circumcircle and rounded corners.

A regular curve-polygon with cusp corners can be obtained as a particular case, like the Reuleaux triangle.

Finally, the proposed formulation has been implemented in a Matlab code and several examples are reported.

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