The paper has presented an application of Kakeya-Besicovitch, third example about commutation of finite element beam endpoints inside of arbitrary small zone. This area is a hypocycloid with three cusped points at that inner tangent has a constant length independent by the point position of its inner tangent, which being rotated in clock-way it’s came back to its original position with its endpoints reversed. The application is a hydraulic pump compound by one rotated piston with elliptical section which is rolling in a fixed chamber with hypocycloid form and three cusped rounded tips after a curvature equal with major axe ellipse endpoints curvatures. The rolling motion is imposed by eccentric exterior source that acting inside of cylindrical pocket located in the center of elliptic piston, which divided the hypocycloid in three equal parts at 120° from each other. The pump could be working as a hydraulic motor which is endowed with rotating distributor that can feed each chamber with variable volume one by one due to moving the piston. The pump’s relevance is given by its efficiency, allowing a large flow capacity to a lower spindle speed, ensured a constant ratio spindle speed which working silence and a large stability.

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