hypocycloidal

A corollary to this proposition goes further by pointing out that, as the radius of the sphere is increased indefinitely, its surface approaches a plane surface and the law of the hypocycloidal asymptotically approaches Huygens's law of the cycloidal pendulum.

Newton's Philosophiae Naturalis Principia Mathematica Smith, George 2007

This not only validates Huygens's measurement of surface gravity, but also provides a formula that can be used to determine the error associated with using Huygens's theory rather than the theory of the hypocycloidal pendulum.

Newton's Philosophiae Naturalis Principia Mathematica Smith, George 2007

If you have a choice of machines, a stand mixer whose beater both spins on its shaft and traces a curlicue path from the center to the edge of the bowl a “hypocycloidal” or planetary motion beats the whites more evenly and leaves less unfoamed.

On Food and Cooking, The Science and Lore of the Kitchen Harold McGee 2004

If you have a choice of machines, a stand mixer whose beater both spins on its shaft and traces a curlicue path from the center to the edge of the bowl a “hypocycloidal” or planetary motion beats the whites more evenly and leaves less unfoamed.

On Food and Cooking, The Science and Lore of the Kitchen Harold McGee 2004

A curious arrangement of pin-gearing is shown in Fig. 38: in this case the diameter of the pinion is half that of the annular wheel, and the latter being the driver, the elementary hypocycloidal faces of its teeth are diameters of its pitch circle; the derived working tooth-outlines for pins of sensible diameter are parallels to these diameters, of which fact advantage is taken to make the pins turn in blocks which slide in straight slots as shown.

Scientific American Supplement, No. 470, January 3, 1885 Various

Newton recognized this concern and addressed it in Propositions 48 through 52 by extending Huygens's theory of the cycloidal pendulum to cover the hypocycloidal pendulum ” that is, a cycloidal path produced when the generating circle rolls along the inside of a sphere instead of along a flat surface.

Newton's Philosophiae Naturalis Principia Mathematica Smith, George 2007