Definitions
from The Century Dictionary.
 In the form of an epicycloid; depending upon the properties of the epicycloid.
from the GNU version of the Collaborative International Dictionary of English.
 adjective Pertaining to the epicycloid, or having its properties.
 adjective a device for producing straightline motion from circular motion, on the principle that a pin fastened in the periphery of a gear wheel will describe a straight line when the wheel rolls around inside a fixed internal gear of twice its diameter.
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 adjective Of or pertaining to an
epicycloid .
Etymologies
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

The gear segments, eighteen in number, are made of gun iron, and the teeth are machinecut, epicycloidal in form.
Burroughs' Encyclopaedia of Astounding Facts and Useful Information, 1889

For instance, if the lens requires to be ground down near the centre, the epicycloidal strokes must be nearly central; the tool must never overhang very much.

V¹ = v '(1  5/4) =  ¼v': the planet wheel, or epicycloidal yoke, then, has the higher speed, so that if it be desired to "gear up," and drive the propeller faster than the engine goes (and this, we believe, was the purpose of the inventor), the pinwheel must be made the driver; which is the reverse of advantageous in respect to the relative amounts of approaching and receding action.

The carrying is done continuously by a train of epicycloidal wheels.
Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary"

From point of division 4, step off on L four points of division, as _a_, _b_, _c_, _d_; and _d_ will be another point on the epicycloidal curve.

Were it possible to divide the ellipse accurately, there would be no difficulty in laying out these curves; but having substituted the circular arcs, we must now roll the generating circle upon these as bases, thus forming true epicycloidal teeth, of which those lying upon the same approximating arc will be exactly alike.

With the compasses set to the radius of divisions 1, 2, etc., step off on arc M the five divisions, N, O, S, T, V, and at V will be a point on the epicycloidal curve.

The only person 'oo might' ave connected the epicycloidal gears correctly was one Pyecroft, when he was told that Mr. Vickery would go up country that same evening to take over certain naval ammunition left after the war in Bloemfontein Fort.

It is selfevident that the hypocycloid must return into itself at the point of beginning, without crossing: each branch, then, must subtend an aliquot part of the circumference, and can be traced also by another and a smaller describing circle, whose diameter therefore must be an aliquot part of the diameter of the outer pitchcircle; and since this last must be equal to the sum of the diameters of the two describing circles, it follows that the radii of the pitch circles must be to each other in the ratio of two successive integers; and this is also the ratio of the number of pins to that of the epicycloidal branches.
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