This is the equation obtained when the center of the curve (as a centered trochoid) is taken to be the origin.

More generally, the superposition of a gyration and a uniform perpendicular drift is a trochoid.

A common trochoid, also called a cycloid, has cusps at the points where P touches the L.

In geometry, a centered trochoid is the roulette formed by a circle rolling along another circle.

If we shift this horizontally by a/2 we obtain the equation in the usual form for a centered trochoid:

Alternatively, a centered trochoid can be defined as the path traced by the sum of two vectors, each moving at a uniform speed in a circle.

If the rolling curve is a circle and the fixed curve is a line then the roulette is a trochoid.

The ratio of the rates of motion and whether the moving axis translates in a straight or circular path determines the shape of the trochoid.

Trochoid: refers to any of the cycloid, the curtate cycloid and the prolate cycloid.

A prolate, or extended trochoid is traced by the tip of a paddle when a boat is driven with constant velocity by paddle wheels; this curve contains loops.

This produces the Dual generation theorem which states that, with the exception of the special case discussed below, any centered trochoid can be generated in two essentially different ways as the roulette of a circle rolling on another circle.

As a circle of radius a rolls without slipping along a line L, the center C moves parallel to L, and every other point P in the rotating plane rigidly attached to the circle traces the curve called the trochoid.

Of these, ten were particularly special and included the machine to cut the trochoid block.

"You can call it also trochoid or cycloid, but it is much the same.

Lubrication is dry sump, with a trochoid pump.

Lubrication is wet sump using a trochoid pump; an oil radiator assists with cooling.

Gear pumps trochoid pumps and vane pumps are all commonly used.

Higher temperatures and pressures affected both apex seals and the chrome-on-steel-on-aluminum coating of the trochoid surface.

The surface of the trochoid chamber which the apex seals rubbed along was coated with a CEM (composite electrochemical material) consisting of nickel silicone carbide.

The shell has a typical trochoid shape with a spire angle of approximately 72 degrees and nearly smooth sided until the body whorls which are slightly inflated at the shoulder with a rounded periphery.

The guided rotor compressor (GRC) is a positive-displacement rotary compressor based upon an envoluted trochoid geometry which utilizes a parallel trochoid curve to define its basic compression volume.

Making the trochoid profile "oversized", by the radius of the apex seal tip, was recognized as essential to seal, in three planes, and this was retained unchanged, but made heavier initially, and later changed to more rugged Curtiss-Wright patented designs that still retained the cylindrical pin.