The cycloidal gear profile is a form of toothed

gear A gear is a rotating circular machine part having cut teeth or, in the case of a cogwheel or gearwheel, inserted teeth (called ''cogs''), which mesh with another (compatible) toothed part to transmit (convert) torque and speed. The basic ...

used in mechanical

clock A clock or a timepiece is a device used to measure and indicate time. The clock is one of the oldest human inventions, meeting the need to measure intervals of time shorter than the natural units such as the day, the lunar month and t ...

s, rather than the

involute gear The involute gear profile is the most commonly used system for gearing today, with cycloid gearing still used for some specialties such as clocks. In an involute gear, the profiles of the teeth are ''involutes of a circle.'' The involute of a cir ...

form used for most other gears. The gear tooth profile is based on the

epicycloid In geometry, an epicycloid is a plane curve produced by tracing the path of a chosen point on the circumference of a circle—called an ''epicycle''—which rolls without slipping around a fixed circle. It is a particular kind of roulette. Equati ...

and

hypocycloid In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. As the radius of the larger circle is increased, the hypocycloid becomes more like the cycloid cre ...

curves, which are the curves generated by a circle rolling around the outside and inside of another circle, respectively. When two toothed gears mesh, an imaginary circle, the ''pitch circle'', can be drawn around the centre of either gear through the point where their teeth make contact. The curves of the teeth outside the pitch circle are known as the ''addenda'', and the curves of the tooth spaces inside the pitch circle are known as the ''dedenda''. An addendum of one gear rests inside a dedendum of the other gear. In the cycloidal gears, the addenda of the wheel teeth are convex epi-cycloidal and the dedenda of the pinion are concave hypocycloidal curves generated by the same generating circle. This ensures that the motion of one gear is transferred to the other at locally constant angular velocity. The size of the generating circle may be freely chosen, mostly independent of the number of teeth. Cycloidal rotor construction - 2 lobes

Roots blower The Roots-type blower is a positive displacement lobe pump which operates by pumping a fluid with a pair of meshing lobes resembling a set of stretched gears. Fluid is trapped in pockets surrounding the lobes and carried from the intake si ...

is one extreme, a form of cycloid gear where the ratio of the pitch diameter to the generating circle diameter equals twice the number of lobes. In a two-lobed blower, the generating circle is one-fourth the diameter of the pitch circles, and the teeth form complete epi- and hypo-cycloidal arcs. In clockmaking, the generating circle diameter is commonly chosen to be one-half the pitch diameter of one of the gears. This results in a dedendum which is a simple straight radial line, and therefore easy to shape and polish with hand tools. The addenda are not complete epicycloids, but portions of two different ones which intersect at a point, resulting in a "

gothic arch A pointed arch, ogival arch, or Gothic arch is an arch with a pointed crown, whose two curving sides meet at a relatively sharp angle at the top of the arch. This architectural element was particularly important in Gothic architecture. The earlie ...

" tooth profile. A limitation of this gear is that it works for a constant distance between centers of two gears. This condition -in most of the cases- is impractical because of involvement of vibration, and thus in most of the cases, an involute profile of the gear is used. There is some dispute over the invention of cycloidal gears. Those involved include

Gérard Desargues Girard Desargues (; 21 February 1591 – September 1661) was a French mathematician and engineer, who is considered one of the founders of projective geometry. Desargues' theorem, the Desargues graph, and the crater Desargues on the Moon a ...

, Philippe de La Hire, Ole Rømer, and

Charles Étienne Louis Camus Charles Étienne Louis Camus (25 August 1699 – 2 February 1768), was a French mathematician and mechanician who was born at Crécy-en-Brie, near Meaux. He studied mathematics, civil and military architecture, and astronomy after leaving Collè ...

. A

cycloid In geometry, a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another cu ...

(as used for the flank shape of a cycloidal gear) is constructed by rolling a ''rolling circle'' on a ''base circle''. If the diameter of this rolling circle is chosen to be infinitely large, a ''straight line'' is obtained. The resulting cycloid is then called an

involute In mathematics, an involute (also known as an evolvent) is a particular type of curve that is dependent on another shape or curve. An involute of a curve is the locus of a point on a piece of taut string as the string is either unwrapped from or ...

and the gear is called an

. In this respect involute gears are only a special case of cycloidal gears.

References

* Ross, D. S. (2010). "The inverse trochoid problem". J. Franklin Institute. 347 (7): 1281-1308 (2010). https://doi.org/10.1016/j.jfranklin.2010.06.003

External links

Designing cycloidal gearsKinematic Models for Design Digital Library (KMODDL)
br /> Movies and photos of hundreds of working mechanical-systems models at Cornell University. Also includes a
e-book library
of classic texts on mechanical design and engineering.
2 and 4-cog cycloidal gears in motion
{{Gears Gears Roulettes (curve)

See also

References

External links