The cycloidal gear profile is a form of toothed gear used in mechanical clocks. This is the page for mechanical Gears For other uses see Gear (disambiguation For the gear-like device used to drive a roller chain see Sprocket Circadian Locomotor Output Cycles Kaput, or Clock is a gene which encodes proteins regulating Circadian rhythm. The gear tooth profile is based on the epicycloid and hypocycloid curves, which are the curves generated by a circle rolling round the outside (respectively inside) of another circle. This is the page for mechanical Gears For other uses see Gear (disambiguation For the gear-like device used to drive a roller chain see Sprocket In Geometry, an epicycloid is a plane Curve produced by tracing the path of a chosen point of a Circle &mdash called epicycle &mdash which rolls without 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
When two toothed gears mesh, an imaginary circle, the pitch circle, can be drawn around the centre of either gear through the point at which 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 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. Do not confuse with Angular frequency The unit for angular velocity is rad/s
Usually the pinion radius is made equal to the generating circle diameter since this gives radial dedenda which are convenient to manufacture on a hobbing machine. A pinion is usually the smallest Gear in a gear drive train A hobbing machine is a special form of Milling machine that cuts Gears It is the major industrial process for cutting (as opposed to grinding spur gears of
There is some dispute over the invention of cycloidal gears; those involved include Gérard Desargues, Philippe de La Hire, Ole Rømer, and Charles Étienne Louis Camus. Girard Desargues ( February 21 or March 2, 1591 -October 1661 was a French Mathematician and engineer who is considered one of Philippe de La Hire (or Lahire or Phillipe de La Hire) ( March 18, 1640 — April 21, 1718) was a French Ole Christensen Rømer (o(ːlə ˈʁœːˀmɐ in Danish 25 September 1644, Århus – 19 September 1710, Copenhagen) Charles Étienne Louis Camus ( August 25, 1699 – February 2, 1768) French Mathematician and mechanician
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