Cycloid gear
Encyclopedia
The cycloidal gear profile is a form of toothed gear
used in mechanical clock
s. The gear tooth profile is based on the epicycloid
and hypocycloid
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 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
.
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
.
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
.
Gear
A gear is a rotating machine part having cut teeth, or cogs, which mesh with another toothed part in order to transmit torque. Two or more gears working in tandem are called a transmission and can produce a mechanical advantage through a gear ratio and thus may be considered a simple machine....
used in mechanical clock
Clock
A clock is an instrument used to indicate, keep, and co-ordinate time. The word clock is derived ultimately from the Celtic words clagan and clocca meaning "bell". A silent instrument missing such a mechanism has traditionally been known as a timepiece...
s. The gear tooth profile is based on the epicycloid
Epicycloid
In geometry, an epicycloid is a plane curve produced by tracing the path of a chosen point of a circle — called an epicycle — which rolls without slipping around a fixed circle...
and hypocycloid
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...
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 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
Angular velocity
In physics, the angular velocity is a vector quantity which specifies the angular speed of an object and the axis about which the object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per...
.
Usually the pinion
Pinion
A pinion is a round gear used in several applications:*usually the smallest gear in a gear drive train, although in the case of John Blenkinsop's Salamanca, the pinion was rather large...
radius is made equal to the generating circle diameter since this gives radial dedenda which are convenient to manufacture on a hobbing machine
Hobbing machine
Hobbing is a machining process for making gears, splines, and sprockets on a hobbing machine, which is a special type of milling machine. The teeth or splines are progressively cut into the workpiece by a series of cuts made by a cutting tool called a hob...
.
There is some dispute over the invention of cycloidal gears; those involved include Gérard Desargues
Gérard Desargues
Girard Desargues 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 are named in his honour.Born in Lyon, Desargues came from a family devoted to service to the French...
, Philippe de La Hire
Philippe de La Hire
Philippe de La Hire was a French mathematician and astronomer. According to Bernard le Bovier de Fontenelle he was an "academy unto himself"....
, Ole Rømer, and Charles Étienne Louis Camus
Charles Étienne Louis Camus
Charles Étienne Louis Camus , was a French mathematician and mechanician who was born at Crecy-en-Brie, near Meaux....
.
External links
- Designing cycloidal gears
- Kinematic Models for Design Digital Library (KMODDL)
Movies and photos of hundreds of working mechanical-systems models at Cornell University. Also includes an e-book library of classic texts on mechanical design and engineering. - 2 and 4-cog cycloidal gears in motion