Cycloid gear: Difference between revisions
Clocks are one of the few mechanisms where a cycloid is used |
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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. |
The '''cycloidal gear''' profile is a form of toothed [[gear]] used in mechanical [[clock]]s, rather than the [[involute]] form used for most other gears. 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. |
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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. |
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. |
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Revision as of 05:36, 8 August 2013
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The cycloidal gear profile is a form of toothed gear used in mechanical clocks, rather than the involute form used for most other gears. 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. [citation needed]
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.
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