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rolling together without slip. In the case of non-circular gears, those circles are replaced with anything different from a circle. For this reason NCGs in most cases are not round, but round NCGs that look like regular gears are also possible (small ratio variations result from meshing area
410:
Each wheel must be cyclic in its angular coordinates. If the shape of the first wheel is known, the shape of the second can often be found using the above equations. If the relationship between the angles is specified, the shapes of both wheels can often be determined analytically as well.
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Assuming that the point of contact lies on the line connecting the axles, in order for the gears to touch without slipping, the velocity of each wheel must be equal at the point of contact and perpendicular to the line connecting the axles, which implies that:
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distance, could prove impossible to support, and such gears require very tight manufacturing tolerances and assembling problems arise. Because of complicated
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Noncircular Gears: Design and
Generation by Faydor L. Litvin, Alfonso Fuentes-Aznar, Ignacio Gonzalez-Perez, and Kenichi Hayasaka
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Generally, NCGs should meet all the requirements of regular gearing but in some cases, for example variable
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describe the rotation of the first and second gears respectively. This equation can be formally solved as:
981:
183:
113:
634:{\displaystyle {\frac {dz_{2}}{z_{2}}}={\frac {r_{1}(z_{1})}{a-r_{1}(z_{1})}}\,{\frac {dz_{1}}{z_{1}}}}
853:{\displaystyle \ln(z_{2})=\ln(K)+\int {\frac {r_{1}(z_{1})}{a-r_{1}(z_{1})}}\,{\frac {dz_{1}}{z_{1}}}}
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when analyzing this problem. Assuming the radius of the first gear wheel is known as a function of
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design with special characteristics and purpose. While a regular gear is optimized to transmit
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Ignoring the gear teeth for the moment (i.e. assuming the gear teeth are very small), let
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be the radius of the second gear wheel as a function of angle from its axis of rotation
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be the radius of the first gear wheel as a function of angle from the axis of rotation
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71:), window shade panel drives, mechanical presses and high torque hydraulic engines.
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Laczik - Design and
Manufacturing of Non-Circular Gears by Given Transfer Function
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250:. If the axles remain fixed, the distance between the axles is also fixed:
997:"Gear geometry and applied theory" by Faydor L. Litvin and Alfonso Fuentes
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Maurice
Lacroix Masterpiece Regulateur Roue Carree. Squaring the Circle.
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to another engaged member with minimum noise and wear and with maximum
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Zarebski I., Salacinski T.: Designing of non-circular gears
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325:{\displaystyle r_{1}(\theta _{1})+r_{2}(\theta _{2})=a\,}
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and more. Common applications include textile machines,
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Kinematic Models for Design
Digital Library (KMODDL)
414:It is more convenient to use the circular variable
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55:, a non-circular gear's main objective might be
967:Historic Video of Non-Circular Gears on YouTube
992:Laczik- Involute Profile of Non-Circular Gears
926:Laczik- Involute Profile of Non-Circular Gears
74:A regular gear pair can be represented as two
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1002:A paper on designing of non-circular gears
102:technology is used instead of generation.
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69:continuously variable transmissions
16:Gear in a shape other than a circle
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1200:Continuously variable transmission
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216:{\displaystyle r_{2}(\theta _{2})}
146:{\displaystyle r_{1}(\theta _{1})}
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486:{\displaystyle dz=iz\,d\theta }
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443:{\displaystyle z=e^{i\theta }}
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100:electrical discharge machining
59:variations, axle displacement
1:
1077:Epicyclic (planetary) gearing
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454:, and using the relationship
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243:{\displaystyle \theta _{2}}
173:{\displaystyle \theta _{1}}
10:
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1013: (archived 2014-05-09)
988: (archived 2013-06-05)
1321:Spur gear corrected tooth
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31:Another non-circular gear
23:Non-circular gear example
106:Mathematical description
90:, NCGs are most likely
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888:{\displaystyle \ln(K)}
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1243:Shaft-driven bicycle
972:The Eye of an Artist
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1082:Sun and planet gear
982:The Gear Oscillator
1311:Gear manufacturing
1147:Geartooth profiles
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1062:Spur gear systems
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1072:Rack and pinion
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1011:Wayback Machine
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1180:Differential
1175:Transmission
1128:Spiral bevel
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61:oscillations
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36:
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1306:Chain drive
1266:Wheel train
1138:Herringbone
1301:Belt drive
1286:Ball screw
1233:Derailleur
1067:Worm drive
899:References
180:, and let
92:spur gears
53:efficiency
1316:Freewheel
1296:Jackscrew
1291:Leadscrew
1168:Mechanics
874:
789:−
752:∫
737:
712:
570:−
481:θ
436:θ
389:θ
362:θ
304:θ
275:θ
232:θ
202:θ
162:θ
132:θ
1336:Category
1279:See also
1258:Horology
1248:Sprocket
1238:Hub gear
1221:Bicycles
1214:Examples
1185:Coupling
1154:Involute
88:geometry
67:, CVTs (
1159:Cycloid
1133:Helical
1055:Systems
1009:at the
984:at the
96:molding
76:circles
1228:Cogset
1205:Offset
1106:Shapes
863:where
644:where
49:torque
1342:Gears
1190:Train
1123:Crown
1118:Bevel
1048:Gears
57:ratio
1113:Spur
671:and
94:and
84:axle
45:gear
98:or
41:NCG
1338::
932:^
907:^
871:ln
734:ln
709:ln
35:A
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