5158:
planets have "timing marks" (or "relative gear mesh phase" in technical term). The assembly conditions of compound planetary gears are more restrictive than simple planetary gears, and they must be assembled in the correct initial orientation relative to each other, or their teeth will not simultaneously engage the sun and ring gear at opposite ends of the planet, leading to very rough running and short life. In 2015, a traction based variant of the "stepped-planet" design was developed at the Delft
University of Technology, which relies on compression of the stepped planet elements to achieve torque transmission. The use of traction elements eliminates the need to "timing marks" as well as the restrictive assembly conditions as typically found. Compound planetary gears can easily achieve larger transmission ratio with equal or smaller volume. For example, compound planets with teeth in a 2:1 ratio with a 50T ring gear would give the same effect as a 100T ring gear, but with half the actual diameter.
152:
5195:. Idler gears are used between sun gear and the planets to cause the sun gear to rotate in the same direction as the ring gear when the planet carrier is stationary. At low input speed, because of the load on the output, the sun will be stationary and the planet carrier will rotate in the direction of the ring gear. Given a high enough load, the turbine of the torque converter will remain stationary, the energy will be dissipated and the torque converter pump will slip. If the input speed is increased to overcome the load the converter turbine will turn the output shaft. Because the torque converter itself is a load on the planet carrier, a force will be exerted on the sun gear. Both the planet carrier and the sun gear extract energy from the system and apply it to the output shaft.
129:, which meshes with the planet gears. Planetary gears (or epicyclic gears) are typically classified as simple or compound planetary gears. Simple planetary gears have one sun, one ring, one carrier, and one planet set. Compound planetary gears involve one or more of the following three types of structures: meshed-planet (there are at least two more planets in mesh with each other in each planet train), stepped-planet (there exists a shaft connection between two planets in each planet train), and multi-stage structures (the system contains two or more planet sets). Compared to simple planetary gears, compound planetary gears have the advantages of larger reduction ratio, higher torque-to-weight ratio, and more flexible configurations.
4585:
5351:
5237:
wear quickly and sometimes crack. But the planetary speed reducer has multiple gear contacting surfaces with a larger area that can distribute the loading evenly around the central axis. Multiple gear surfaces share the load, including any instantaneous impact loading, evenly, which makes them more resistant to damage from higher torque. The housing and bearing parts are also less likely to be damaged from high loading as only the planet carrier bearings experience significant lateral force from the transmission of torque, radial forces oppose each other and are balanced, and axial forces only arise when using helical gears.
5388:
4788:
5372:
5204:
27:
5312:
543:
83:
6715:
843:
6705:
5251:
5363:
5128:
2762:
614:
4564:
3180:
4356:
3034:
2905:
1505:
237:. Two facing gears were rotated around slightly different centers; one drove the other, not with meshed teeth but with a pin inserted into a slot on the second. As the slot drove the second gear, the radius of driving would change, thus invoking a speeding up and slowing down of the driven gear in each revolution.
1365:
838:{\displaystyle {\begin{aligned}N_{\text{s}}\,\omega _{\text{s}}+N_{\text{p}}\,\omega _{\text{p}}-\left(N_{\text{s}}+N_{\text{p}}\,\right)\,\omega _{\text{c}}&=0\\N_{\text{r}}\,\omega _{\text{r}}-N_{\text{p}}\,\omega _{\text{p}}-\left(N_{\text{r}}-N_{\text{p}}\right)\,\omega _{\text{c}}&=0\end{aligned}}}
1238:
4778:
is a convenient way to distinguish the sun gears of the two epicyclic gear trains. Ring gears are normally fixed in most applications as this arrangement will have a good reduction capacity. The second sun gear serves the same purpose as the ring gear of a simple planetary gear train but clearly does
476:
If one is to create an asymmetric carrier frame with non-equiangular planet gears, say to create some kind of mechanical vibration in the system, one must make the teething such that the above equation complies with the "imaginary gears". For example, in the case where a carrier frame is intended to
166:
Epicyclic gearing is also available which consists of a sun, a carrier, and two planets which mesh with each other. One planet meshes with the sun gear, while the second planet meshes with the ring gear. For this case, when the carrier is fixed, the ring gear rotates in the same direction as the sun
5232:
In a typical application, the drive power connects to the sun gear. The sun gear then drives the planetary gears assembled with the external gear ring to operate. The whole set of planetary gear system revolves on its own axis and along the external gear ring where the output shaft connected to the
5177:
gear, where a very high reduction ratio in a small package was needed. This had two outer ring gears, each half the thickness of the other gears. One of these two ring gears was held fixed and had one tooth fewer than did the other. Therefore, several turns of the "sun" gear made the "planet" gears
4798:
Some epicyclic gear trains employ two planetary gears which mesh with each other. One of these planets meshes with the sun gear, the other planet meshes with the ring gear. This results in different ratios being generated by the planetary and also causes the sun gear to rotate in the same direction
5157:
Some designs use "stepped-planet" which have two differently-sized gears on either end of a common shaft. The small end engages the sun, while the large end engages the ring gear. This may be necessary to achieve smaller step changes in gear ratio when the overall package size is limited. Compound
217:
that form epicyclic gear trains to predict the motions of the planets. Accurate predictions of the movement of the Sun, Moon, and the five planets, Mercury, Venus, Mars, Jupiter, and Saturn, across the sky assumed that each followed a trajectory traced by a point on the planet gear of an epicyclic
5236:
The method of motion of a planetary gear structure is different from traditional parallel gears. Traditional gears rely on a small number of contact points between two gears to transfer the driving force. In this case, all the loading is concentrated on a few contacting surfaces, making the gears
5216:
Planetary gear trains provide high power density in comparison to standard parallel axis gear trains. They provide a reduction in volume, multiple kinematic combinations, purely torsional reactions, and coaxial shafting. Disadvantages include high bearing loads, constant lubrication requirements,
5335:
are easy to 3D print, it has become very popular to 3D print a moving herringbone planetary gear system for teaching children how gears work. An advantage of herringbone gears is that they don't fall out of the ring and don't need a mounting plate, allowing the moving parts to be clearly seen.
1951:
In one arrangement, the planetary carrier (green in the diagram above) is held stationary, and the sun gear (yellow) is used as input. In that case, the planetary gears simply rotate about their own axes (i.e., spin) at a rate determined by the number of teeth in each gear. If the sun gear has
4375:
3042:
5327:
A geared-down motor must turn farther and faster in order to produce the same output movement in the 3D printer which is advantageous if it is not outweighed by the slower movement speed. If the stepper motor has to turn farther then it also has to take more steps to move the printer a given
1618:
3741:— Torque of carrier. For all three, these are the torques applied to the mechanism (input torques). Output torques have the reverse sign of input torques. These torque ratios can be derived using the law of conservation of energy. Applied to a single stage this equation is expressed as:
4174:
4155:
2619:
5328:
distance; therefore, the geared-down stepper motor has a smaller minimum step-size than the same stepper motor without a gearbox. While down-gearing improves precision in unidirectional motion, it adds backlash to the system and so reduces its absolute positioning accuracy.
5220:
The efficiency loss in a planetary gear train is typically about 3% per stage. This type of efficiency ensures that a high proportion (about 97%) of the energy being input is transmitted through the gearbox, rather than being wasted on mechanical losses inside the gearbox.
2913:
2784:
1112:
5228:
The planetary gear train also provides stability due to an even distribution of mass and increased rotational stiffness. Torque applied radially onto the gears of a planetary gear train is transferred radially by the gear, without lateral pressure on the gear teeth.
3942:
The fundamental formula of the planetary gear train with a rotating carrier is obtained by recognizing that this formula remains true if the angular velocities of the sun, planet and ring gears are computed relative to the carrier angular velocity. This becomes,
2495:
50:
mounted so that the center of one gear (the "planet") revolves around the center of the other (the "sun"). A carrier connects the centers of the two gears and rotates, to carry the planet gear(s) around the sun gear. The planet and sun gears mesh so that their
1373:
5350:
3190:
In epicyclic gears, two speeds must be known, in order to determine the third speed. However, in a steady state condition, only one torque must be known, in order to determine the other two torques. The equations which determine torque are:
1246:
1120:
5323:
for a few different reasons. Planetary gear boxes can provide a large gear ratio in a small, light-weight package. Some people install such gearboxes to get more accurate 3D prints by gearing-down the movement of their stepper motors.
1874:
915:
5211:
with stationary ring gear and rotating planet carrier as input. Planet gears are extended into cylindrical cutters, rotating around the pencil that is placed on the sun axis. The axes of planetary gears join at the pencil sharpening
3845:
A convenient approach to determine the various speed ratios available in a planetary gear train begins by considering the speed ratio of the gear train when the carrier is held fixed. This is known as the fixed carrier train ratio.
5161:
More planet and sun gear units can be placed in series in the same housing (where the output shaft of the first stage becomes the input shaft of the next stage) providing a larger (or smaller) gear ratio. This is the way most
4559:{\displaystyle {\frac {-\omega _{c}}{\omega _{r}-\omega _{c}}}=R,\quad {\mbox{or}}\quad {\frac {\omega _{r}}{\omega _{c}}}=1-{\frac {1}{R}},\quad {\mbox{so}}\quad {\frac {\omega _{r}}{\omega _{c}}}=1+{\frac {N_{s}}{N_{r}}}.}
3175:{\displaystyle \alpha _{\text{c}}={\frac {{\text{N}}_{\text{s}}}{{\text{N}}_{\text{s}}+{\text{N}}_{\text{r}}}}\alpha _{\text{s}}+{\frac {{\text{N}}_{\text{r}}}{{\text{N}}_{\text{s}}+{\text{N}}_{\text{r}}}}\alpha _{\text{r}}}
489:
of an epicyclic gearing system is somewhat non-intuitive, particularly because there are several ways in which an input rotation can be converted into an output rotation. The four basic components of the epicyclic gear are:
3832:
4871:
4688:
4024:
3934:
1516:
5224:
The load in a planetary gear train is shared among multiple planets; therefore, torque capability is greatly increased. The more planets in the system, the greater the load ability and the higher the torque density.
2756:
5190:
More than one member of a system can serve as an output. As an example, the input is connected to the ring gear, the sun gear is connected to the output and the planet carrier is connected to the output through a
4766:
4351:{\displaystyle {\frac {\omega _{s}-\omega _{c}}{-\omega _{c}}}=R,\quad {\mbox{or}}\quad {\frac {\omega _{s}}{\omega _{c}}}=1-R,\quad {\mbox{so}}\quad {\frac {\omega _{s}}{\omega _{c}}}=1+{\frac {N_{r}}{N_{s}}}.}
367:
2390:
The ring gear may also be held fixed, with input provided to the planetary gear carrier; output rotation is then produced from the sun gear. This configuration will produce an increase in gear ratio, equal to
4571:
Each of the speed ratios available to a simple planetary gear train can be obtained by using band brakes to hold and release the carrier, sun or ring gears as needed. This provides the basic structure for an
3654:
3506:
3423:
3340:
4596:
is constructed from two identical coaxial epicyclic gear trains assembled with a single carrier such that their planet gears are engaged. This forms a planetary gear train with a fixed carrier train ratio
4044:
2385:
2277:
1773:
2502:
2329:
2189:
2062:
1934:
5054:
5116:
4794:
of epicyclic gearing with 56-tooth ring gear locked (1), 24-tooth sun gear locked (2), carrier with 16-tooth planetary gears locked (3) and direct drive (4) – numbers denote relative angular speed
3029:{\displaystyle \alpha _{\text{r}}={\frac {{\text{N}}_{\text{s}}+{\text{N}}_{\text{r}}}{{\text{N}}_{\text{r}}}}\alpha _{\text{c}}-{\frac {{\text{N}}_{\text{s}}}{{\text{N}}_{\text{r}}}}\alpha _{\text{s}}}
2900:{\displaystyle \alpha _{\text{s}}={\frac {{\text{N}}_{\text{s}}+{\text{N}}_{\text{r}}}{{\text{N}}_{\text{s}}}}\alpha _{\text{c}}-{\frac {{\text{N}}_{\text{r}}}{{\text{N}}_{\text{s}}}}\alpha _{\text{r}}}
1667:
4987:
2679:
5233:
planetary carrier achieves the goal of speed reduction. A higher reduction ratio can be achieved by doubling the multiple staged gears and planetary gears which can operate within the same ring gear.
3571:
3257:
1012:
988:
5166:
work. In some cases multiple stages may even share the same ring gear which can be extended down the length of the transmission, or even be a structural part of the casing of smaller gearboxes.
619:
3849:
In the case of a simple planetary gear train formed by a carrier supporting a planet gear engaged with a sun and ring gear, the fixed carrier train ratio is computed as the speed ratio of the
2394:
4925:
1710:, receiving power from the system. The ratio of input rotation to output rotation is dependent upon the number of teeth in each of the gears, and upon which component is held stationary.
5964:
5387:
2692:, the sun is usually stationary, being keyed to the axle or even machined directly onto it. The planetary gear carrier is used as input. In this case the gear ratio is simply given by
412:
1500:{\displaystyle \omega _{\text{c}}={\frac {N_{\text{s}}}{\,N_{\text{s}}+N_{\text{r}}\,}}\,\omega _{\text{s}}+{\frac {N_{\text{r}}}{\,N_{\text{s}}+N_{\text{r}}\,}}\,\omega _{\text{r}}}
1700:
608:
The overall gear ratio of a simple planetary gearset can be calculated using the following two equations, representing the sun-planet and planet-ring interactions respectively:
2140:
2008:
1979:
2191:
turns for each turn of the planetary gears. For instance, if the ring gear has 64 teeth, and the planets 16 teeth, one clockwise turn of a planet gear results in
449:
302:
1360:{\displaystyle \omega _{\text{r}}={\frac {\,N_{\text{s}}+N_{\text{r}}\,}{N_{\text{r}}}}\,\omega _{\text{c}}-{\frac {\,N_{\text{s}}\,}{N_{\text{r}}}}\,\omega _{\text{s}}}
3739:
3712:
3685:
477:
contain planet gears spaced 0°, 50°, 120°, and 230°, one is to calculate as if there are actually 36 planetary gears (10° equiangular), rather than the four real ones.
1233:{\displaystyle \omega _{\text{s}}={\frac {\,N_{\text{s}}+N_{\text{r}}\,}{N_{\text{s}}}}\,\omega _{\text{c}}-{\frac {\,N_{\text{r}}\,}{N_{\text{s}}}}\omega _{\text{r}}}
1781:
4588:
A spur gear differential constructed by engaging the planet gears of two co-axial epicyclic gear trains. The casing is the carrier for this planetary gear train.
854:
1940:
These relationships can be used to analyze any epicyclic system, including those, such as hybrid vehicle transmissions, where two of the components are used as
471:
62:
An epicyclic gear train can be assembled so the planet gear rolls on the inside of the pitch circle of an outer gear ring, or ring gear, sometimes called an
5356:
Split ring, compound planet, epicyclic gears of a car rear-view mirror positioner. This has a ratio from input sun gear to output black ring gear of −5/352.
5315:
Animation of a printable gear set. Legend: driving shaft and sun gear (green), ring gear (dark gray), planet gears (blue), driven shaft and carrier (red).
2113:
Rotation of the planet gears can in turn drive the ring gear (not depicted in diagram), at a speed corresponding to the gear ratios: If the ring gear has
546:
In this example, the carrier (green) is held stationary while the sun gear (yellow) is used as input. Analysis assumes a common gear design modulus. The
189:, circa 80 BCE, had gearing which was able to closely match the Moon's elliptical path through the heavens, and even to correct for the nine-year
5142:"Compound planetary gear" is a general concept and it refers to any planetary gears involving one or more of the following three types of structures:
3748:
2499:
If the ring gear is held stationary and the sun gear is used as the input, the planet carrier will be the output. The gear ratio in this case will be
86:
The red marks show the relative displacement of the sun gear and carrier, when the sun gear is rotated 180° clockwise and the ring gear is held fixed.
4805:
4610:
1613:{\displaystyle -{\frac {\,N_{\text{r}}\,}{N_{\text{s}}}}={\frac {\,\omega _{\text{s}}-\omega _{\text{c}}\,}{\omega _{\text{r}}-\omega _{\text{c}}}}}
5890:
3949:
3859:
255:, a vertically revolving bookstand containing epicyclic gearing with two levels of planetary gears to maintain proper orientation of the books.
5371:
2695:
4771:
Thus, the angular velocity of the carrier of a spur gear differential is the average of the angular velocities of the sun and ring gears.
4699:
310:
5972:
5461:
4150:{\displaystyle {\frac {\omega _{s}}{\omega _{r}}}=R,\quad {\mbox{so}}\quad {\frac {\omega _{s}}{\omega _{r}}}=-{\frac {N_{r}}{N_{s}}}.}
3577:
3429:
3346:
3263:
2614:{\displaystyle \,1/\left(1+{\tfrac {\,N_{\text{r}}\,}{N_{\text{s}}}}\right)={\tfrac {N_{\text{s}}}{\,N_{\text{s}}+N_{\text{r}}\,}}\;,}
2338:
2230:
1716:
2285:
2145:
2013:
1885:
151:
4996:
5063:
4029:
This formula provides a simple way to determine the speed ratios for the simple planetary gear train under different conditions:
1626:
1107:{\displaystyle N_{\text{s}}\,\omega _{\text{s}}+N_{\text{r}}\,\omega _{\text{r}}=(N_{\text{s}}+N_{\text{r}})\,\omega _{\text{c}}}
70:. By choosing to hold one component or another—the planetary carrier, the ring gear, or the sun gear—stationary, three different
4935:
2624:
3512:
3198:
175:
Around 500 BCE, the Greeks invented the idea of epicycles, of circles travelling on the circular orbits. With this theory
5394:
940:
6318:
30:
This planetary gear train consists of a sun gear (yellow), planet gears (blue) and carrier (green) inside a ring gear (red)
5716:
6434:
6164:
5423:
5272:
2490:{\displaystyle \;1+{\tfrac {\,N_{\text{r}}\,}{N_{\text{s}}}}={\tfrac {\,N_{\text{s}}+N_{\text{r}}\,}{N_{\text{s}}}}~.}
5764:
5609:
5582:
5298:
5280:
6444:
6144:
5686:
4593:
137:
121:, which itself may rotate relative to the sun gear. Epicyclic gearing systems also incorporate the use of an outer
5876:
4879:
6003:
5138:
with the smaller planet series meshing with the sun wheel and the larger planet series meshing with the ring gear
2681:
This is the lowest gear ratio attainable with an epicyclic gear train. This type of gearing is sometimes used in
5626:
55:
roll without slip. If the sun gear is held fixed, then a point on the pitch circle of the planet gear traces an
6391:
5735:
5570:
5276:
2103:
377:
193:
of that path. (The Greeks interpreted the motion they saw, not as elliptical, but rather as epicyclic motion.)
5599:
6469:
5378:
4584:
1672:
6739:
5842:
5466:
5127:
6544:
5806:
Miller, John M. (May 2006). "Hybrid electric vehicle propulsion system architectures of the e-CVT type".
3837:
In the cases where gears are accelerating, or to account for friction, these equations must be modified.
5178:
complete a single revolution, which in turn made the rotating ring gear rotate by a single tooth like a
6381:
5471:
4791:
2778:
From the above formulae, we can also derive the accelerations of the sun, ring and carrier, which are:
2116:
1984:
1955:
6680:
6569:
6509:
6474:
6285:
5482:
1669:
In many epicyclic gearing systems, one of these three basic components is held stationary (hence set
6459:
6311:
5555:
5261:
5849:
P. A. Simionescu (1998-09-01). "A Unified
Approach to the Assembly Condition of Epicyclic Gears".
427:
280:
6429:
6401:
6139:
5265:
4787:
2064:
For instance, if the sun gear has 24 teeth, and each planet has 16 teeth, then the ratio is
1713:
Alternatively, in the special case where the number of teeth on each gear meets the relationship
6419:
6409:
5799:
5163:
4573:
3717:
3690:
3663:
240:
5549:
4799:
as the ring gear when the planet carrier is the stationary. The fundamental equation becomes:
5756:
5708:
5417:
5412:
277:
In order that the planet gear teeth mesh properly with both the sun and ring gears, assuming
226:
214:
199:
186:
5969:
1869:{\displaystyle n\,\omega _{\text{s}}+(2+n)\,\omega _{\text{r}}-2(1+n)\,\omega _{\text{c}}=0}
6514:
6449:
6207:
5815:
5641:
910:{\displaystyle \omega _{\text{r}},\omega _{\text{s}},\omega _{\text{p}},\omega _{\text{c}}}
5788:
550:(blue) turn in a ratio determined by the number of teeth in each gear. Here, the ratio is
243:, an English abbot of St. Albans monastery, later described epicyclic gearing for an
8:
6539:
6519:
6304:
6051:
6046:
5996:
5819:
5645:
6685:
6590:
6275:
5831:
5657:
5146:(there are at least two or more planets in mesh with each other in each planet train),
513:(s): Usually two to four peripheral gears, all of the same size, that mesh between the
456:
244:
234:
5789:"How to derive and calculate epicyclic gear ratio equations in planetary gear systems"
5692:(Report). NASA Reference Publication. Vol. 1152. AVSCOM Technical Report 84-C-15.
185:
in 148 CE was able to approximate planetary paths observed crossing the sky. The
6704:
6414:
6366:
6348:
6265:
6092:
6061:
5770:
5760:
5749:
5731:
5722:
5712:
5605:
5578:
604:
the rate of the sun gear, in the opposite direction. An outer ring gear is not shown.
230:
167:
gear, thus providing a reversal in direction compared to standard epicyclic gearing.
133:
20:
5661:
5331:
One popular use of 3D printed planetary gear systems is as toys for children. Since
66:. Such an assembly of a planet engaging both a sun gear and a ring gear is called a
26:
6554:
6361:
6102:
5858:
5835:
5823:
5649:
5476:
5332:
5208:
5192:
5132:
918:
259:
248:
210:
176:
16:
Two gears mounted so the center of one gear revolves around the center of the other
6574:
6504:
6159:
6056:
6036:
5976:
5891:"52514 Caterpillar Tractor D8 Bulldozer Powershift Transmission Promotional Film"
5429:
5179:
71:
43:
5949:
5944:
5936:, movies and photos of hundreds of working mechanical-systems models at Cornell.
5150:(there exists a shaft connection between two planets in each planet train), and
3853:
formed by the sun, planet and ring gears on the fixed carrier. This is given by
3827:{\displaystyle \tau _{r}\omega _{r}+\tau _{c}\omega _{c}+\tau _{s}\omega _{s}=0}
6744:
6675:
6489:
6484:
6375:
6371:
6169:
5989:
5487:
5450:
2766:
5933:
5774:
5726:
4866:{\displaystyle (R-1)\omega _{\text{c}}=R\omega _{\text{r}}-\omega _{\text{s}}}
4683:{\displaystyle {\frac {\omega _{s}-\omega _{c}}{\omega _{r}-\omega _{c}}}=-1,}
6733:
6718:
6657:
6642:
6622:
6549:
6386:
6356:
6149:
6118:
5954:
5827:
5705:
Revolving
Architecture: A history of buildings that rotate, swivel, and pivot
5653:
5203:
4019:{\displaystyle R={\frac {\omega _{s}-\omega _{c}}{\omega _{r}-\omega _{c}}}.}
3929:{\displaystyle R={\frac {\omega _{s}}{\omega _{r}}}=-{\frac {N_{r}}{N_{s}}}.}
1702:
for whichever gear is stationary); one of the two remaining components is an
538:: An outer ring with inward-facing teeth that mesh with the planetary gear(s)
6627:
6564:
6534:
6529:
6123:
5439:
5311:
5170:
4604:
In this case, the fundamental formula for the planetary gear train yields,
2335:
So, with the planetary carrier locked, one turn of the sun gear results in
542:
52:
2223:
clockwise turns of the ring gear. Extending this case from the one above:
229:, circa 80 BCE, to adjust the displayed position of the Moon for the
6708:
6632:
6605:
6600:
6464:
6454:
6270:
6230:
5393:
One of three sets of three gears inside the planet carrier of a Ford FMX
5320:
219:
2751:{\displaystyle {\tfrac {\,N_{\text{s}}+N_{\text{r}}\,}{N_{\text{r}}}}~.}
144:(see below). Further, the sun, planet carrier and ring axes are usually
82:
6690:
6652:
6494:
6327:
6250:
6197:
6154:
6087:
6082:
6031:
5918:
Gears and Their
Vibration: A Basic Approach to Understanding Gear Noise
5434:
3850:
2685:
and construction equipment to provide high torque to the drive wheels.
486:
304:
equally spaced planet gears, the following equation must be satisfied:
190:
141:
132:
The axes of all gears are usually parallel, but for special cases like
56:
5939:
5862:
5173:, a special variation of epicyclic gearing was developed for portable
480:
6647:
6637:
6559:
6524:
6280:
6260:
6255:
6077:
6026:
5684:
5493:
252:
155:
5250:
4761:{\displaystyle \omega _{c}={\frac {1}{2}}(\omega _{s}+\omega _{r}).}
6439:
6222:
6212:
6202:
6097:
5455:
5362:
5135:
2689:
2682:
362:{\displaystyle {\frac {N_{\text{s}}+N_{\text{r}}}{n_{\text{p}}}}=A}
205:
181:
5445:
507:
gear(s) symmetrically and separated, all meshed with the sun gear
145:
5490:– First major manufacturer of bicycle hubs using planetary gears
4779:
not have the internal gear mate that is typical of a ring gear.
3649:{\displaystyle \tau _{s}=-\tau _{c}{\frac {N_{s}}{N_{r}+N_{s}}}}
3501:{\displaystyle \tau _{c}=-\tau _{s}{\frac {N_{r}+N_{s}}{N_{s}}}}
3418:{\displaystyle \tau _{c}=-\tau _{r}{\frac {N_{r}+N_{s}}{N_{r}}}}
3335:{\displaystyle \tau _{r}=-\tau _{c}{\frac {N_{r}}{N_{r}+N_{s}}}}
1706:, providing power to the system, while the last component is an
262:
designed and constructed the first mill with epicycloidal teeth
6610:
6424:
6192:
5959:
5604:(2nd ed.). Oxford, UK: Butterworth-Heinemann. p. 58.
106:
4774:
In discussing the spur gear differential, the use of the term
3185:
2773:
2380:{\displaystyle \;-{\tfrac {\,N_{\text{s}}\,}{N_{\text{r}}}}\;}
2272:{\displaystyle \,-{\tfrac {\,N_{\text{s}}\,}{N_{\text{p}}}}\,}
1768:{\displaystyle \,N_{\text{r}}=N_{\text{s}}+2\,N_{\text{p}}\;,}
117:. Typically, the planet gears are mounted on a movable arm or
6595:
6499:
6296:
5746:
5577:(4th ed.). Cheltenham, UK: Nelson Thornes. p. 244.
5174:
2324:{\displaystyle \,{\tfrac {\,N_{\text{p}}\,}{N_{\text{r}}}}\,}
2184:{\displaystyle \,{\tfrac {\,N_{\text{p}}\,}{N_{\text{r}}}}\,}
2057:{\displaystyle -{\tfrac {\,N_{\text{s}}\,}{N_{\text{p}}}}\;.}
1929:{\displaystyle n={\tfrac {\,N_{\text{s}}\,}{N_{\text{p}}}}\;}
247:
in the 14th century. In 1588, Italian military engineer
5049:{\displaystyle \omega _{\text{r}}=\omega _{\text{c}}(R-1)/R}
2761:
6617:
6012:
5111:{\displaystyle \omega _{\text{s}}=-\omega _{\text{c}}(R-1)}
4782:
1662:{\displaystyle \omega _{\text{r}}\neq \omega _{\text{c}}~.}
98:
47:
4982:{\displaystyle \omega _{\text{r}}=\omega _{\text{s}}(1/R)}
2674:{\displaystyle \;N_{\text{s}}:N_{\text{s}}+N_{\text{r}}~.}
140:, they can be placed at an angle, introducing elements of
6338:
3566:{\displaystyle \tau _{s}=\tau _{r}{\frac {N_{s}}{N_{r}}}}
3252:{\displaystyle \tau _{r}=\tau _{s}{\frac {N_{r}}{N_{s}}}}
5981:
5707:. New York, NY: Princeton Architectural Press. p.
5515:
5513:
5511:
4489:
4434:
4281:
4233:
4083:
3939:
In this calculation the planet gear is an idler gear.
2758:
The number of teeth in the planet gear is irrelevant.
2700:
2565:
2527:
2439:
2406:
2347:
2291:
2239:
2151:
2021:
1896:
983:{\displaystyle N_{\text{r}},N_{\text{s}},N_{\text{p}}}
5519:
J. J. Uicker, G. R. Pennock and J. E. Shigley, 2003,
5066:
4999:
4938:
4882:
4808:
4702:
4613:
4378:
4177:
4047:
3952:
3862:
3751:
3720:
3693:
3666:
3580:
3515:
3432:
3349:
3266:
3201:
3045:
2916:
2787:
2698:
2627:
2505:
2397:
2341:
2288:
2233:
2148:
2119:
2016:
1987:
1958:
1888:
1784:
1719:
1675:
1629:
1519:
1376:
1249:
1123:
1015:
943:
857:
617:
459:
430:
380:
313:
283:
5934:
Kinematic Models for Design
Digital Library (KMODDL)
5755:. Toronto, ON: University of Toronto Press. p.
2110:
turns of each of the planet gear(s) about its axis.
272:
5751:
Science and
Technology in the Industrial Revolution
5508:
5496:- a wheel that incorporates a planetary gear system
481:
Gear speed ratios of conventional epicyclic gearing
5748:
5740:
5685:Coy, J.J.; Townsend, D.P.; Zaretsky, E.V. (1985).
5618:
5110:
5048:
4981:
4919:
4865:
4760:
4682:
4558:
4350:
4149:
4018:
3928:
3826:
3733:
3706:
3679:
3648:
3565:
3500:
3417:
3334:
3251:
3174:
3028:
2899:
2750:
2673:
2613:
2489:
2379:
2323:
2271:
2183:
2134:
2056:
2002:
1973:
1928:
1868:
1767:
1694:
1661:
1612:
1499:
1359:
1232:
1106:
982:
909:
837:
465:
451:is the number of planet gears in the assembly and
443:
406:
361:
296:
5597:
1775:the equation can be re-written as the following:
6731:
5848:
5920:. Marcel Dekker, New York and MacMillan, London
5805:
5571:"Planetary gearing and unidirectional clutches"
5154:(the system contains two or more planet sets).
5531:
5529:
19:For the ring gear used in starter motors, see
6312:
5997:
5955:The "Interactive Planetary Gearset tutorial"
4920:{\displaystyle R=-N_{\text{r}}/N_{\text{s}}}
3840:
5702:
5537:Kinematics and Dynamics of Planar Machinery
5526:
5279:. Unsourced material may be challenged and
5122:
3186:Torque ratios of standard epicyclic gearing
2774:Accelerations of standard epicyclic gearing
101:system consisting of one or more outer, or
6319:
6305:
6004:
5990:
5970:Short Cuts for Analyzing Planetary Gearing
5905:Gear Drive Systems: Design and Application
5462:NuVinci continuously variable transmission
5420:– ancient mechanical astronomical computer
2628:
2607:
2398:
2376:
2342:
2050:
1925:
1761:
5299:Learn how and when to remove this message
4579:
2727:
2703:
2602:
2578:
2541:
2530:
2506:
2466:
2442:
2420:
2409:
2361:
2350:
2320:
2305:
2294:
2289:
2268:
2253:
2242:
2234:
2180:
2165:
2154:
2149:
2131:
2120:
2035:
2024:
1999:
1988:
1970:
1959:
1910:
1899:
1849:
1817:
1788:
1750:
1720:
1581:
1557:
1537:
1526:
1486:
1482:
1458:
1431:
1427:
1403:
1346:
1332:
1321:
1304:
1290:
1266:
1206:
1195:
1178:
1164:
1140:
1093:
1050:
1026:
810:
763:
739:
704:
698:
656:
632:
588:; meaning that each planet gear turns at
407:{\displaystyle N_{\text{s}},N_{\text{r}}}
5747:Musson, A.E.; Robinson, Eric H. (1969).
5627:"The Antikythera Mechanism reconsidered"
5575:Fundamentals of Motor Vehicle Technology
5310:
5217:inaccessibility, and design complexity.
5202:
5126:
4786:
4783:Gear ratio of reversed epicyclic gearing
4583:
2760:
1006:from which we can derive the following:
541:
150:
81:
25:
5568:
5442:– had a 2 speed planetary transmission.
5319:Planetary gears have become popular in
2106:turn of the sun gear produces 1.5
6732:
5808:IEEE Transactions on Power Electronics
5624:
1695:{\displaystyle \omega _{\text{...}}=0}
6300:
5985:
5680:
5678:
2282:One turn of a planet gear results in
5940:"Epicyclic gearing animation in SVG"
5598:Harrison, H.; Nettleton, T. (1994).
5277:adding citations to reliable sources
5244:
2227:One turn of the sun gear results in
2142:teeth, then the ring will rotate by
218:gear train. This curve is called an
196:In the 2nd century AD treatise
5601:Principles of Engineering Mechanics
13:
6435:Continuously variable transmission
6165:Continuously variable transmission
5675:
5523:Oxford University Press, New York.
5521:Theory of Machines and Mechanisms,
5424:Continuously variable transmission
5185:
2769:AM bicycle hub (ring gear removed)
2010:teeth, then the ratio is equal to
258:French mathematician and engineer
225:Epicyclic gearing was used in the
14:
6756:
5927:
5634:Interdisciplinary Science Reviews
4162:2. The ring gear is held fixed, ω
273:Requirements for non-interference
6714:
6713:
6703:
5945:"Animation of Epicyclic gearing"
5386:
5370:
5361:
5349:
5249:
4363:3. The sun gear is held fixed, ω
2135:{\displaystyle \,N_{\text{r}}\,}
2003:{\displaystyle \,N_{\text{p}}\,}
1981:teeth, and each planet gear has
1974:{\displaystyle \,N_{\text{s}}\,}
1936:is the sun-to-planet gear ratio.
5910:
5897:
5883:
5869:
5781:
4495:
4487:
4440:
4432:
4287:
4279:
4239:
4231:
4089:
4081:
4032:1. The carrier is held fixed, ω
990:are the number of teeth of the
414:are the number of teeth of the
160:Le diverse et artifiose machine
6326:
5696:
5591:
5562:
5542:
5479:– 14-ratio bicycle hub gearbox
5379:Pratt & Whitney Canada PT6
5240:
5105:
5093:
5035:
5023:
4976:
4962:
4821:
4809:
4752:
4726:
1846:
1834:
1814:
1802:
1090:
1064:
1:
6470:Automated manual transmission
6042:Epicyclic (planetary) gearing
5501:
5198:
5136:internally geared bicycle hub
5131:Stepped planet series of the
5118:when the ring gear is locked.
2621:which may also be written as
263:
5851:Journal of Mechanical Design
5467:Ravigneaux planetary gearset
3687:— Torque of ring (annulus),
1948:relative to the two inputs.
444:{\displaystyle n_{\text{p}}}
297:{\displaystyle n_{\text{p}}}
109:, revolving about a central
7:
6545:Semi-automatic transmission
5703:Randl, Chad (15 May 2008).
5405:
4989:when the carrier is locked,
233:, and even for its orbital
77:
46:assembly consisting of two
10:
6761:
6382:Internal combustion engine
5472:Lepelletier gear mechanism
5339:
170:
158:, from Agostino Ramelli's
18:
6699:
6681:Hybrid vehicle drivetrain
6668:
6583:
6570:Transmission control unit
6510:Limited-slip differential
6475:Electrorheological clutch
6400:
6347:
6334:
6286:Spur gear corrected tooth
6243:
6221:
6185:
6178:
6132:
6111:
6070:
6019:
6011:
5907:. Marcel Dekker, New York
5483:Simpson planetary gearset
3841:Fixed carrier train ratio
3734:{\displaystyle \tau _{c}}
3707:{\displaystyle \tau _{s}}
3680:{\displaystyle \tau _{r}}
1944:with the third providing
6460:Dual-clutch transmission
5950:The "Power Split Device"
5828:10.1109/TPEL.2006.872372
5654:10.1179/030801807X163670
5569:Hillier, V.A.W. (2001).
5556:University of California
5123:Compound planetary gears
2387:turns of the ring gear.
231:ellipticity of its orbit
6430:Constant-velocity joint
5164:automatic transmissions
5056:when the sun is locked,
6410:Automatic transmission
5316:
5213:
5152:multi-stage structures
5139:
5112:
5050:
4983:
4921:
4867:
4795:
4762:
4684:
4594:spur gear differential
4589:
4580:Spur gear differential
4574:automatic transmission
4560:
4352:
4151:
4020:
3930:
3828:
3735:
3708:
3681:
3650:
3567:
3502:
3419:
3336:
3253:
3176:
3030:
2901:
2770:
2765:Compound planets of a
2752:
2675:
2615:
2491:
2381:
2331:turns of the ring gear
2325:
2273:
2185:
2136:
2102:; this means that one
2058:
2004:
1975:
1930:
1870:
1769:
1696:
1663:
1614:
1501:
1361:
1234:
1108:
984:
911:
839:
605:
467:
445:
408:
363:
298:
241:Richard of Wallingford
215:deferent and epicycles
163:
87:
31:
5903:Lynwander, P., 1983,
5625:Wright, M.T. (2007).
5418:Antikythera mechanism
5413:Hypocycloidal gearing
5314:
5206:
5130:
5113:
5051:
4984:
4922:
4868:
4790:
4763:
4685:
4587:
4561:
4353:
4152:
4021:
3931:
3829:
3736:
3709:
3682:
3651:
3568:
3503:
3420:
3337:
3254:
3177:
3031:
2902:
2764:
2753:
2676:
2616:
2492:
2382:
2326:
2274:
2186:
2137:
2059:
2005:
1976:
1931:
1871:
1770:
1697:
1664:
1615:
1502:
1362:
1235:
1109:
985:
912:
840:
545:
468:
446:
409:
364:
299:
227:Antikythera Mechanism
200:Mathematical Syntaxis
187:Antikythera Mechanism
154:
85:
29:
6515:Locking differential
6450:Direct-shift gearbox
6208:Shaft-driven bicycle
5916:Smith, J. D., 1983,
5558:. 1913. p. 979.
5551:Machinery, Volume 19
5458:, for bicycles, etc.
5273:improve this section
5064:
4997:
4936:
4880:
4806:
4700:
4611:
4376:
4175:
4045:
3950:
3860:
3749:
3718:
3691:
3664:
3578:
3513:
3430:
3347:
3264:
3199:
3043:
2914:
2785:
2696:
2625:
2503:
2395:
2339:
2286:
2279:turns of the planets
2231:
2146:
2117:
2014:
1985:
1956:
1886:
1782:
1717:
1673:
1627:
1517:
1374:
1247:
1121:
1013:
941:
855:
615:
503:: Holds one or more
457:
428:
378:
311:
281:
68:planetary gear train
36:epicyclic gear train
6740:Epicyclical gearing
6540:Preselector gearbox
6520:Manual transmission
6047:Sun and planet gear
5820:2006ITPE...21..756M
5646:2007ISRv...32...27W
5381:gas turbine engine.
5377:Reduction gears on
5207:The mechanism of a
422:, respectively and
6686:Electric generator
6591:Wheel hub assembly
6276:Gear manufacturing
6112:Geartooth profiles
5975:2021-02-25 at the
5877:"Archimedes Drive"
5317:
5214:
5140:
5108:
5046:
4979:
4929:which results in:
4917:
4863:
4796:
4758:
4680:
4590:
4556:
4493:
4438:
4348:
4285:
4237:
4147:
4087:
4016:
3926:
3824:
3731:
3704:
3677:
3646:
3563:
3498:
3415:
3332:
3249:
3172:
3026:
2897:
2771:
2748:
2740:
2671:
2611:
2605:
2554:
2487:
2479:
2433:
2377:
2374:
2321:
2318:
2269:
2266:
2181:
2178:
2132:
2054:
2048:
2000:
1971:
1926:
1923:
1866:
1765:
1692:
1659:
1610:
1497:
1357:
1230:
1104:
980:
937:respectively, and
919:angular velocities
907:
835:
833:
606:
497:: The central gear
473:is a whole number
463:
441:
404:
359:
294:
245:astronomical clock
235:apsidal precession
164:
88:
32:
6727:
6726:
6480:Epicyclic gearing
6349:Automotive engine
6294:
6293:
6239:
6238:
6062:Non-circular gear
6027:Spur gear systems
5965:Planetary Gearbox
5893:. 10 August 2022.
5863:10.1115/1.2829172
5333:herringbone gears
5309:
5308:
5301:
5090:
5074:
5020:
5007:
4959:
4946:
4914:
4899:
4860:
4847:
4831:
4724:
4666:
4601: = −1.
4551:
4518:
4492:
4482:
4463:
4437:
4421:
4343:
4310:
4284:
4262:
4236:
4220:
4142:
4112:
4086:
4070:
4011:
3921:
3891:
3714:— Torque of sun,
3644:
3561:
3496:
3413:
3330:
3247:
3169:
3160:
3156:
3151:
3141:
3136:
3128:
3123:
3111:
3102:
3098:
3093:
3083:
3078:
3070:
3065:
3053:
3023:
3014:
3011:
3006:
2999:
2994:
2982:
2973:
2970:
2965:
2957:
2952:
2942:
2937:
2924:
2894:
2885:
2882:
2877:
2870:
2865:
2853:
2844:
2841:
2836:
2828:
2823:
2813:
2808:
2795:
2744:
2739:
2736:
2724:
2711:
2667:
2662:
2649:
2636:
2604:
2599:
2586:
2574:
2553:
2550:
2538:
2483:
2478:
2475:
2463:
2450:
2432:
2429:
2417:
2373:
2370:
2358:
2317:
2314:
2302:
2265:
2262:
2250:
2177:
2174:
2162:
2128:
2047:
2044:
2032:
1996:
1967:
1922:
1919:
1907:
1857:
1825:
1796:
1758:
1741:
1728:
1683:
1655:
1650:
1637:
1608:
1604:
1591:
1578:
1565:
1549:
1546:
1534:
1494:
1484:
1479:
1466:
1454:
1439:
1429:
1424:
1411:
1399:
1384:
1354:
1344:
1341:
1329:
1312:
1302:
1299:
1287:
1274:
1257:
1227:
1218:
1215:
1203:
1186:
1176:
1173:
1161:
1148:
1131:
1101:
1087:
1074:
1058:
1047:
1034:
1023:
977:
964:
951:
904:
891:
878:
865:
818:
802:
789:
771:
760:
747:
736:
712:
695:
682:
664:
653:
640:
629:
466:{\displaystyle A}
438:
401:
388:
351:
348:
337:
324:
291:
134:pencil sharpeners
95:planetary gearing
91:Epicyclic gearing
74:can be realized.
40:planetary gearset
38:(also known as a
21:Starter ring gear
6752:
6717:
6716:
6707:
6584:Wheels and tires
6555:Torque converter
6321:
6314:
6307:
6298:
6297:
6183:
6182:
6006:
5999:
5992:
5983:
5982:
5921:
5914:
5908:
5901:
5895:
5894:
5887:
5881:
5880:
5873:
5867:
5866:
5846:
5840:
5839:
5803:
5797:
5796:
5785:
5779:
5778:
5754:
5744:
5738:
5730:
5700:
5694:
5693:
5691:
5682:
5673:
5672:
5670:
5668:
5631:
5622:
5616:
5615:
5595:
5589:
5588:
5566:
5560:
5559:
5546:
5540:
5539:, Prentice Hall.
5533:
5524:
5517:
5477:Rohloff Speedhub
5390:
5374:
5365:
5353:
5304:
5297:
5293:
5290:
5284:
5253:
5245:
5209:pencil sharpener
5193:torque converter
5133:Rohloff Speedhub
5117:
5115:
5114:
5109:
5092:
5091:
5088:
5076:
5075:
5072:
5055:
5053:
5052:
5047:
5042:
5022:
5021:
5018:
5009:
5008:
5005:
4988:
4986:
4985:
4980:
4972:
4961:
4960:
4957:
4948:
4947:
4944:
4926:
4924:
4923:
4918:
4916:
4915:
4912:
4906:
4901:
4900:
4897:
4872:
4870:
4869:
4864:
4862:
4861:
4858:
4849:
4848:
4845:
4833:
4832:
4829:
4767:
4765:
4764:
4759:
4751:
4750:
4738:
4737:
4725:
4717:
4712:
4711:
4689:
4687:
4686:
4681:
4667:
4665:
4664:
4663:
4651:
4650:
4640:
4639:
4638:
4626:
4625:
4615:
4565:
4563:
4562:
4557:
4552:
4550:
4549:
4540:
4539:
4530:
4519:
4517:
4516:
4507:
4506:
4497:
4494:
4490:
4483:
4475:
4464:
4462:
4461:
4452:
4451:
4442:
4439:
4435:
4422:
4420:
4419:
4418:
4406:
4405:
4395:
4394:
4393:
4380:
4357:
4355:
4354:
4349:
4344:
4342:
4341:
4332:
4331:
4322:
4311:
4309:
4308:
4299:
4298:
4289:
4286:
4282:
4263:
4261:
4260:
4251:
4250:
4241:
4238:
4234:
4221:
4219:
4218:
4217:
4204:
4203:
4202:
4190:
4189:
4179:
4156:
4154:
4153:
4148:
4143:
4141:
4140:
4131:
4130:
4121:
4113:
4111:
4110:
4101:
4100:
4091:
4088:
4084:
4071:
4069:
4068:
4059:
4058:
4049:
4025:
4023:
4022:
4017:
4012:
4010:
4009:
4008:
3996:
3995:
3985:
3984:
3983:
3971:
3970:
3960:
3935:
3933:
3932:
3927:
3922:
3920:
3919:
3910:
3909:
3900:
3892:
3890:
3889:
3880:
3879:
3870:
3833:
3831:
3830:
3825:
3817:
3816:
3807:
3806:
3794:
3793:
3784:
3783:
3771:
3770:
3761:
3760:
3740:
3738:
3737:
3732:
3730:
3729:
3713:
3711:
3710:
3705:
3703:
3702:
3686:
3684:
3683:
3678:
3676:
3675:
3655:
3653:
3652:
3647:
3645:
3643:
3642:
3641:
3629:
3628:
3618:
3617:
3608:
3606:
3605:
3590:
3589:
3572:
3570:
3569:
3564:
3562:
3560:
3559:
3550:
3549:
3540:
3538:
3537:
3525:
3524:
3507:
3505:
3504:
3499:
3497:
3495:
3494:
3485:
3484:
3483:
3471:
3470:
3460:
3458:
3457:
3442:
3441:
3424:
3422:
3421:
3416:
3414:
3412:
3411:
3402:
3401:
3400:
3388:
3387:
3377:
3375:
3374:
3359:
3358:
3341:
3339:
3338:
3333:
3331:
3329:
3328:
3327:
3315:
3314:
3304:
3303:
3294:
3292:
3291:
3276:
3275:
3258:
3256:
3255:
3250:
3248:
3246:
3245:
3236:
3235:
3226:
3224:
3223:
3211:
3210:
3181:
3179:
3178:
3173:
3171:
3170:
3167:
3161:
3159:
3158:
3157:
3154:
3152:
3149:
3143:
3142:
3139:
3137:
3134:
3130:
3129:
3126:
3124:
3121:
3118:
3113:
3112:
3109:
3103:
3101:
3100:
3099:
3096:
3094:
3091:
3085:
3084:
3081:
3079:
3076:
3072:
3071:
3068:
3066:
3063:
3060:
3055:
3054:
3051:
3035:
3033:
3032:
3027:
3025:
3024:
3021:
3015:
3013:
3012:
3009:
3007:
3004:
3001:
3000:
2997:
2995:
2992:
2989:
2984:
2983:
2980:
2974:
2972:
2971:
2968:
2966:
2963:
2960:
2959:
2958:
2955:
2953:
2950:
2944:
2943:
2940:
2938:
2935:
2931:
2926:
2925:
2922:
2906:
2904:
2903:
2898:
2896:
2895:
2892:
2886:
2884:
2883:
2880:
2878:
2875:
2872:
2871:
2868:
2866:
2863:
2860:
2855:
2854:
2851:
2845:
2843:
2842:
2839:
2837:
2834:
2831:
2830:
2829:
2826:
2824:
2821:
2815:
2814:
2811:
2809:
2806:
2802:
2797:
2796:
2793:
2757:
2755:
2754:
2749:
2742:
2741:
2738:
2737:
2734:
2728:
2726:
2725:
2722:
2713:
2712:
2709:
2701:
2680:
2678:
2677:
2672:
2665:
2664:
2663:
2660:
2651:
2650:
2647:
2638:
2637:
2634:
2620:
2618:
2617:
2612:
2606:
2603:
2601:
2600:
2597:
2588:
2587:
2584:
2576:
2575:
2572:
2566:
2560:
2556:
2555:
2552:
2551:
2548:
2542:
2540:
2539:
2536:
2528:
2514:
2496:
2494:
2493:
2488:
2481:
2480:
2477:
2476:
2473:
2467:
2465:
2464:
2461:
2452:
2451:
2448:
2440:
2434:
2431:
2430:
2427:
2421:
2419:
2418:
2415:
2407:
2386:
2384:
2383:
2378:
2375:
2372:
2371:
2368:
2362:
2360:
2359:
2356:
2348:
2330:
2328:
2327:
2322:
2319:
2316:
2315:
2312:
2306:
2304:
2303:
2300:
2292:
2278:
2276:
2275:
2270:
2267:
2264:
2263:
2260:
2254:
2252:
2251:
2248:
2240:
2222:
2220:
2219:
2216:
2213:
2206:
2204:
2203:
2200:
2197:
2190:
2188:
2187:
2182:
2179:
2176:
2175:
2172:
2166:
2164:
2163:
2160:
2152:
2141:
2139:
2138:
2133:
2130:
2129:
2126:
2108:counterclockwise
2101:
2099:
2098:
2095:
2092:
2088:
2082:
2080:
2079:
2076:
2073:
2069:
2063:
2061:
2060:
2055:
2049:
2046:
2045:
2042:
2036:
2034:
2033:
2030:
2022:
2009:
2007:
2006:
2001:
1998:
1997:
1994:
1980:
1978:
1977:
1972:
1969:
1968:
1965:
1935:
1933:
1932:
1927:
1924:
1921:
1920:
1917:
1911:
1909:
1908:
1905:
1897:
1875:
1873:
1872:
1867:
1859:
1858:
1855:
1827:
1826:
1823:
1798:
1797:
1794:
1774:
1772:
1771:
1766:
1760:
1759:
1756:
1743:
1742:
1739:
1730:
1729:
1726:
1701:
1699:
1698:
1693:
1685:
1684:
1681:
1668:
1666:
1665:
1660:
1653:
1652:
1651:
1648:
1639:
1638:
1635:
1619:
1617:
1616:
1611:
1609:
1607:
1606:
1605:
1602:
1593:
1592:
1589:
1582:
1580:
1579:
1576:
1567:
1566:
1563:
1555:
1550:
1548:
1547:
1544:
1538:
1536:
1535:
1532:
1524:
1506:
1504:
1503:
1498:
1496:
1495:
1492:
1485:
1483:
1481:
1480:
1477:
1468:
1467:
1464:
1456:
1455:
1452:
1446:
1441:
1440:
1437:
1430:
1428:
1426:
1425:
1422:
1413:
1412:
1409:
1401:
1400:
1397:
1391:
1386:
1385:
1382:
1366:
1364:
1363:
1358:
1356:
1355:
1352:
1345:
1343:
1342:
1339:
1333:
1331:
1330:
1327:
1319:
1314:
1313:
1310:
1303:
1301:
1300:
1297:
1291:
1289:
1288:
1285:
1276:
1275:
1272:
1264:
1259:
1258:
1255:
1239:
1237:
1236:
1231:
1229:
1228:
1225:
1219:
1217:
1216:
1213:
1207:
1205:
1204:
1201:
1193:
1188:
1187:
1184:
1177:
1175:
1174:
1171:
1165:
1163:
1162:
1159:
1150:
1149:
1146:
1138:
1133:
1132:
1129:
1113:
1111:
1110:
1105:
1103:
1102:
1099:
1089:
1088:
1085:
1076:
1075:
1072:
1060:
1059:
1056:
1049:
1048:
1045:
1036:
1035:
1032:
1025:
1024:
1021:
989:
987:
986:
981:
979:
978:
975:
966:
965:
962:
953:
952:
949:
916:
914:
913:
908:
906:
905:
902:
893:
892:
889:
880:
879:
876:
867:
866:
863:
844:
842:
841:
836:
834:
820:
819:
816:
809:
805:
804:
803:
800:
791:
790:
787:
773:
772:
769:
762:
761:
758:
749:
748:
745:
738:
737:
734:
714:
713:
710:
703:
699:
697:
696:
693:
684:
683:
680:
666:
665:
662:
655:
654:
651:
642:
641:
638:
631:
630:
627:
603:
601:
600:
597:
594:
587:
585:
584:
581:
578:
574:
568:
566:
565:
562:
559:
555:
472:
470:
469:
464:
450:
448:
447:
442:
440:
439:
436:
413:
411:
410:
405:
403:
402:
399:
390:
389:
386:
368:
366:
365:
360:
352:
350:
349:
346:
340:
339:
338:
335:
326:
325:
322:
315:
303:
301:
300:
295:
293:
292:
289:
268:
265:
249:Agostino Ramelli
211:Claudius Ptolemy
177:Claudius Ptolemy
6760:
6759:
6755:
6754:
6753:
6751:
6750:
6749:
6730:
6729:
6728:
6723:
6695:
6664:
6579:
6575:Universal joint
6505:Hotchkiss drive
6396:
6343:
6330:
6325:
6295:
6290:
6235:
6217:
6174:
6160:Bicycle gearing
6128:
6107:
6066:
6057:Cycloidal drive
6037:Rack and pinion
6015:
6010:
5977:Wayback Machine
5930:
5925:
5924:
5915:
5911:
5902:
5898:
5889:
5888:
5884:
5875:
5874:
5870:
5847:
5843:
5804:
5800:
5787:
5786:
5782:
5767:
5745:
5741:
5719:
5718:978-156898681-4
5701:
5697:
5689:
5683:
5676:
5666:
5664:
5629:
5623:
5619:
5612:
5596:
5592:
5585:
5567:
5563:
5548:
5547:
5543:
5535:B. Paul, 1979,
5534:
5527:
5518:
5509:
5504:
5499:
5430:Cycloidal drive
5408:
5403:
5402:
5401:
5398:
5391:
5382:
5375:
5366:
5357:
5354:
5342:
5305:
5294:
5288:
5285:
5270:
5254:
5243:
5201:
5188:
5186:Power splitting
5180:cycloidal drive
5125:
5087:
5083:
5071:
5067:
5065:
5062:
5061:
5038:
5017:
5013:
5004:
5000:
4998:
4995:
4994:
4968:
4956:
4952:
4943:
4939:
4937:
4934:
4933:
4911:
4907:
4902:
4896:
4892:
4881:
4878:
4877:
4857:
4853:
4844:
4840:
4828:
4824:
4807:
4804:
4803:
4785:
4746:
4742:
4733:
4729:
4716:
4707:
4703:
4701:
4698:
4697:
4659:
4655:
4646:
4642:
4641:
4634:
4630:
4621:
4617:
4616:
4614:
4612:
4609:
4608:
4582:
4545:
4541:
4535:
4531:
4529:
4512:
4508:
4502:
4498:
4496:
4488:
4474:
4457:
4453:
4447:
4443:
4441:
4433:
4414:
4410:
4401:
4397:
4396:
4389:
4385:
4381:
4379:
4377:
4374:
4373:
4366:
4337:
4333:
4327:
4323:
4321:
4304:
4300:
4294:
4290:
4288:
4280:
4256:
4252:
4246:
4242:
4240:
4232:
4213:
4209:
4205:
4198:
4194:
4185:
4181:
4180:
4178:
4176:
4173:
4172:
4165:
4136:
4132:
4126:
4122:
4120:
4106:
4102:
4096:
4092:
4090:
4082:
4064:
4060:
4054:
4050:
4048:
4046:
4043:
4042:
4035:
4004:
4000:
3991:
3987:
3986:
3979:
3975:
3966:
3962:
3961:
3959:
3951:
3948:
3947:
3915:
3911:
3905:
3901:
3899:
3885:
3881:
3875:
3871:
3869:
3861:
3858:
3857:
3843:
3812:
3808:
3802:
3798:
3789:
3785:
3779:
3775:
3766:
3762:
3756:
3752:
3750:
3747:
3746:
3742:
3725:
3721:
3719:
3716:
3715:
3698:
3694:
3692:
3689:
3688:
3671:
3667:
3665:
3662:
3661:
3659:
3637:
3633:
3624:
3620:
3619:
3613:
3609:
3607:
3601:
3597:
3585:
3581:
3579:
3576:
3575:
3555:
3551:
3545:
3541:
3539:
3533:
3529:
3520:
3516:
3514:
3511:
3510:
3490:
3486:
3479:
3475:
3466:
3462:
3461:
3459:
3453:
3449:
3437:
3433:
3431:
3428:
3427:
3407:
3403:
3396:
3392:
3383:
3379:
3378:
3376:
3370:
3366:
3354:
3350:
3348:
3345:
3344:
3323:
3319:
3310:
3306:
3305:
3299:
3295:
3293:
3287:
3283:
3271:
3267:
3265:
3262:
3261:
3241:
3237:
3231:
3227:
3225:
3219:
3215:
3206:
3202:
3200:
3197:
3196:
3192:
3188:
3166:
3162:
3153:
3148:
3147:
3138:
3133:
3132:
3131:
3125:
3120:
3119:
3117:
3108:
3104:
3095:
3090:
3089:
3080:
3075:
3074:
3073:
3067:
3062:
3061:
3059:
3050:
3046:
3044:
3041:
3040:
3020:
3016:
3008:
3003:
3002:
2996:
2991:
2990:
2988:
2979:
2975:
2967:
2962:
2961:
2954:
2949:
2948:
2939:
2934:
2933:
2932:
2930:
2921:
2917:
2915:
2912:
2911:
2891:
2887:
2879:
2874:
2873:
2867:
2862:
2861:
2859:
2850:
2846:
2838:
2833:
2832:
2825:
2820:
2819:
2810:
2805:
2804:
2803:
2801:
2792:
2788:
2786:
2783:
2782:
2776:
2733:
2729:
2721:
2717:
2708:
2704:
2702:
2699:
2697:
2694:
2693:
2659:
2655:
2646:
2642:
2633:
2629:
2626:
2623:
2622:
2596:
2592:
2583:
2579:
2577:
2571:
2567:
2564:
2547:
2543:
2535:
2531:
2529:
2526:
2519:
2515:
2510:
2504:
2501:
2500:
2472:
2468:
2460:
2456:
2447:
2443:
2441:
2438:
2426:
2422:
2414:
2410:
2408:
2405:
2396:
2393:
2392:
2367:
2363:
2355:
2351:
2349:
2346:
2340:
2337:
2336:
2311:
2307:
2299:
2295:
2293:
2290:
2287:
2284:
2283:
2259:
2255:
2247:
2243:
2241:
2238:
2232:
2229:
2228:
2217:
2214:
2211:
2210:
2208:
2201:
2198:
2195:
2194:
2192:
2171:
2167:
2159:
2155:
2153:
2150:
2147:
2144:
2143:
2125:
2121:
2118:
2115:
2114:
2096:
2093:
2090:
2089:
2086:
2084:
2077:
2074:
2071:
2070:
2067:
2065:
2041:
2037:
2029:
2025:
2023:
2020:
2015:
2012:
2011:
1993:
1989:
1986:
1983:
1982:
1964:
1960:
1957:
1954:
1953:
1916:
1912:
1904:
1900:
1898:
1895:
1887:
1884:
1883:
1854:
1850:
1822:
1818:
1793:
1789:
1783:
1780:
1779:
1755:
1751:
1738:
1734:
1725:
1721:
1718:
1715:
1714:
1680:
1676:
1674:
1671:
1670:
1647:
1643:
1634:
1630:
1628:
1625:
1624:
1601:
1597:
1588:
1584:
1583:
1575:
1571:
1562:
1558:
1556:
1554:
1543:
1539:
1531:
1527:
1525:
1523:
1518:
1515:
1514:
1491:
1487:
1476:
1472:
1463:
1459:
1457:
1451:
1447:
1445:
1436:
1432:
1421:
1417:
1408:
1404:
1402:
1396:
1392:
1390:
1381:
1377:
1375:
1372:
1371:
1351:
1347:
1338:
1334:
1326:
1322:
1320:
1318:
1309:
1305:
1296:
1292:
1284:
1280:
1271:
1267:
1265:
1263:
1254:
1250:
1248:
1245:
1244:
1224:
1220:
1212:
1208:
1200:
1196:
1194:
1192:
1183:
1179:
1170:
1166:
1158:
1154:
1145:
1141:
1139:
1137:
1128:
1124:
1122:
1119:
1118:
1098:
1094:
1084:
1080:
1071:
1067:
1055:
1051:
1044:
1040:
1031:
1027:
1020:
1016:
1014:
1011:
1010:
974:
970:
961:
957:
948:
944:
942:
939:
938:
931:planetary gears
901:
897:
888:
884:
875:
871:
862:
858:
856:
853:
852:
832:
831:
821:
815:
811:
799:
795:
786:
782:
781:
777:
768:
764:
757:
753:
744:
740:
733:
729:
726:
725:
715:
709:
705:
692:
688:
679:
675:
674:
670:
661:
657:
650:
646:
637:
633:
626:
622:
618:
616:
613:
612:
598:
595:
592:
591:
589:
582:
579:
576:
575:
572:
570:
563:
560:
557:
556:
553:
551:
548:planetary gears
483:
458:
455:
454:
435:
431:
429:
426:
425:
398:
394:
385:
381:
379:
376:
375:
345:
341:
334:
330:
321:
317:
316:
314:
312:
309:
308:
288:
284:
282:
279:
278:
275:
266:
173:
80:
24:
17:
12:
11:
5:
6758:
6748:
6747:
6742:
6725:
6724:
6722:
6721:
6711:
6700:
6697:
6696:
6694:
6693:
6688:
6683:
6678:
6676:Electric motor
6672:
6670:
6666:
6665:
6663:
6662:
6661:
6660:
6655:
6650:
6645:
6640:
6635:
6630:
6625:
6615:
6614:
6613:
6608:
6603:
6593:
6587:
6585:
6581:
6580:
6578:
6577:
6572:
6567:
6562:
6557:
6552:
6547:
6542:
6537:
6532:
6527:
6522:
6517:
6512:
6507:
6502:
6497:
6492:
6490:Friction drive
6487:
6485:Fluid coupling
6482:
6477:
6472:
6467:
6462:
6457:
6452:
6447:
6442:
6437:
6432:
6427:
6422:
6417:
6412:
6406:
6404:
6398:
6397:
6395:
6394:
6389:
6384:
6379:
6376:Plug-in hybrid
6369:
6364:
6359:
6353:
6351:
6345:
6344:
6335:
6332:
6331:
6324:
6323:
6316:
6309:
6301:
6292:
6291:
6289:
6288:
6283:
6278:
6273:
6268:
6263:
6258:
6253:
6247:
6245:
6241:
6240:
6237:
6236:
6234:
6233:
6227:
6225:
6219:
6218:
6216:
6215:
6210:
6205:
6200:
6195:
6189:
6187:
6180:
6176:
6175:
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6167:
6162:
6157:
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6147:
6142:
6136:
6134:
6130:
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6121:
6115:
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6109:
6108:
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6100:
6095:
6090:
6085:
6080:
6074:
6072:
6068:
6067:
6065:
6064:
6059:
6054:
6052:Harmonic drive
6049:
6044:
6039:
6034:
6029:
6023:
6021:
6017:
6016:
6009:
6008:
6001:
5994:
5986:
5980:
5979:
5967:
5962:
5957:
5952:
5947:
5942:
5937:
5929:
5928:External links
5926:
5923:
5922:
5909:
5896:
5882:
5868:
5857:(3): 448–453.
5841:
5814:(3): 756–767.
5798:
5780:
5765:
5739:
5717:
5695:
5674:
5617:
5610:
5590:
5583:
5561:
5541:
5525:
5506:
5505:
5503:
5500:
5498:
5497:
5491:
5488:Sturmey Archer
5485:
5480:
5474:
5469:
5464:
5459:
5453:
5451:Harmonic drive
5448:
5443:
5437:
5432:
5427:
5421:
5415:
5409:
5407:
5404:
5400:
5399:
5392:
5385:
5383:
5376:
5369:
5367:
5360:
5358:
5355:
5348:
5345:
5344:
5343:
5341:
5338:
5307:
5306:
5257:
5255:
5248:
5242:
5239:
5200:
5197:
5187:
5184:
5148:stepped-planet
5124:
5121:
5120:
5119:
5107:
5104:
5101:
5098:
5095:
5086:
5082:
5079:
5070:
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4873:
4856:
4852:
4843:
4839:
4836:
4827:
4823:
4820:
4817:
4814:
4811:
4792:CSS animations
4784:
4781:
4769:
4768:
4757:
4754:
4749:
4745:
4741:
4736:
4732:
4728:
4723:
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3019:
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2929:
2920:
2908:
2907:
2890:
2858:
2849:
2818:
2800:
2791:
2775:
2772:
2767:Sturmey-Archer
2747:
2732:
2720:
2716:
2707:
2670:
2658:
2654:
2645:
2641:
2632:
2610:
2595:
2591:
2582:
2570:
2563:
2559:
2546:
2534:
2525:
2522:
2518:
2513:
2509:
2486:
2471:
2459:
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2437:
2425:
2413:
2404:
2401:
2366:
2354:
2345:
2333:
2332:
2310:
2298:
2280:
2258:
2246:
2237:
2170:
2158:
2124:
2053:
2040:
2028:
2019:
1992:
1963:
1938:
1937:
1915:
1903:
1894:
1891:
1877:
1876:
1865:
1862:
1853:
1848:
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1508:
1507:
1490:
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1471:
1462:
1450:
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1420:
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1407:
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1380:
1368:
1367:
1350:
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1325:
1317:
1308:
1295:
1283:
1279:
1270:
1262:
1253:
1241:
1240:
1223:
1211:
1199:
1191:
1182:
1169:
1157:
1153:
1144:
1136:
1127:
1115:
1114:
1097:
1092:
1083:
1079:
1070:
1066:
1063:
1054:
1043:
1039:
1030:
1019:
1004:
1003:
973:
969:
960:
956:
947:
900:
896:
887:
883:
874:
870:
861:
846:
845:
830:
827:
824:
822:
814:
808:
798:
794:
785:
780:
776:
767:
756:
752:
743:
732:
728:
727:
724:
721:
718:
716:
708:
702:
691:
687:
678:
673:
669:
660:
649:
645:
636:
625:
621:
620:
540:
539:
521:
508:
498:
482:
479:
462:
434:
397:
393:
384:
370:
369:
358:
355:
344:
333:
329:
320:
287:
274:
271:
213:used rotating
172:
169:
79:
76:
44:gear reduction
15:
9:
6:
4:
3:
2:
6757:
6746:
6743:
6741:
6738:
6737:
6735:
6720:
6712:
6710:
6706:
6702:
6701:
6698:
6692:
6689:
6687:
6684:
6682:
6679:
6677:
6674:
6673:
6671:
6667:
6659:
6656:
6654:
6651:
6649:
6646:
6644:
6641:
6639:
6636:
6634:
6631:
6629:
6626:
6624:
6621:
6620:
6619:
6616:
6612:
6609:
6607:
6604:
6602:
6599:
6598:
6597:
6594:
6592:
6589:
6588:
6586:
6582:
6576:
6573:
6571:
6568:
6566:
6563:
6561:
6558:
6556:
6553:
6551:
6550:Shift-by-wire
6548:
6546:
6543:
6541:
6538:
6536:
6533:
6531:
6528:
6526:
6523:
6521:
6518:
6516:
6513:
6511:
6508:
6506:
6503:
6501:
6498:
6496:
6493:
6491:
6488:
6486:
6483:
6481:
6478:
6476:
6473:
6471:
6468:
6466:
6463:
6461:
6458:
6456:
6453:
6451:
6448:
6446:
6443:
6441:
6438:
6436:
6433:
6431:
6428:
6426:
6423:
6421:
6418:
6416:
6413:
6411:
6408:
6407:
6405:
6403:
6399:
6393:
6390:
6388:
6387:Petrol engine
6385:
6383:
6380:
6377:
6373:
6370:
6368:
6365:
6363:
6360:
6358:
6357:Diesel engine
6355:
6354:
6352:
6350:
6346:
6342:
6340:
6333:
6329:
6322:
6317:
6315:
6310:
6308:
6303:
6302:
6299:
6287:
6284:
6282:
6279:
6277:
6274:
6272:
6269:
6267:
6264:
6262:
6259:
6257:
6254:
6252:
6249:
6248:
6246:
6242:
6232:
6229:
6228:
6226:
6224:
6220:
6214:
6211:
6209:
6206:
6204:
6201:
6199:
6196:
6194:
6191:
6190:
6188:
6184:
6181:
6177:
6171:
6168:
6166:
6163:
6161:
6158:
6156:
6153:
6151:
6148:
6146:
6143:
6141:
6138:
6137:
6135:
6131:
6125:
6122:
6120:
6117:
6116:
6114:
6110:
6104:
6101:
6099:
6096:
6094:
6091:
6089:
6086:
6084:
6081:
6079:
6076:
6075:
6073:
6069:
6063:
6060:
6058:
6055:
6053:
6050:
6048:
6045:
6043:
6040:
6038:
6035:
6033:
6030:
6028:
6025:
6024:
6022:
6018:
6014:
6007:
6002:
6000:
5995:
5993:
5988:
5987:
5984:
5978:
5974:
5971:
5968:
5966:
5963:
5961:
5960:Prius Gearbox
5958:
5956:
5953:
5951:
5948:
5946:
5943:
5941:
5938:
5935:
5932:
5931:
5919:
5913:
5906:
5900:
5892:
5886:
5878:
5872:
5864:
5860:
5856:
5852:
5845:
5837:
5833:
5829:
5825:
5821:
5817:
5813:
5809:
5802:
5794:
5790:
5784:
5776:
5772:
5768:
5766:9780802016379
5762:
5758:
5753:
5752:
5743:
5737:
5733:
5728:
5724:
5720:
5714:
5710:
5706:
5699:
5688:
5681:
5679:
5663:
5659:
5655:
5651:
5647:
5643:
5639:
5635:
5628:
5621:
5613:
5611:0-34-056831-3
5607:
5603:
5602:
5594:
5586:
5584:0-74-870531-7
5580:
5576:
5572:
5565:
5557:
5553:
5552:
5545:
5538:
5532:
5530:
5522:
5516:
5514:
5512:
5507:
5495:
5492:
5489:
5486:
5484:
5481:
5478:
5475:
5473:
5470:
5468:
5465:
5463:
5460:
5457:
5454:
5452:
5449:
5447:
5444:
5441:
5438:
5436:
5433:
5431:
5428:
5425:
5422:
5419:
5416:
5414:
5411:
5410:
5396:
5389:
5384:
5380:
5373:
5368:
5364:
5359:
5352:
5347:
5346:
5337:
5334:
5329:
5325:
5322:
5313:
5303:
5300:
5292:
5289:February 2021
5282:
5278:
5274:
5268:
5267:
5263:
5258:This section
5256:
5252:
5247:
5246:
5238:
5234:
5230:
5226:
5222:
5218:
5210:
5205:
5196:
5194:
5183:
5181:
5176:
5172:
5167:
5165:
5159:
5155:
5153:
5149:
5145:
5144:meshed-planet
5137:
5134:
5129:
5102:
5099:
5096:
5084:
5080:
5077:
5068:
5060:
5059:
5043:
5039:
5032:
5029:
5026:
5014:
5010:
5001:
4993:
4992:
4973:
4969:
4965:
4953:
4949:
4940:
4932:
4931:
4930:
4927:
4908:
4903:
4893:
4889:
4886:
4883:
4854:
4850:
4841:
4837:
4834:
4825:
4818:
4815:
4812:
4802:
4801:
4800:
4793:
4789:
4780:
4777:
4772:
4755:
4747:
4743:
4739:
4734:
4730:
4721:
4718:
4713:
4708:
4704:
4696:
4695:
4694:
4677:
4674:
4671:
4668:
4660:
4656:
4652:
4647:
4643:
4635:
4631:
4627:
4622:
4618:
4607:
4606:
4605:
4602:
4600:
4595:
4586:
4577:
4575:
4553:
4546:
4542:
4536:
4532:
4526:
4523:
4520:
4513:
4509:
4503:
4499:
4484:
4479:
4476:
4471:
4468:
4465:
4458:
4454:
4448:
4444:
4429:
4426:
4423:
4415:
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4402:
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4390:
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4371:
4370:
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4345:
4338:
4334:
4328:
4324:
4318:
4315:
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4305:
4301:
4295:
4291:
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4270:
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4264:
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4243:
4228:
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4210:
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4199:
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4191:
4186:
4182:
4171:
4170:
4169:
4168:
4167:
4144:
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4133:
4127:
4123:
4117:
4114:
4107:
4103:
4097:
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4078:
4075:
4072:
4065:
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4055:
4051:
4041:
4040:
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4037:
4030:
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3997:
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3893:
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3872:
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3863:
3856:
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3854:
3852:
3847:
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3818:
3813:
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3803:
3799:
3795:
3790:
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3780:
3776:
3772:
3767:
3763:
3757:
3753:
3745:
3744:
3743:
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3722:
3699:
3695:
3672:
3668:
3638:
3634:
3630:
3625:
3621:
3614:
3610:
3602:
3598:
3594:
3591:
3586:
3582:
3574:
3556:
3552:
3546:
3542:
3534:
3530:
3526:
3521:
3517:
3509:
3491:
3487:
3480:
3476:
3472:
3467:
3463:
3454:
3450:
3446:
3443:
3438:
3434:
3426:
3408:
3404:
3397:
3393:
3389:
3384:
3380:
3371:
3367:
3363:
3360:
3355:
3351:
3343:
3324:
3320:
3316:
3311:
3307:
3300:
3296:
3288:
3284:
3280:
3277:
3272:
3268:
3260:
3242:
3238:
3232:
3228:
3220:
3216:
3212:
3207:
3203:
3195:
3194:
3193:
3163:
3144:
3114:
3105:
3086:
3056:
3047:
3039:
3038:
3017:
2985:
2976:
2945:
2927:
2918:
2910:
2909:
2888:
2856:
2847:
2816:
2798:
2789:
2781:
2780:
2779:
2768:
2763:
2759:
2745:
2730:
2718:
2714:
2705:
2691:
2686:
2684:
2668:
2656:
2652:
2643:
2639:
2630:
2608:
2593:
2589:
2580:
2568:
2561:
2557:
2544:
2532:
2523:
2520:
2516:
2511:
2507:
2497:
2484:
2469:
2457:
2453:
2444:
2435:
2423:
2411:
2402:
2399:
2388:
2364:
2352:
2343:
2308:
2296:
2281:
2256:
2244:
2235:
2226:
2225:
2224:
2168:
2156:
2122:
2111:
2109:
2105:
2051:
2038:
2026:
2017:
1990:
1961:
1949:
1947:
1943:
1913:
1901:
1892:
1889:
1882:
1881:
1880:
1863:
1860:
1851:
1843:
1840:
1837:
1831:
1828:
1819:
1811:
1808:
1805:
1799:
1790:
1785:
1778:
1777:
1776:
1762:
1752:
1747:
1744:
1735:
1731:
1722:
1711:
1709:
1705:
1689:
1686:
1677:
1656:
1644:
1640:
1631:
1598:
1594:
1585:
1572:
1568:
1559:
1551:
1540:
1528:
1520:
1513:
1512:
1511:
1488:
1473:
1469:
1460:
1448:
1442:
1433:
1418:
1414:
1405:
1393:
1387:
1378:
1370:
1369:
1348:
1335:
1323:
1315:
1306:
1293:
1281:
1277:
1268:
1260:
1251:
1243:
1242:
1221:
1209:
1197:
1189:
1180:
1167:
1155:
1151:
1142:
1134:
1125:
1117:
1116:
1095:
1081:
1077:
1068:
1061:
1052:
1041:
1037:
1028:
1017:
1009:
1008:
1007:
1002:respectively.
1001:
997:
993:
971:
967:
958:
954:
945:
936:
935:carrier frame
932:
928:
924:
920:
898:
894:
885:
881:
872:
868:
859:
851:
850:
849:
828:
825:
823:
812:
806:
796:
792:
783:
778:
774:
765:
754:
750:
741:
730:
722:
719:
717:
706:
700:
689:
685:
676:
671:
667:
658:
647:
643:
634:
623:
611:
610:
609:
549:
544:
537:
533:
529:
525:
522:
520:
516:
512:
509:
506:
502:
501:Carrier frame
499:
496:
493:
492:
491:
488:
478:
474:
460:
452:
432:
423:
421:
417:
395:
391:
382:
373:
356:
353:
342:
331:
327:
318:
307:
306:
305:
285:
270:
261:
256:
254:
251:invented the
250:
246:
242:
238:
236:
232:
228:
223:
221:
216:
212:
208:
207:
202:
201:
194:
192:
188:
184:
183:
178:
168:
161:
157:
153:
149:
147:
143:
139:
138:differentials
135:
130:
128:
124:
120:
116:
112:
108:
104:
100:
96:
92:
84:
75:
73:
69:
65:
60:
58:
54:
53:pitch circles
49:
45:
41:
37:
28:
22:
6628:Racing slick
6565:Transfer box
6535:Park-by-wire
6530:Parking pawl
6479:
6445:Differential
6420:Direct-drive
6402:Transmission
6392:Steam engine
6337:Part of the
6336:
6145:Differential
6140:Transmission
6093:Spiral bevel
6041:
5917:
5912:
5904:
5899:
5885:
5871:
5854:
5850:
5844:
5811:
5807:
5801:
5792:
5783:
5750:
5742:
5704:
5698:
5665:. Retrieved
5640:(1): 27–43.
5637:
5633:
5620:
5600:
5593:
5574:
5564:
5550:
5544:
5536:
5520:
5440:Ford Model T
5397:transmission
5330:
5326:
5318:
5295:
5286:
5271:Please help
5259:
5235:
5231:
5227:
5223:
5219:
5215:
5189:
5171:World War II
5168:
5160:
5156:
5151:
5147:
5143:
5141:
4928:
4875:
4797:
4775:
4773:
4770:
4692:
4603:
4598:
4591:
4570:
4362:
4161:
4031:
4028:
3941:
3938:
3848:
3844:
3836:
3658:
3189:
2777:
2687:
2498:
2389:
2334:
2112:
2107:
1950:
1945:
1941:
1939:
1878:
1712:
1707:
1703:
1622:
1509:
1005:
999:
995:
991:
934:
930:
926:
922:
847:
607:
547:
536:Annular gear
535:
532:Annulus gear
531:
527:
523:
518:
514:
510:
504:
500:
494:
484:
475:
453:
424:
419:
415:
374:
371:
276:
257:
239:
224:
204:
197:
195:
180:
174:
165:
159:
131:
126:
122:
118:
114:
110:
102:
94:
90:
89:
67:
64:annulus gear
63:
61:
39:
35:
33:
6606:Alloy wheel
6465:Drive wheel
6455:Drive shaft
6415:Chain drive
6271:Chain drive
6231:Wheel train
6103:Herringbone
5321:3D printing
5241:3D printing
2688:In bicycle
1000:planet gear
998:, and each
511:Planet gear
267: 1650
220:epitrochoid
105:, gears or
72:gear ratios
6734:Categories
6691:Alternator
6339:Automobile
6328:Powertrain
6266:Belt drive
6251:Ball screw
6198:Derailleur
6032:Worm drive
5793:buseco.net
5775:1036858215
5736:1568986815
5727:1036836698
5502:References
5435:Epicycloid
5395:Ravigneaux
5199:Advantages
3851:gear train
487:gear ratio
191:precession
142:bevel gear
57:epicycloid
6560:Transaxle
6525:Manumatic
6495:Gearshift
6367:Fuel cell
6281:Freewheel
6261:Jackscrew
6256:Leadscrew
6133:Mechanics
5494:Uni Wheel
5260:does not
5100:−
5085:ω
5081:−
5069:ω
5030:−
5015:ω
5002:ω
4954:ω
4941:ω
4890:−
4855:ω
4851:−
4842:ω
4826:ω
4816:−
4776:ring gear
4744:ω
4731:ω
4705:ω
4672:−
4657:ω
4653:−
4644:ω
4632:ω
4628:−
4619:ω
4510:ω
4500:ω
4472:−
4455:ω
4445:ω
4412:ω
4408:−
4399:ω
4387:ω
4383:−
4302:ω
4292:ω
4271:−
4254:ω
4244:ω
4211:ω
4207:−
4196:ω
4192:−
4183:ω
4118:−
4104:ω
4094:ω
4062:ω
4052:ω
4002:ω
3998:−
3989:ω
3977:ω
3973:−
3964:ω
3897:−
3883:ω
3873:ω
3810:ω
3800:τ
3787:ω
3777:τ
3764:ω
3754:τ
3723:τ
3696:τ
3669:τ
3599:τ
3595:−
3583:τ
3531:τ
3518:τ
3451:τ
3447:−
3435:τ
3368:τ
3364:−
3352:τ
3285:τ
3281:−
3269:τ
3217:τ
3204:τ
3164:α
3106:α
3048:α
3018:α
2986:−
2977:α
2919:α
2889:α
2857:−
2848:α
2790:α
2690:hub gears
2344:−
2236:−
2104:clockwise
2018:−
1852:ω
1829:−
1820:ω
1791:ω
1678:ω
1645:ω
1641:≠
1632:ω
1599:ω
1595:−
1586:ω
1573:ω
1569:−
1560:ω
1521:−
1489:ω
1434:ω
1379:ω
1349:ω
1316:−
1307:ω
1252:ω
1222:ω
1190:−
1181:ω
1126:ω
1096:ω
1053:ω
1029:ω
992:ring gear
923:ring gear
899:ω
886:ω
873:ω
860:ω
813:ω
793:−
775:−
766:ω
751:−
742:ω
707:ω
668:−
659:ω
635:ω
528:Moon gear
524:Ring gear
519:ring gear
505:planetary
420:ring gear
260:Desargues
253:bookwheel
156:Bookwheel
115:sun wheel
6719:Category
6658:Tubeless
6643:Run-flat
6623:Off-road
6440:Coupling
6362:Electric
6244:See also
6223:Horology
6213:Sprocket
6203:Hub gear
6186:Bicycles
6179:Examples
6150:Coupling
6119:Involute
5973:Archived
5662:54663891
5456:Hub gear
5406:See also
2683:tractors
2085:−
2066:−
1623:only if
996:sun gear
927:sun gear
917:are the
571:−
552:−
517:and the
515:sun gear
495:Sun gear
418:and the
416:sun gear
206:Almagest
203:(a.k.a.
182:Almagest
125:gear or
111:sun gear
78:Overview
6124:Cycloid
6098:Helical
6020:Systems
5836:4986932
5816:Bibcode
5687:Gearing
5642:Bibcode
5446:Gearbox
5340:Gallery
5281:removed
5266:sources
5169:During
3660:where:
2221:
2209:
2205:
2193:
2100:
2081:
921:of the
602:
590:
586:
567:
179:in the
171:History
146:coaxial
127:annulus
119:carrier
107:pinions
59:curve.
42:) is a
6709:Portal
6669:Hybrid
6633:Radial
6611:Hubcap
6425:Clutch
6372:Hybrid
6341:series
6193:Cogset
6170:Offset
6071:Shapes
5834:
5773:
5763:
5734:
5725:
5715:
5667:20 May
5660:
5608:
5581:
5212:angle.
4876:where
2743:
2666:
2482:
1946:output
1942:inputs
1879:where
1708:output
1654:
994:, the
933:, and
848:where
372:where
162:, 1588
103:planet
6745:Gears
6653:Spare
6596:Wheel
6500:Giubo
6155:Train
6088:Crown
6083:Bevel
6013:Gears
5832:S2CID
5690:(PDF)
5658:S2CID
5630:(PDF)
5426:(CVT)
5175:radar
4367:=0,
4166:=0,
4036:=0,
2207:, or
2083:, or
1704:input
569:, or
534:, or
97:is a
48:gears
6648:Snow
6638:Rain
6618:Tire
6078:Spur
5771:OCLC
5761:ISBN
5732:ISBN
5723:OCLC
5713:ISBN
5669:2014
5606:ISBN
5579:ISBN
5264:any
5262:cite
1510:and
485:The
198:The
136:and
123:ring
99:gear
6601:Rim
5859:doi
5855:120
5824:doi
5650:doi
5275:by
4693:or
2202:64
2078:16
1682:...
564:16
209:),
113:or
93:or
34:An
6736::
5853:.
5830:.
5822:.
5812:21
5810:.
5791:.
5769:.
5759:.
5757:69
5721:.
5711:.
5709:19
5677:^
5656:.
5648:.
5638:32
5636:.
5632:.
5573:.
5554:.
5528:^
5510:^
5182:.
4592:A
4576:.
4491:so
4436:or
4283:so
4235:or
4085:so
2218:4
2196:16
2097:2
2072:24
929:,
925:,
599:2
583:2
558:24
530:,
526:,
269:.
264:c.
222:.
148:.
6378:)
6374:(
6320:e
6313:t
6306:v
6005:e
5998:t
5991:v
5879:.
5865:.
5861::
5838:.
5826::
5818::
5795:.
5777:.
5729:.
5671:.
5652::
5644::
5614:.
5587:.
5302:)
5296:(
5291:)
5287:(
5283:.
5269:.
5106:)
5103:1
5097:R
5094:(
5089:c
5078:=
5073:s
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5040:/
5036:)
5033:1
5027:R
5024:(
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5011:=
5006:r
4977:)
4974:R
4970:/
4966:1
4963:(
4958:s
4950:=
4945:r
4913:s
4909:N
4904:/
4898:r
4894:N
4887:=
4884:R
4859:s
4846:r
4838:R
4835:=
4830:c
4822:)
4819:1
4813:R
4810:(
4756:.
4753:)
4748:r
4740:+
4735:s
4727:(
4722:2
4719:1
4714:=
4709:c
4678:,
4675:1
4669:=
4661:c
4648:r
4636:c
4623:s
4599:R
4554:.
4547:r
4543:N
4537:s
4533:N
4527:+
4524:1
4521:=
4514:c
4504:r
4485:,
4480:R
4477:1
4469:1
4466:=
4459:c
4449:r
4430:,
4427:R
4424:=
4416:c
4403:r
4391:c
4365:s
4346:.
4339:s
4335:N
4329:r
4325:N
4319:+
4316:1
4313:=
4306:c
4296:s
4277:,
4274:R
4268:1
4265:=
4258:c
4248:s
4229:,
4226:R
4223:=
4215:c
4200:c
4187:s
4164:r
4145:.
4138:s
4134:N
4128:r
4124:N
4115:=
4108:r
4098:s
4079:,
4076:R
4073:=
4066:r
4056:s
4034:c
4014:.
4006:c
3993:r
3981:c
3968:s
3957:=
3954:R
3924:.
3917:s
3913:N
3907:r
3903:N
3894:=
3887:r
3877:s
3867:=
3864:R
3822:0
3819:=
3814:s
3804:s
3796:+
3791:c
3781:c
3773:+
3768:r
3758:r
3727:c
3700:s
3673:r
3639:s
3635:N
3631:+
3626:r
3622:N
3615:s
3611:N
3603:c
3592:=
3587:s
3557:r
3553:N
3547:s
3543:N
3535:r
3527:=
3522:s
3492:s
3488:N
3481:s
3477:N
3473:+
3468:r
3464:N
3455:s
3444:=
3439:c
3409:r
3405:N
3398:s
3394:N
3390:+
3385:r
3381:N
3372:r
3361:=
3356:c
3325:s
3321:N
3317:+
3312:r
3308:N
3301:r
3297:N
3289:c
3278:=
3273:r
3243:s
3239:N
3233:r
3229:N
3221:s
3213:=
3208:r
3168:r
3155:r
3150:N
3145:+
3140:s
3135:N
3127:r
3122:N
3115:+
3110:s
3097:r
3092:N
3087:+
3082:s
3077:N
3069:s
3064:N
3057:=
3052:c
3022:s
3010:r
3005:N
2998:s
2993:N
2981:c
2969:r
2964:N
2956:r
2951:N
2946:+
2941:s
2936:N
2928:=
2923:r
2893:r
2881:s
2876:N
2869:r
2864:N
2852:c
2840:s
2835:N
2827:r
2822:N
2817:+
2812:s
2807:N
2799:=
2794:s
2746:.
2735:r
2731:N
2723:r
2719:N
2715:+
2710:s
2706:N
2669:.
2661:r
2657:N
2653:+
2648:s
2644:N
2640::
2635:s
2631:N
2609:,
2598:r
2594:N
2590:+
2585:s
2581:N
2573:s
2569:N
2562:=
2558:)
2549:s
2545:N
2537:r
2533:N
2524:+
2521:1
2517:(
2512:/
2508:1
2485:.
2474:s
2470:N
2462:r
2458:N
2454:+
2449:s
2445:N
2436:=
2428:s
2424:N
2416:r
2412:N
2403:+
2400:1
2369:r
2365:N
2357:s
2353:N
2313:r
2309:N
2301:p
2297:N
2261:p
2257:N
2249:s
2245:N
2215:/
2212:1
2199:/
2173:r
2169:N
2161:p
2157:N
2127:r
2123:N
2094:/
2091:3
2087:+
2075:/
2068:+
2052:.
2043:p
2039:N
2031:s
2027:N
1995:p
1991:N
1966:s
1962:N
1918:p
1914:N
1906:s
1902:N
1893:=
1890:n
1864:0
1861:=
1856:c
1847:)
1844:n
1841:+
1838:1
1835:(
1832:2
1824:r
1815:)
1812:n
1809:+
1806:2
1803:(
1800:+
1795:s
1786:n
1763:,
1757:p
1753:N
1748:2
1745:+
1740:s
1736:N
1732:=
1727:r
1723:N
1690:0
1687:=
1657:.
1649:c
1636:r
1603:c
1590:r
1577:c
1564:s
1552:=
1545:s
1541:N
1533:r
1529:N
1493:r
1478:r
1474:N
1470:+
1465:s
1461:N
1453:r
1449:N
1443:+
1438:s
1423:r
1419:N
1415:+
1410:s
1406:N
1398:s
1394:N
1388:=
1383:c
1353:s
1340:r
1336:N
1328:s
1324:N
1311:c
1298:r
1294:N
1286:r
1282:N
1278:+
1273:s
1269:N
1261:=
1256:r
1226:r
1214:s
1210:N
1202:r
1198:N
1185:c
1172:s
1168:N
1160:r
1156:N
1152:+
1147:s
1143:N
1135:=
1130:s
1100:c
1091:)
1086:r
1082:N
1078:+
1073:s
1069:N
1065:(
1062:=
1057:r
1046:r
1042:N
1038:+
1033:s
1022:s
1018:N
976:p
972:N
968:,
963:s
959:N
955:,
950:r
946:N
903:c
895:,
890:p
882:,
877:s
869:,
864:r
829:0
826:=
817:c
807:)
801:p
797:N
788:r
784:N
779:(
770:p
759:p
755:N
746:r
735:r
731:N
723:0
720:=
711:c
701:)
694:p
690:N
686:+
681:s
677:N
672:(
663:p
652:p
648:N
644:+
639:s
628:s
624:N
596:/
593:3
580:/
577:3
573:+
561:/
554:+
461:A
437:p
433:n
400:r
396:N
392:,
387:s
383:N
357:A
354:=
347:p
343:n
336:r
332:N
328:+
323:s
319:N
290:p
286:n
23:.
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