5169:
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.
163:
5206:. 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.
140:, 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.
4596:
5362:
5248:
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.
5399:
4799:
5383:
5215:
38:
5323:
554:
94:
6750:
854:
6740:
5262:
5374:
5139:
2773:
625:
4575:
3191:
4367:
3045:
2916:
1516:
248:. 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.
1376:
849:{\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}}}
1249:
4789:
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
487:
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
177:
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
5243:
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
5188:
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
4809:
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
5168:
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
228:
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
5247:
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
5227:
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,
5346:
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.
1962:
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
4386:
3053:
5338:
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
1629:
3752:— 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:
4185:
4166:
2630:
5339:
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.
5231:
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.
2924:
2795:
1123:
5239:
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.
3953:
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,
2506:
61:
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
1384:
5361:
3201:
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:
1257:
1131:
5334:
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.
1885:
926:
5222:
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
3856:
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.
5172:
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
4570:{\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}}}.}
3186:{\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}}}
500:
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:
3843:
4882:
4699:
4035:
3945:
1527:
5235:
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.
2767:
5201:
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
4777:
4362:{\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}}}.}
378:
2401:
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
4582:
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
3665:
3517:
3434:
3351:
4607:
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
4055:
2396:
2288:
1784:
2513:
2340:
2200:
2073:
1945:
5065:
5127:
4805:
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
3040:{\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}}}
2911:{\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}}}
1678:
4998:
2690:
5244:
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.
3582:
3268:
1023:
999:
5177:
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.
630:
3860:
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
2405:
4936:
1721:, 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.
5999:
5398:
2703:, 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
423:
1511:{\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}}}
1711:
619:
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:
2151:
2019:
1990:
2202:
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
460:
313:
1371:{\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}}}
3750:
3723:
3696:
488:
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.
1244:{\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}}}
1792:
4599:
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.
865:
1951:
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
482:
73:
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
5367:
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.
5326:
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).
2124:
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
557:
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
200:, 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
5153:"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:
3759:
2510:
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
97:
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.
4816:
4621:
1624:{\displaystyle -{\frac {\,N_{\text{r}}\,}{N_{\text{s}}}}={\frac {\,\omega _{\text{s}}-\omega _{\text{c}}\,}{\omega _{\text{r}}-\omega _{\text{c}}}}}
5925:
3960:
3870:
266:, a vertically revolving bookstand containing epicyclic gearing with two levels of planetary gears to maintain proper orientation of the books.
5382:
2706:
4782:
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.
4710:
321:
6007:
5472:
4161:{\displaystyle {\frac {\omega _{s}}{\omega _{r}}}=R,\quad {\mbox{so}}\quad {\frac {\omega _{s}}{\omega _{r}}}=-{\frac {N_{r}}{N_{s}}}.}
3588:
3440:
3357:
3274:
2625:{\displaystyle \,1/\left(1+{\tfrac {\,N_{\text{r}}\,}{N_{\text{s}}}}\right)={\tfrac {N_{\text{s}}}{\,N_{\text{s}}+N_{\text{r}}\,}}\;,}
2349:
2241:
1727:
2296:
2156:
2024:
1896:
162:
5007:
5074:
4040:
This formula provides a simple way to determine the speed ratios for the simple planetary gear train under different conditions:
1637:
1118:{\displaystyle N_{\text{s}}\,\omega _{\text{s}}+N_{\text{r}}\,\omega _{\text{r}}=(N_{\text{s}}+N_{\text{r}})\,\omega _{\text{c}}}
81:. By choosing to hold one component or another—the planetary carrier, the ring gear, or the sun gear—stationary, three different
4946:
2635:
3523:
3209:
186:
Around 500 BCE, the Greeks invented the idea of epicycles, of circles travelling on the circular orbits. With this theory
5405:
951:
6353:
41:
This planetary gear train consists of a sun gear (yellow), planet gears (blue) and carrier (green) inside a ring gear (red)
5751:
6469:
6199:
5434:
5283:
2501:{\displaystyle \;1+{\tfrac {\,N_{\text{r}}\,}{N_{\text{s}}}}={\tfrac {\,N_{\text{s}}+N_{\text{r}}\,}{N_{\text{s}}}}~.}
5799:
5620:
5593:
5309:
17:
5291:
6479:
6179:
5721:
4604:
148:
132:, which itself may rotate relative to the sun gear. Epicyclic gearing systems also incorporate the use of an outer
5911:
4890:
6038:
5149:
with the smaller planet series meshing with the sun wheel and the larger planet series meshing with the ring gear
2692:
This is the lowest gear ratio attainable with an epicyclic gear train. This type of gearing is sometimes used in
5661:
66:
roll without slip. If the sun gear is held fixed, then a point on the pitch circle of the planet gear traces an
6426:
5770:
5581:
5287:
2114:
388:
204:
of that path. (The Greeks interpreted the motion they saw, not as elliptical, but rather as epicyclic motion.)
5610:
6504:
5389:
4595:
1683:
6774:
5877:
5477:
5138:
6579:
5841:
Miller, John M. (May 2006). "Hybrid electric vehicle propulsion system architectures of the e-CVT type".
3848:
In the cases where gears are accelerating, or to account for friction, these equations must be modified.
5189:
complete a single revolution, which in turn made the rotating ring gear rotate by a single tooth like a
6416:
5482:
4802:
2789:
From the above formulae, we can also derive the accelerations of the sun, ring and carrier, which are:
2127:
1995:
1966:
6715:
6604:
6544:
6509:
6320:
5493:
1680:
In many epicyclic gearing systems, one of these three basic components is held stationary (hence set
6494:
6346:
5566:
5272:
5884:
P. A. Simionescu (1998-09-01). "A Unified
Approach to the Assembly Condition of Epicyclic Gears".
438:
291:
6464:
6436:
6174:
5276:
4798:
2075:
For instance, if the sun gear has 24 teeth, and each planet has 16 teeth, then the ratio is
1724:
Alternatively, in the special case where the number of teeth on each gear meets the relationship
6454:
6444:
5834:
5174:
4584:
3728:
3701:
3674:
251:
5560:
4810:
as the ring gear when the planet carrier is the stationary. The fundamental equation becomes:
5791:
5743:
5428:
5423:
288:
In order that the planet gear teeth mesh properly with both the sun and ring gears, assuming
237:
225:
210:
197:
6004:
1880:{\displaystyle n\,\omega _{\text{s}}+(2+n)\,\omega _{\text{r}}-2(1+n)\,\omega _{\text{c}}=0}
6549:
6484:
6242:
5850:
5676:
921:{\displaystyle \omega _{\text{r}},\omega _{\text{s}},\omega _{\text{p}},\omega _{\text{c}}}
5823:
561:(blue) turn in a ratio determined by the number of teeth in each gear. Here, the ratio is
254:, an English abbot of St. Albans monastery, later described epicyclic gearing for an
8:
6574:
6554:
6339:
6086:
6081:
6031:
5854:
5680:
6720:
6625:
6310:
5866:
5692:
5636:
5157:(there are at least two or more planets in mesh with each other in each planet train),
524:(s): Usually two to four peripheral gears, all of the same size, that mesh between the
467:
255:
245:
5824:"How to derive and calculate epicyclic gear ratio equations in planetary gear systems"
5727:(Report). NASA Reference Publication. Vol. 1152. AVSCOM Technical Report 84-C-15.
196:
in 148 CE was able to approximate planetary paths observed crossing the sky. The
6739:
6449:
6401:
6383:
6300:
6127:
6096:
5805:
5795:
5784:
5766:
5757:
5747:
5616:
5589:
615:
the rate of the sun gear, in the opposite direction. An outer ring gear is not shown.
241:
178:
gear, thus providing a reversal in direction compared to standard epicyclic gearing.
144:
31:
5696:
5342:
One popular use of 3D printed planetary gear systems is as toys for children. Since
77:. Such an assembly of a planet engaging both a sun gear and a ring gear is called a
37:
6589:
6396:
6137:
5893:
5870:
5858:
5684:
5487:
5343:
5219:
5203:
5143:
929:
270:
259:
221:
187:
27:
Two gears mounted so the center of one gear revolves around the center of the other
6609:
6539:
6194:
6091:
6071:
6011:
5926:"52514 Caterpillar Tractor D8 Bulldozer Powershift Transmission Promotional Film"
5440:
5190:
82:
54:
5984:
5979:
5971:, movies and photos of hundreds of working mechanical-systems models at Cornell.
5161:(there exists a shaft connection between two planets in each planet train), and
3864:
formed by the sun, planet and ring gears on the fixed carrier. This is given by
3838:{\displaystyle \tau _{r}\omega _{r}+\tau _{c}\omega _{c}+\tau _{s}\omega _{s}=0}
6779:
6710:
6524:
6519:
6410:
6406:
6204:
6024:
5498:
5461:
2777:
5968:
5809:
5761:
4877:{\displaystyle (R-1)\omega _{\text{c}}=R\omega _{\text{r}}-\omega _{\text{s}}}
4694:{\displaystyle {\frac {\omega _{s}-\omega _{c}}{\omega _{r}-\omega _{c}}}=-1,}
6768:
6753:
6692:
6677:
6657:
6584:
6421:
6391:
6184:
6153:
5989:
5862:
5740:
Revolving
Architecture: A history of buildings that rotate, swivel, and pivot
5688:
5214:
4030:{\displaystyle R={\frac {\omega _{s}-\omega _{c}}{\omega _{r}-\omega _{c}}}.}
3940:{\displaystyle R={\frac {\omega _{s}}{\omega _{r}}}=-{\frac {N_{r}}{N_{s}}}.}
1713:
for whichever gear is stationary); one of the two remaining components is an
549:: An outer ring with inward-facing teeth that mesh with the planetary gear(s)
6662:
6599:
6569:
6564:
6158:
5450:
5322:
5181:
4615:
In this case, the fundamental formula for the planetary gear train yields,
2346:
So, with the planetary carrier locked, one turn of the sun gear results in
553:
63:
2234:
clockwise turns of the ring gear. Extending this case from the one above:
240:, circa 80 BCE, to adjust the displayed position of the Moon for the
6743:
6667:
6640:
6635:
6499:
6489:
6305:
6265:
5404:
One of three sets of three gears inside the planet carrier of a Ford FMX
5331:
230:
2762:{\displaystyle {\tfrac {\,N_{\text{s}}+N_{\text{r}}\,}{N_{\text{r}}}}~.}
155:(see below). Further, the sun, planet carrier and ring axes are usually
93:
6725:
6687:
6529:
6362:
6285:
6232:
6189:
6122:
6117:
6066:
5953:
Gears and Their
Vibration: A Basic Approach to Understanding Gear Noise
5445:
3861:
2696:
and construction equipment to provide high torque to the drive wheels.
497:
315:
equally spaced planet gears, the following equation must be satisfied:
201:
152:
143:
The axes of all gears are usually parallel, but for special cases like
67:
5974:
5897:
5184:, a special variation of epicyclic gearing was developed for portable
491:
6682:
6672:
6594:
6559:
6315:
6295:
6290:
6112:
6061:
5719:
5504:
263:
166:
5261:
4772:{\displaystyle \omega _{c}={\frac {1}{2}}(\omega _{s}+\omega _{r}).}
6474:
6257:
6247:
6237:
6132:
5466:
5373:
5146:
2700:
2693:
373:{\displaystyle {\frac {N_{\text{s}}+N_{\text{r}}}{n_{\text{p}}}}=A}
216:
192:
5456:
518:
gear(s) symmetrically and separated, all meshed with the sun gear
156:
5501:– First major manufacturer of bicycle hubs using planetary gears
4790:
not have the internal gear mate that is typical of a ring gear.
3660:{\displaystyle \tau _{s}=-\tau _{c}{\frac {N_{s}}{N_{r}+N_{s}}}}
3512:{\displaystyle \tau _{c}=-\tau _{s}{\frac {N_{r}+N_{s}}{N_{s}}}}
3429:{\displaystyle \tau _{c}=-\tau _{r}{\frac {N_{r}+N_{s}}{N_{r}}}}
3346:{\displaystyle \tau _{r}=-\tau _{c}{\frac {N_{r}}{N_{r}+N_{s}}}}
1717:, providing power to the system, while the last component is an
273:
designed and constructed the first mill with epicycloidal teeth
6645:
6459:
6227:
5994:
5615:(2nd ed.). Oxford, UK: Butterworth-Heinemann. p. 58.
117:
4785:
In discussing the spur gear differential, the use of the term
3196:
2784:
2391:{\displaystyle \;-{\tfrac {\,N_{\text{s}}\,}{N_{\text{r}}}}\;}
2283:{\displaystyle \,-{\tfrac {\,N_{\text{s}}\,}{N_{\text{p}}}}\,}
1779:{\displaystyle \,N_{\text{r}}=N_{\text{s}}+2\,N_{\text{p}}\;,}
128:. Typically, the planet gears are mounted on a movable arm or
6630:
6534:
6331:
5781:
5588:(4th ed.). Cheltenham, UK: Nelson Thornes. p. 244.
5185:
2335:{\displaystyle \,{\tfrac {\,N_{\text{p}}\,}{N_{\text{r}}}}\,}
2195:{\displaystyle \,{\tfrac {\,N_{\text{p}}\,}{N_{\text{r}}}}\,}
2068:{\displaystyle -{\tfrac {\,N_{\text{s}}\,}{N_{\text{p}}}}\;.}
1940:{\displaystyle n={\tfrac {\,N_{\text{s}}\,}{N_{\text{p}}}}\;}
258:
in the 14th century. In 1588, Italian military engineer
5060:{\displaystyle \omega _{\text{r}}=\omega _{\text{c}}(R-1)/R}
2772:
6652:
6047:
5122:{\displaystyle \omega _{\text{s}}=-\omega _{\text{c}}(R-1)}
4793:
1673:{\displaystyle \omega _{\text{r}}\neq \omega _{\text{c}}~.}
109:
58:
4993:{\displaystyle \omega _{\text{r}}=\omega _{\text{s}}(1/R)}
2685:{\displaystyle \;N_{\text{s}}:N_{\text{s}}+N_{\text{r}}~.}
151:, they can be placed at an angle, introducing elements of
6373:
3577:{\displaystyle \tau _{s}=\tau _{r}{\frac {N_{s}}{N_{r}}}}
3263:{\displaystyle \tau _{r}=\tau _{s}{\frac {N_{r}}{N_{s}}}}
6016:
5742:. New York, NY: Princeton Architectural Press. p.
5526:
5524:
5522:
4500:
4445:
4292:
4244:
4094:
3950:
In this calculation the planet gear is an idler gear.
2769:
The number of teeth in the planet gear is irrelevant.
2711:
2576:
2538:
2450:
2417:
2358:
2302:
2250:
2162:
2032:
1907:
994:{\displaystyle N_{\text{r}},N_{\text{s}},N_{\text{p}}}
5530:
J. J. Uicker, G. R. Pennock and J. E. Shigley, 2003,
5077:
5010:
4949:
4893:
4819:
4713:
4624:
4389:
4188:
4058:
3963:
3873:
3762:
3731:
3704:
3677:
3591:
3526:
3443:
3360:
3277:
3212:
3056:
2927:
2798:
2709:
2638:
2516:
2408:
2352:
2299:
2244:
2159:
2130:
2027:
1998:
1969:
1899:
1795:
1730:
1686:
1640:
1530:
1387:
1260:
1134:
1026:
954:
868:
628:
470:
441:
391:
324:
294:
5969:
Kinematic Models for Design
Digital Library (KMODDL)
5790:. Toronto, ON: University of Toronto Press. p.
2121:
turns of each of the planet gear(s) about its axis.
283:
5786:
Science and
Technology in the Industrial Revolution
5775:
5519:
5507:- a wheel that incorporates a planetary gear system
492:
Gear speed ratios of conventional epicyclic gearing
5783:
5720:Coy, J.J.; Townsend, D.P.; Zaretsky, E.V. (1985).
5653:
5121:
5059:
4992:
4930:
4876:
4771:
4693:
4569:
4361:
4160:
4029:
3939:
3837:
3744:
3717:
3690:
3659:
3576:
3511:
3428:
3345:
3262:
3185:
3039:
2910:
2761:
2684:
2624:
2500:
2390:
2334:
2282:
2194:
2145:
2067:
2013:
1984:
1939:
1879:
1778:
1705:
1672:
1623:
1510:
1370:
1243:
1117:
993:
920:
848:
476:
462:is the number of planet gears in the assembly and
454:
417:
372:
307:
5608:
1786:the equation can be re-written as the following:
6766:
5883:
5955:. Marcel Dekker, New York and MacMillan, London
5840:
5637:"What are planetary gears and how do they work"
5582:"Planetary gearing and unidirectional clutches"
5165:(the system contains two or more planet sets).
5542:
5540:
30:For the ring gear used in starter motors, see
6347:
6032:
5990:The "Interactive Planetary Gearset tutorial"
4931:{\displaystyle R=-N_{\text{r}}/N_{\text{s}}}
3851:
5737:
5548:Kinematics and Dynamics of Planar Machinery
5537:
5290:. Unsourced material may be challenged and
5133:
3197:Torque ratios of standard epicyclic gearing
2785:Accelerations of standard epicyclic gearing
112:system consisting of one or more outer, or
6354:
6340:
6039:
6025:
6005:Short Cuts for Analyzing Planetary Gearing
5940:Gear Drive Systems: Design and Application
5473:NuVinci continuously variable transmission
5431:– ancient mechanical astronomical computer
2639:
2618:
2409:
2387:
2353:
2061:
1936:
1772:
5310:Learn how and when to remove this message
4590:
2738:
2714:
2613:
2589:
2552:
2541:
2517:
2477:
2453:
2431:
2420:
2372:
2361:
2331:
2316:
2305:
2300:
2279:
2264:
2253:
2245:
2191:
2176:
2165:
2160:
2142:
2131:
2046:
2035:
2010:
1999:
1981:
1970:
1921:
1910:
1860:
1828:
1799:
1761:
1731:
1592:
1568:
1548:
1537:
1497:
1493:
1469:
1442:
1438:
1414:
1357:
1343:
1332:
1315:
1301:
1277:
1217:
1206:
1189:
1175:
1151:
1104:
1061:
1037:
821:
774:
750:
715:
709:
667:
643:
599:; meaning that each planet gear turns at
418:{\displaystyle N_{\text{s}},N_{\text{r}}}
5782:Musson, A.E.; Robinson, Eric H. (1969).
5662:"The Antikythera Mechanism reconsidered"
5586:Fundamentals of Motor Vehicle Technology
5321:
5228:inaccessibility, and design complexity.
5213:
5137:
4797:
4794:Gear ratio of reversed epicyclic gearing
4594:
2771:
1017:from which we can derive the following:
552:
161:
92:
36:
5579:
5453:– had a 2 speed planetary transmission.
5330:Planetary gears have become popular in
2117:turn of the sun gear produces 1.5
14:
6767:
5843:IEEE Transactions on Power Electronics
5659:
1706:{\displaystyle \omega _{\text{...}}=0}
6335:
6020:
5715:
5713:
2293:One turn of a planet gear results in
5975:"Epicyclic gearing animation in SVG"
5609:Harrison, H.; Nettleton, T. (1994).
5288:adding citations to reliable sources
5255:
2238:One turn of the sun gear results in
2153:teeth, then the ring will rotate by
229:gear train. This curve is called an
207:In the 2nd century AD treatise
5612:Principles of Engineering Mechanics
24:
6470:Continuously variable transmission
6200:Continuously variable transmission
5710:
5534:Oxford University Press, New York.
5532:Theory of Machines and Mechanisms,
5435:Continuously variable transmission
5196:
2780:AM bicycle hub (ring gear removed)
2021:teeth, then the ratio is equal to
269:French mathematician and engineer
236:Epicyclic gearing was used in the
25:
6791:
5962:
5669:Interdisciplinary Science Reviews
4173:2. The ring gear is held fixed, ω
284:Requirements for non-interference
6749:
6748:
6738:
5980:"Animation of Epicyclic gearing"
5397:
5381:
5372:
5360:
5260:
4374:3. The sun gear is held fixed, ω
2146:{\displaystyle \,N_{\text{r}}\,}
2014:{\displaystyle \,N_{\text{p}}\,}
1992:teeth, and each planet gear has
1985:{\displaystyle \,N_{\text{s}}\,}
1947:is the sun-to-planet gear ratio.
5945:
5932:
5918:
5904:
5816:
4506:
4498:
4451:
4443:
4298:
4290:
4250:
4242:
4100:
4092:
4043:1. The carrier is held fixed, ω
1001:are the number of teeth of the
425:are the number of teeth of the
171:Le diverse et artifiose machine
6361:
5731:
5629:
5602:
5573:
5553:
5490:– 14-ratio bicycle hub gearbox
5390:Pratt & Whitney Canada PT6
5251:
5116:
5104:
5046:
5034:
4987:
4973:
4832:
4820:
4763:
4737:
1857:
1845:
1825:
1813:
1101:
1075:
13:
1:
6505:Automated manual transmission
6077:Epicyclic (planetary) gearing
5641:Power Transmission Components
5512:
5209:
5147:internally geared bicycle hub
5142:Stepped planet series of the
5129:when the ring gear is locked.
2632:which may also be written as
274:
5886:Journal of Mechanical Design
5478:Ravigneaux planetary gearset
3698:— Torque of ring (annulus),
1959:relative to the two inputs.
455:{\displaystyle n_{\text{p}}}
308:{\displaystyle n_{\text{p}}}
120:, revolving about a central
7:
6580:Semi-automatic transmission
5738:Randl, Chad (15 May 2008).
5416:
5000:when the carrier is locked,
244:, and even for its orbital
88:
57:assembly consisting of two
10:
6796:
6417:Internal combustion engine
5483:Lepelletier gear mechanism
5350:
181:
169:, from Agostino Ramelli's
29:
6734:
6716:Hybrid vehicle drivetrain
6703:
6618:
6605:Transmission control unit
6545:Limited-slip differential
6510:Electrorheological clutch
6435:
6382:
6369:
6321:Spur gear corrected tooth
6278:
6256:
6220:
6213:
6167:
6146:
6105:
6054:
6046:
5942:. Marcel Dekker, New York
5494:Simpson planetary gearset
3852:Fixed carrier train ratio
3745:{\displaystyle \tau _{c}}
3718:{\displaystyle \tau _{s}}
3691:{\displaystyle \tau _{r}}
1955:with the third providing
6495:Dual-clutch transmission
5985:The "Power Split Device"
5863:10.1109/TPEL.2006.872372
5689:10.1179/030801807X163670
5580:Hillier, V.A.W. (2001).
5567:University of California
5134:Compound planetary gears
2398:turns of the ring gear.
242:ellipticity of its orbit
6465:Constant-velocity joint
5175:automatic transmissions
5067:when the sun is locked,
6445:Automatic transmission
5327:
5224:
5163:multi-stage structures
5150:
5123:
5061:
4994:
4932:
4878:
4806:
4773:
4695:
4605:spur gear differential
4600:
4591:Spur gear differential
4585:automatic transmission
4571:
4363:
4162:
4031:
3941:
3839:
3746:
3719:
3692:
3661:
3578:
3513:
3430:
3347:
3264:
3187:
3041:
2912:
2781:
2776:Compound planets of a
2763:
2686:
2626:
2502:
2392:
2342:turns of the ring gear
2336:
2284:
2196:
2147:
2113:; this means that one
2069:
2015:
1986:
1941:
1881:
1780:
1707:
1674:
1625:
1512:
1372:
1245:
1119:
995:
922:
850:
616:
478:
456:
419:
374:
309:
252:Richard of Wallingford
226:deferent and epicycles
174:
98:
42:
5938:Lynwander, P., 1983,
5660:Wright, M.T. (2007).
5429:Antikythera mechanism
5424:Hypocycloidal gearing
5325:
5217:
5141:
5124:
5062:
4995:
4933:
4879:
4801:
4774:
4696:
4598:
4572:
4364:
4163:
4032:
3942:
3840:
3747:
3720:
3693:
3662:
3579:
3514:
3431:
3348:
3265:
3188:
3042:
2913:
2775:
2764:
2687:
2627:
2503:
2393:
2337:
2285:
2197:
2148:
2070:
2016:
1987:
1942:
1882:
1781:
1708:
1675:
1626:
1513:
1373:
1246:
1120:
996:
923:
851:
556:
479:
457:
420:
375:
310:
238:Antikythera Mechanism
211:Mathematical Syntaxis
198:Antikythera Mechanism
165:
96:
40:
6550:Locking differential
6485:Direct-shift gearbox
6243:Shaft-driven bicycle
5951:Smith, J. D., 1983,
5569:. 1913. p. 979.
5562:Machinery, Volume 19
5469:, for bicycles, etc.
5284:improve this section
5075:
5008:
4947:
4891:
4817:
4711:
4622:
4387:
4186:
4056:
3961:
3871:
3760:
3729:
3702:
3675:
3589:
3524:
3441:
3358:
3275:
3210:
3054:
2925:
2796:
2707:
2636:
2514:
2406:
2350:
2297:
2290:turns of the planets
2242:
2157:
2128:
2025:
1996:
1967:
1897:
1793:
1728:
1684:
1638:
1528:
1385:
1258:
1132:
1024:
952:
866:
626:
514:: Holds one or more
468:
439:
389:
322:
292:
79:planetary gear train
47:epicyclic gear train
6775:Epicyclical gearing
6575:Preselector gearbox
6555:Manual transmission
6082:Sun and planet gear
5855:2006ITPE...21..756M
5681:2007ISRv...32...27W
5392:gas turbine engine.
5388:Reduction gears on
5218:The mechanism of a
433:, respectively and
6721:Electric generator
6626:Wheel hub assembly
6311:Gear manufacturing
6147:Geartooth profiles
6010:2021-02-25 at the
5912:"Archimedes Drive"
5328:
5225:
5151:
5119:
5057:
4990:
4940:which results in:
4928:
4874:
4807:
4769:
4691:
4601:
4567:
4504:
4449:
4359:
4296:
4248:
4158:
4098:
4027:
3937:
3835:
3742:
3715:
3688:
3657:
3574:
3509:
3426:
3343:
3260:
3183:
3037:
2908:
2782:
2759:
2751:
2682:
2622:
2616:
2565:
2498:
2490:
2444:
2388:
2385:
2332:
2329:
2280:
2277:
2192:
2189:
2143:
2065:
2059:
2011:
1982:
1937:
1934:
1877:
1776:
1703:
1670:
1621:
1508:
1368:
1241:
1115:
991:
948:respectively, and
930:angular velocities
918:
846:
844:
617:
508:: The central gear
484:is a whole number
474:
452:
415:
370:
305:
256:astronomical clock
246:apsidal precession
175:
99:
43:
6762:
6761:
6515:Epicyclic gearing
6384:Automotive engine
6329:
6328:
6274:
6273:
6097:Non-circular gear
6062:Spur gear systems
6000:Planetary Gearbox
5928:. 10 August 2022.
5898:10.1115/1.2829172
5344:herringbone gears
5320:
5319:
5312:
5101:
5085:
5031:
5018:
4970:
4957:
4925:
4910:
4871:
4858:
4842:
4735:
4677:
4612: = −1.
4562:
4529:
4503:
4493:
4474:
4448:
4432:
4354:
4321:
4295:
4273:
4247:
4231:
4153:
4123:
4097:
4081:
4022:
3932:
3902:
3725:— Torque of sun,
3655:
3572:
3507:
3424:
3341:
3258:
3180:
3171:
3167:
3162:
3152:
3147:
3139:
3134:
3122:
3113:
3109:
3104:
3094:
3089:
3081:
3076:
3064:
3034:
3025:
3022:
3017:
3010:
3005:
2993:
2984:
2981:
2976:
2968:
2963:
2953:
2948:
2935:
2905:
2896:
2893:
2888:
2881:
2876:
2864:
2855:
2852:
2847:
2839:
2834:
2824:
2819:
2806:
2755:
2750:
2747:
2735:
2722:
2678:
2673:
2660:
2647:
2615:
2610:
2597:
2585:
2564:
2561:
2549:
2494:
2489:
2486:
2474:
2461:
2443:
2440:
2428:
2384:
2381:
2369:
2328:
2325:
2313:
2276:
2273:
2261:
2188:
2185:
2173:
2139:
2058:
2055:
2043:
2007:
1978:
1933:
1930:
1918:
1868:
1836:
1807:
1769:
1752:
1739:
1694:
1666:
1661:
1648:
1619:
1615:
1602:
1589:
1576:
1560:
1557:
1545:
1505:
1495:
1490:
1477:
1465:
1450:
1440:
1435:
1422:
1410:
1395:
1365:
1355:
1352:
1340:
1323:
1313:
1310:
1298:
1285:
1268:
1238:
1229:
1226:
1214:
1197:
1187:
1184:
1172:
1159:
1142:
1112:
1098:
1085:
1069:
1058:
1045:
1034:
988:
975:
962:
915:
902:
889:
876:
829:
813:
800:
782:
771:
758:
747:
723:
706:
693:
675:
664:
651:
640:
477:{\displaystyle A}
449:
412:
399:
362:
359:
348:
335:
302:
145:pencil sharpeners
106:planetary gearing
102:Epicyclic gearing
85:can be realized.
51:planetary gearset
49:(also known as a
32:Starter ring gear
18:Planetary gearbox
16:(Redirected from
6787:
6752:
6751:
6742:
6619:Wheels and tires
6590:Torque converter
6356:
6349:
6342:
6333:
6332:
6218:
6217:
6041:
6034:
6027:
6018:
6017:
5956:
5949:
5943:
5936:
5930:
5929:
5922:
5916:
5915:
5908:
5902:
5901:
5881:
5875:
5874:
5838:
5832:
5831:
5820:
5814:
5813:
5789:
5779:
5773:
5765:
5735:
5729:
5728:
5726:
5717:
5708:
5707:
5705:
5703:
5666:
5657:
5651:
5650:
5648:
5647:
5633:
5627:
5626:
5606:
5600:
5599:
5577:
5571:
5570:
5557:
5551:
5550:, Prentice Hall.
5544:
5535:
5528:
5488:Rohloff Speedhub
5401:
5385:
5376:
5364:
5315:
5308:
5304:
5301:
5295:
5264:
5256:
5220:pencil sharpener
5204:torque converter
5144:Rohloff Speedhub
5128:
5126:
5125:
5120:
5103:
5102:
5099:
5087:
5086:
5083:
5066:
5064:
5063:
5058:
5053:
5033:
5032:
5029:
5020:
5019:
5016:
4999:
4997:
4996:
4991:
4983:
4972:
4971:
4968:
4959:
4958:
4955:
4937:
4935:
4934:
4929:
4927:
4926:
4923:
4917:
4912:
4911:
4908:
4883:
4881:
4880:
4875:
4873:
4872:
4869:
4860:
4859:
4856:
4844:
4843:
4840:
4778:
4776:
4775:
4770:
4762:
4761:
4749:
4748:
4736:
4728:
4723:
4722:
4700:
4698:
4697:
4692:
4678:
4676:
4675:
4674:
4662:
4661:
4651:
4650:
4649:
4637:
4636:
4626:
4576:
4574:
4573:
4568:
4563:
4561:
4560:
4551:
4550:
4541:
4530:
4528:
4527:
4518:
4517:
4508:
4505:
4501:
4494:
4486:
4475:
4473:
4472:
4463:
4462:
4453:
4450:
4446:
4433:
4431:
4430:
4429:
4417:
4416:
4406:
4405:
4404:
4391:
4368:
4366:
4365:
4360:
4355:
4353:
4352:
4343:
4342:
4333:
4322:
4320:
4319:
4310:
4309:
4300:
4297:
4293:
4274:
4272:
4271:
4262:
4261:
4252:
4249:
4245:
4232:
4230:
4229:
4228:
4215:
4214:
4213:
4201:
4200:
4190:
4167:
4165:
4164:
4159:
4154:
4152:
4151:
4142:
4141:
4132:
4124:
4122:
4121:
4112:
4111:
4102:
4099:
4095:
4082:
4080:
4079:
4070:
4069:
4060:
4036:
4034:
4033:
4028:
4023:
4021:
4020:
4019:
4007:
4006:
3996:
3995:
3994:
3982:
3981:
3971:
3946:
3944:
3943:
3938:
3933:
3931:
3930:
3921:
3920:
3911:
3903:
3901:
3900:
3891:
3890:
3881:
3844:
3842:
3841:
3836:
3828:
3827:
3818:
3817:
3805:
3804:
3795:
3794:
3782:
3781:
3772:
3771:
3751:
3749:
3748:
3743:
3741:
3740:
3724:
3722:
3721:
3716:
3714:
3713:
3697:
3695:
3694:
3689:
3687:
3686:
3666:
3664:
3663:
3658:
3656:
3654:
3653:
3652:
3640:
3639:
3629:
3628:
3619:
3617:
3616:
3601:
3600:
3583:
3581:
3580:
3575:
3573:
3571:
3570:
3561:
3560:
3551:
3549:
3548:
3536:
3535:
3518:
3516:
3515:
3510:
3508:
3506:
3505:
3496:
3495:
3494:
3482:
3481:
3471:
3469:
3468:
3453:
3452:
3435:
3433:
3432:
3427:
3425:
3423:
3422:
3413:
3412:
3411:
3399:
3398:
3388:
3386:
3385:
3370:
3369:
3352:
3350:
3349:
3344:
3342:
3340:
3339:
3338:
3326:
3325:
3315:
3314:
3305:
3303:
3302:
3287:
3286:
3269:
3267:
3266:
3261:
3259:
3257:
3256:
3247:
3246:
3237:
3235:
3234:
3222:
3221:
3192:
3190:
3189:
3184:
3182:
3181:
3178:
3172:
3170:
3169:
3168:
3165:
3163:
3160:
3154:
3153:
3150:
3148:
3145:
3141:
3140:
3137:
3135:
3132:
3129:
3124:
3123:
3120:
3114:
3112:
3111:
3110:
3107:
3105:
3102:
3096:
3095:
3092:
3090:
3087:
3083:
3082:
3079:
3077:
3074:
3071:
3066:
3065:
3062:
3046:
3044:
3043:
3038:
3036:
3035:
3032:
3026:
3024:
3023:
3020:
3018:
3015:
3012:
3011:
3008:
3006:
3003:
3000:
2995:
2994:
2991:
2985:
2983:
2982:
2979:
2977:
2974:
2971:
2970:
2969:
2966:
2964:
2961:
2955:
2954:
2951:
2949:
2946:
2942:
2937:
2936:
2933:
2917:
2915:
2914:
2909:
2907:
2906:
2903:
2897:
2895:
2894:
2891:
2889:
2886:
2883:
2882:
2879:
2877:
2874:
2871:
2866:
2865:
2862:
2856:
2854:
2853:
2850:
2848:
2845:
2842:
2841:
2840:
2837:
2835:
2832:
2826:
2825:
2822:
2820:
2817:
2813:
2808:
2807:
2804:
2768:
2766:
2765:
2760:
2753:
2752:
2749:
2748:
2745:
2739:
2737:
2736:
2733:
2724:
2723:
2720:
2712:
2691:
2689:
2688:
2683:
2676:
2675:
2674:
2671:
2662:
2661:
2658:
2649:
2648:
2645:
2631:
2629:
2628:
2623:
2617:
2614:
2612:
2611:
2608:
2599:
2598:
2595:
2587:
2586:
2583:
2577:
2571:
2567:
2566:
2563:
2562:
2559:
2553:
2551:
2550:
2547:
2539:
2525:
2507:
2505:
2504:
2499:
2492:
2491:
2488:
2487:
2484:
2478:
2476:
2475:
2472:
2463:
2462:
2459:
2451:
2445:
2442:
2441:
2438:
2432:
2430:
2429:
2426:
2418:
2397:
2395:
2394:
2389:
2386:
2383:
2382:
2379:
2373:
2371:
2370:
2367:
2359:
2341:
2339:
2338:
2333:
2330:
2327:
2326:
2323:
2317:
2315:
2314:
2311:
2303:
2289:
2287:
2286:
2281:
2278:
2275:
2274:
2271:
2265:
2263:
2262:
2259:
2251:
2233:
2231:
2230:
2227:
2224:
2217:
2215:
2214:
2211:
2208:
2201:
2199:
2198:
2193:
2190:
2187:
2186:
2183:
2177:
2175:
2174:
2171:
2163:
2152:
2150:
2149:
2144:
2141:
2140:
2137:
2119:counterclockwise
2112:
2110:
2109:
2106:
2103:
2099:
2093:
2091:
2090:
2087:
2084:
2080:
2074:
2072:
2071:
2066:
2060:
2057:
2056:
2053:
2047:
2045:
2044:
2041:
2033:
2020:
2018:
2017:
2012:
2009:
2008:
2005:
1991:
1989:
1988:
1983:
1980:
1979:
1976:
1946:
1944:
1943:
1938:
1935:
1932:
1931:
1928:
1922:
1920:
1919:
1916:
1908:
1886:
1884:
1883:
1878:
1870:
1869:
1866:
1838:
1837:
1834:
1809:
1808:
1805:
1785:
1783:
1782:
1777:
1771:
1770:
1767:
1754:
1753:
1750:
1741:
1740:
1737:
1712:
1710:
1709:
1704:
1696:
1695:
1692:
1679:
1677:
1676:
1671:
1664:
1663:
1662:
1659:
1650:
1649:
1646:
1630:
1628:
1627:
1622:
1620:
1618:
1617:
1616:
1613:
1604:
1603:
1600:
1593:
1591:
1590:
1587:
1578:
1577:
1574:
1566:
1561:
1559:
1558:
1555:
1549:
1547:
1546:
1543:
1535:
1517:
1515:
1514:
1509:
1507:
1506:
1503:
1496:
1494:
1492:
1491:
1488:
1479:
1478:
1475:
1467:
1466:
1463:
1457:
1452:
1451:
1448:
1441:
1439:
1437:
1436:
1433:
1424:
1423:
1420:
1412:
1411:
1408:
1402:
1397:
1396:
1393:
1377:
1375:
1374:
1369:
1367:
1366:
1363:
1356:
1354:
1353:
1350:
1344:
1342:
1341:
1338:
1330:
1325:
1324:
1321:
1314:
1312:
1311:
1308:
1302:
1300:
1299:
1296:
1287:
1286:
1283:
1275:
1270:
1269:
1266:
1250:
1248:
1247:
1242:
1240:
1239:
1236:
1230:
1228:
1227:
1224:
1218:
1216:
1215:
1212:
1204:
1199:
1198:
1195:
1188:
1186:
1185:
1182:
1176:
1174:
1173:
1170:
1161:
1160:
1157:
1149:
1144:
1143:
1140:
1124:
1122:
1121:
1116:
1114:
1113:
1110:
1100:
1099:
1096:
1087:
1086:
1083:
1071:
1070:
1067:
1060:
1059:
1056:
1047:
1046:
1043:
1036:
1035:
1032:
1000:
998:
997:
992:
990:
989:
986:
977:
976:
973:
964:
963:
960:
927:
925:
924:
919:
917:
916:
913:
904:
903:
900:
891:
890:
887:
878:
877:
874:
855:
853:
852:
847:
845:
831:
830:
827:
820:
816:
815:
814:
811:
802:
801:
798:
784:
783:
780:
773:
772:
769:
760:
759:
756:
749:
748:
745:
725:
724:
721:
714:
710:
708:
707:
704:
695:
694:
691:
677:
676:
673:
666:
665:
662:
653:
652:
649:
642:
641:
638:
614:
612:
611:
608:
605:
598:
596:
595:
592:
589:
585:
579:
577:
576:
573:
570:
566:
483:
481:
480:
475:
461:
459:
458:
453:
451:
450:
447:
424:
422:
421:
416:
414:
413:
410:
401:
400:
397:
379:
377:
376:
371:
363:
361:
360:
357:
351:
350:
349:
346:
337:
336:
333:
326:
314:
312:
311:
306:
304:
303:
300:
279:
276:
260:Agostino Ramelli
222:Claudius Ptolemy
188:Claudius Ptolemy
21:
6795:
6794:
6790:
6789:
6788:
6786:
6785:
6784:
6765:
6764:
6763:
6758:
6730:
6699:
6614:
6610:Universal joint
6540:Hotchkiss drive
6431:
6378:
6365:
6360:
6330:
6325:
6270:
6252:
6209:
6195:Bicycle gearing
6163:
6142:
6101:
6092:Cycloidal drive
6072:Rack and pinion
6050:
6045:
6012:Wayback Machine
5965:
5960:
5959:
5950:
5946:
5937:
5933:
5924:
5923:
5919:
5910:
5909:
5905:
5882:
5878:
5839:
5835:
5822:
5821:
5817:
5802:
5780:
5776:
5754:
5753:978-156898681-4
5736:
5732:
5724:
5718:
5711:
5701:
5699:
5664:
5658:
5654:
5645:
5643:
5635:
5634:
5630:
5623:
5607:
5603:
5596:
5578:
5574:
5559:
5558:
5554:
5546:B. Paul, 1979,
5545:
5538:
5529:
5520:
5515:
5510:
5441:Cycloidal drive
5419:
5414:
5413:
5412:
5409:
5402:
5393:
5386:
5377:
5368:
5365:
5353:
5316:
5305:
5299:
5296:
5281:
5265:
5254:
5212:
5199:
5197:Power splitting
5191:cycloidal drive
5136:
5098:
5094:
5082:
5078:
5076:
5073:
5072:
5049:
5028:
5024:
5015:
5011:
5009:
5006:
5005:
4979:
4967:
4963:
4954:
4950:
4948:
4945:
4944:
4922:
4918:
4913:
4907:
4903:
4892:
4889:
4888:
4868:
4864:
4855:
4851:
4839:
4835:
4818:
4815:
4814:
4796:
4757:
4753:
4744:
4740:
4727:
4718:
4714:
4712:
4709:
4708:
4670:
4666:
4657:
4653:
4652:
4645:
4641:
4632:
4628:
4627:
4625:
4623:
4620:
4619:
4593:
4556:
4552:
4546:
4542:
4540:
4523:
4519:
4513:
4509:
4507:
4499:
4485:
4468:
4464:
4458:
4454:
4452:
4444:
4425:
4421:
4412:
4408:
4407:
4400:
4396:
4392:
4390:
4388:
4385:
4384:
4377:
4348:
4344:
4338:
4334:
4332:
4315:
4311:
4305:
4301:
4299:
4291:
4267:
4263:
4257:
4253:
4251:
4243:
4224:
4220:
4216:
4209:
4205:
4196:
4192:
4191:
4189:
4187:
4184:
4183:
4176:
4147:
4143:
4137:
4133:
4131:
4117:
4113:
4107:
4103:
4101:
4093:
4075:
4071:
4065:
4061:
4059:
4057:
4054:
4053:
4046:
4015:
4011:
4002:
3998:
3997:
3990:
3986:
3977:
3973:
3972:
3970:
3962:
3959:
3958:
3926:
3922:
3916:
3912:
3910:
3896:
3892:
3886:
3882:
3880:
3872:
3869:
3868:
3854:
3823:
3819:
3813:
3809:
3800:
3796:
3790:
3786:
3777:
3773:
3767:
3763:
3761:
3758:
3757:
3753:
3736:
3732:
3730:
3727:
3726:
3709:
3705:
3703:
3700:
3699:
3682:
3678:
3676:
3673:
3672:
3670:
3648:
3644:
3635:
3631:
3630:
3624:
3620:
3618:
3612:
3608:
3596:
3592:
3590:
3587:
3586:
3566:
3562:
3556:
3552:
3550:
3544:
3540:
3531:
3527:
3525:
3522:
3521:
3501:
3497:
3490:
3486:
3477:
3473:
3472:
3470:
3464:
3460:
3448:
3444:
3442:
3439:
3438:
3418:
3414:
3407:
3403:
3394:
3390:
3389:
3387:
3381:
3377:
3365:
3361:
3359:
3356:
3355:
3334:
3330:
3321:
3317:
3316:
3310:
3306:
3304:
3298:
3294:
3282:
3278:
3276:
3273:
3272:
3252:
3248:
3242:
3238:
3236:
3230:
3226:
3217:
3213:
3211:
3208:
3207:
3203:
3199:
3177:
3173:
3164:
3159:
3158:
3149:
3144:
3143:
3142:
3136:
3131:
3130:
3128:
3119:
3115:
3106:
3101:
3100:
3091:
3086:
3085:
3084:
3078:
3073:
3072:
3070:
3061:
3057:
3055:
3052:
3051:
3031:
3027:
3019:
3014:
3013:
3007:
3002:
3001:
2999:
2990:
2986:
2978:
2973:
2972:
2965:
2960:
2959:
2950:
2945:
2944:
2943:
2941:
2932:
2928:
2926:
2923:
2922:
2902:
2898:
2890:
2885:
2884:
2878:
2873:
2872:
2870:
2861:
2857:
2849:
2844:
2843:
2836:
2831:
2830:
2821:
2816:
2815:
2814:
2812:
2803:
2799:
2797:
2794:
2793:
2787:
2744:
2740:
2732:
2728:
2719:
2715:
2713:
2710:
2708:
2705:
2704:
2670:
2666:
2657:
2653:
2644:
2640:
2637:
2634:
2633:
2607:
2603:
2594:
2590:
2588:
2582:
2578:
2575:
2558:
2554:
2546:
2542:
2540:
2537:
2530:
2526:
2521:
2515:
2512:
2511:
2483:
2479:
2471:
2467:
2458:
2454:
2452:
2449:
2437:
2433:
2425:
2421:
2419:
2416:
2407:
2404:
2403:
2378:
2374:
2366:
2362:
2360:
2357:
2351:
2348:
2347:
2322:
2318:
2310:
2306:
2304:
2301:
2298:
2295:
2294:
2270:
2266:
2258:
2254:
2252:
2249:
2243:
2240:
2239:
2228:
2225:
2222:
2221:
2219:
2212:
2209:
2206:
2205:
2203:
2182:
2178:
2170:
2166:
2164:
2161:
2158:
2155:
2154:
2136:
2132:
2129:
2126:
2125:
2107:
2104:
2101:
2100:
2097:
2095:
2088:
2085:
2082:
2081:
2078:
2076:
2052:
2048:
2040:
2036:
2034:
2031:
2026:
2023:
2022:
2004:
2000:
1997:
1994:
1993:
1975:
1971:
1968:
1965:
1964:
1927:
1923:
1915:
1911:
1909:
1906:
1898:
1895:
1894:
1865:
1861:
1833:
1829:
1804:
1800:
1794:
1791:
1790:
1766:
1762:
1749:
1745:
1736:
1732:
1729:
1726:
1725:
1691:
1687:
1685:
1682:
1681:
1658:
1654:
1645:
1641:
1639:
1636:
1635:
1612:
1608:
1599:
1595:
1594:
1586:
1582:
1573:
1569:
1567:
1565:
1554:
1550:
1542:
1538:
1536:
1534:
1529:
1526:
1525:
1502:
1498:
1487:
1483:
1474:
1470:
1468:
1462:
1458:
1456:
1447:
1443:
1432:
1428:
1419:
1415:
1413:
1407:
1403:
1401:
1392:
1388:
1386:
1383:
1382:
1362:
1358:
1349:
1345:
1337:
1333:
1331:
1329:
1320:
1316:
1307:
1303:
1295:
1291:
1282:
1278:
1276:
1274:
1265:
1261:
1259:
1256:
1255:
1235:
1231:
1223:
1219:
1211:
1207:
1205:
1203:
1194:
1190:
1181:
1177:
1169:
1165:
1156:
1152:
1150:
1148:
1139:
1135:
1133:
1130:
1129:
1109:
1105:
1095:
1091:
1082:
1078:
1066:
1062:
1055:
1051:
1042:
1038:
1031:
1027:
1025:
1022:
1021:
985:
981:
972:
968:
959:
955:
953:
950:
949:
942:planetary gears
912:
908:
899:
895:
886:
882:
873:
869:
867:
864:
863:
843:
842:
832:
826:
822:
810:
806:
797:
793:
792:
788:
779:
775:
768:
764:
755:
751:
744:
740:
737:
736:
726:
720:
716:
703:
699:
690:
686:
685:
681:
672:
668:
661:
657:
648:
644:
637:
633:
629:
627:
624:
623:
609:
606:
603:
602:
600:
593:
590:
587:
586:
583:
581:
574:
571:
568:
567:
564:
562:
559:planetary gears
494:
469:
466:
465:
446:
442:
440:
437:
436:
409:
405:
396:
392:
390:
387:
386:
356:
352:
345:
341:
332:
328:
327:
325:
323:
320:
319:
299:
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293:
290:
289:
286:
277:
184:
91:
35:
28:
23:
22:
15:
12:
11:
5:
6793:
6783:
6782:
6777:
6760:
6759:
6757:
6756:
6746:
6735:
6732:
6731:
6729:
6728:
6723:
6718:
6713:
6711:Electric motor
6707:
6705:
6701:
6700:
6698:
6697:
6696:
6695:
6690:
6685:
6680:
6675:
6670:
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6607:
6602:
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6582:
6577:
6572:
6567:
6562:
6557:
6552:
6547:
6542:
6537:
6532:
6527:
6525:Friction drive
6522:
6520:Fluid coupling
6517:
6512:
6507:
6502:
6497:
6492:
6487:
6482:
6477:
6472:
6467:
6462:
6457:
6452:
6447:
6441:
6439:
6433:
6432:
6430:
6429:
6424:
6419:
6414:
6411:Plug-in hybrid
6404:
6399:
6394:
6388:
6386:
6380:
6379:
6370:
6367:
6366:
6359:
6358:
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6125:
6120:
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6103:
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6100:
6099:
6094:
6089:
6087:Harmonic drive
6084:
6079:
6074:
6069:
6064:
6058:
6056:
6052:
6051:
6044:
6043:
6036:
6029:
6021:
6015:
6014:
6002:
5997:
5992:
5987:
5982:
5977:
5972:
5964:
5963:External links
5961:
5958:
5957:
5944:
5931:
5917:
5903:
5892:(3): 448–453.
5876:
5849:(3): 756–767.
5833:
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5774:
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5594:
5572:
5552:
5536:
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5509:
5508:
5502:
5499:Sturmey Archer
5496:
5491:
5485:
5480:
5475:
5470:
5464:
5462:Harmonic drive
5459:
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5318:
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5268:
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5211:
5208:
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5159:stepped-planet
5135:
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4803:CSS animations
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2778:Sturmey-Archer
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445:
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380:
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355:
344:
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331:
298:
285:
282:
224:used rotating
183:
180:
90:
87:
55:gear reduction
26:
9:
6:
4:
3:
2:
6792:
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6611:
6608:
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6601:
6598:
6596:
6593:
6591:
6588:
6586:
6585:Shift-by-wire
6583:
6581:
6578:
6576:
6573:
6571:
6568:
6566:
6563:
6561:
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6556:
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6425:
6423:
6422:Petrol engine
6420:
6418:
6415:
6412:
6408:
6405:
6403:
6400:
6398:
6395:
6393:
6392:Diesel engine
6390:
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6385:
6381:
6377:
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6357:
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6028:
6023:
6022:
6019:
6013:
6009:
6006:
6003:
6001:
5998:
5996:
5995:Prius Gearbox
5993:
5991:
5988:
5986:
5983:
5981:
5978:
5976:
5973:
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5966:
5954:
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5803:
5801:9780802016379
5797:
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5622:0-34-056831-3
5618:
5614:
5613:
5605:
5597:
5595:0-74-870531-7
5591:
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5324:
5314:
5311:
5303:
5300:February 2021
5293:
5289:
5285:
5279:
5278:
5274:
5269:This section
5267:
5263:
5258:
5257:
5249:
5245:
5241:
5237:
5233:
5229:
5221:
5216:
5207:
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5194:
5192:
5187:
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5178:
5176:
5170:
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5164:
5160:
5156:
5155:meshed-planet
5148:
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3567:
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3553:
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3541:
3537:
3532:
3528:
3520:
3502:
3498:
3491:
3487:
3483:
3478:
3474:
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3461:
3457:
3454:
3449:
3445:
3437:
3419:
3415:
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3404:
3400:
3395:
3391:
3382:
3378:
3374:
3371:
3366:
3362:
3354:
3335:
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3327:
3322:
3318:
3311:
3307:
3299:
3295:
3291:
3288:
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3279:
3271:
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3249:
3243:
3239:
3231:
3227:
3223:
3218:
3214:
3206:
3205:
3204:
3174:
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3125:
3116:
3097:
3067:
3058:
3050:
3049:
3028:
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2956:
2938:
2929:
2921:
2920:
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2867:
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2809:
2800:
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2791:
2790:
2779:
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2641:
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2600:
2591:
2579:
2572:
2568:
2555:
2543:
2534:
2531:
2527:
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2518:
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2495:
2480:
2468:
2464:
2455:
2446:
2434:
2422:
2413:
2410:
2399:
2375:
2363:
2354:
2319:
2307:
2292:
2267:
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2246:
2237:
2236:
2235:
2179:
2167:
2133:
2122:
2120:
2116:
2062:
2049:
2037:
2028:
2001:
1972:
1960:
1958:
1954:
1924:
1912:
1903:
1900:
1893:
1892:
1891:
1874:
1871:
1862:
1854:
1851:
1848:
1842:
1839:
1830:
1822:
1819:
1816:
1810:
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1326:
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1292:
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1279:
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1254:
1253:
1232:
1220:
1208:
1200:
1191:
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1166:
1162:
1153:
1145:
1136:
1128:
1127:
1106:
1092:
1088:
1079:
1072:
1063:
1052:
1048:
1039:
1028:
1020:
1019:
1018:
1013:respectively.
1012:
1008:
1004:
982:
978:
969:
965:
956:
947:
946:carrier frame
943:
939:
935:
931:
909:
905:
896:
892:
883:
879:
870:
862:
861:
860:
839:
836:
834:
823:
817:
807:
803:
794:
789:
785:
776:
765:
761:
752:
741:
733:
730:
728:
717:
711:
700:
696:
687:
682:
678:
669:
658:
654:
645:
634:
622:
621:
620:
560:
555:
548:
544:
540:
536:
533:
531:
527:
523:
520:
517:
513:
512:Carrier frame
510:
507:
504:
503:
502:
499:
489:
485:
471:
463:
443:
434:
432:
428:
406:
402:
393:
384:
367:
364:
353:
342:
338:
329:
318:
317:
316:
296:
281:
272:
267:
265:
262:invented the
261:
257:
253:
249:
247:
243:
239:
234:
232:
227:
223:
219:
218:
213:
212:
205:
203:
199:
195:
194:
189:
179:
172:
168:
164:
160:
158:
154:
150:
149:differentials
146:
141:
139:
135:
131:
127:
123:
119:
115:
111:
107:
103:
95:
86:
84:
80:
76:
71:
69:
65:
64:pitch circles
60:
56:
52:
48:
39:
33:
19:
6663:Racing slick
6600:Transfer box
6570:Park-by-wire
6565:Parking pawl
6514:
6480:Differential
6455:Direct-drive
6437:Transmission
6427:Steam engine
6372:Part of the
6371:
6180:Differential
6175:Transmission
6128:Spiral bevel
6076:
5952:
5947:
5939:
5934:
5920:
5906:
5889:
5885:
5879:
5846:
5842:
5836:
5827:
5818:
5785:
5777:
5739:
5733:
5700:. Retrieved
5675:(1): 27–43.
5672:
5668:
5655:
5644:. Retrieved
5640:
5631:
5611:
5604:
5585:
5575:
5561:
5555:
5547:
5531:
5451:Ford Model T
5408:transmission
5341:
5337:
5329:
5306:
5297:
5282:Please help
5270:
5246:
5242:
5238:
5234:
5230:
5226:
5200:
5182:World War II
5179:
5171:
5167:
5162:
5158:
5154:
5152:
4939:
4886:
4808:
4786:
4784:
4781:
4703:
4614:
4609:
4602:
4581:
4373:
4172:
4042:
4039:
3952:
3949:
3859:
3855:
3847:
3669:
3200:
2788:
2698:
2509:
2400:
2345:
2123:
2118:
1961:
1956:
1952:
1950:
1889:
1723:
1718:
1714:
1633:
1520:
1016:
1010:
1006:
1002:
945:
941:
937:
933:
858:
618:
558:
547:Annular gear
546:
543:Annulus gear
542:
538:
534:
529:
525:
521:
515:
511:
505:
495:
486:
464:
435:
430:
426:
385:
382:
287:
268:
250:
235:
215:
208:
206:
191:
185:
176:
170:
142:
137:
133:
129:
125:
121:
113:
105:
101:
100:
78:
75:annulus gear
74:
72:
50:
46:
44:
6641:Alloy wheel
6500:Drive wheel
6490:Drive shaft
6450:Chain drive
6306:Chain drive
6266:Wheel train
6138:Herringbone
5332:3D printing
5252:3D printing
2699:In bicycle
1011:planet gear
1009:, and each
522:Planet gear
278: 1650
231:epitrochoid
116:, gears or
83:gear ratios
6769:Categories
6726:Alternator
6374:Automobile
6363:Powertrain
6301:Belt drive
6286:Ball screw
6233:Derailleur
6067:Worm drive
5828:buseco.net
5810:1036858215
5771:1568986815
5762:1036836698
5646:2024-09-25
5513:References
5446:Epicycloid
5406:Ravigneaux
5210:Advantages
3862:gear train
498:gear ratio
202:precession
153:bevel gear
68:epicycloid
6595:Transaxle
6560:Manumatic
6530:Gearshift
6402:Fuel cell
6316:Freewheel
6296:Jackscrew
6291:Leadscrew
6168:Mechanics
5505:Uni Wheel
5271:does not
5111:−
5096:ω
5092:−
5080:ω
5041:−
5026:ω
5013:ω
4965:ω
4952:ω
4901:−
4866:ω
4862:−
4853:ω
4837:ω
4827:−
4787:ring gear
4755:ω
4742:ω
4716:ω
4683:−
4668:ω
4664:−
4655:ω
4643:ω
4639:−
4630:ω
4521:ω
4511:ω
4483:−
4466:ω
4456:ω
4423:ω
4419:−
4410:ω
4398:ω
4394:−
4313:ω
4303:ω
4282:−
4265:ω
4255:ω
4222:ω
4218:−
4207:ω
4203:−
4194:ω
4129:−
4115:ω
4105:ω
4073:ω
4063:ω
4013:ω
4009:−
4000:ω
3988:ω
3984:−
3975:ω
3908:−
3894:ω
3884:ω
3821:ω
3811:τ
3798:ω
3788:τ
3775:ω
3765:τ
3734:τ
3707:τ
3680:τ
3610:τ
3606:−
3594:τ
3542:τ
3529:τ
3462:τ
3458:−
3446:τ
3379:τ
3375:−
3363:τ
3296:τ
3292:−
3280:τ
3228:τ
3215:τ
3175:α
3117:α
3059:α
3029:α
2997:−
2988:α
2930:α
2900:α
2868:−
2859:α
2801:α
2701:hub gears
2355:−
2247:−
2115:clockwise
2029:−
1863:ω
1840:−
1831:ω
1802:ω
1689:ω
1656:ω
1652:≠
1643:ω
1610:ω
1606:−
1597:ω
1584:ω
1580:−
1571:ω
1532:−
1500:ω
1445:ω
1390:ω
1360:ω
1327:−
1318:ω
1263:ω
1233:ω
1201:−
1192:ω
1137:ω
1107:ω
1064:ω
1040:ω
1003:ring gear
934:ring gear
910:ω
897:ω
884:ω
871:ω
824:ω
804:−
786:−
777:ω
762:−
753:ω
718:ω
679:−
670:ω
646:ω
539:Moon gear
535:Ring gear
530:ring gear
516:planetary
431:ring gear
271:Desargues
264:bookwheel
167:Bookwheel
126:sun wheel
6754:Category
6693:Tubeless
6678:Run-flat
6658:Off-road
6475:Coupling
6397:Electric
6279:See also
6258:Horology
6248:Sprocket
6238:Hub gear
6221:Bicycles
6214:Examples
6185:Coupling
6154:Involute
6008:Archived
5697:54663891
5467:Hub gear
5417:See also
2694:tractors
2096:−
2077:−
1634:only if
1007:sun gear
938:sun gear
928:are the
582:−
563:−
528:and the
526:sun gear
506:Sun gear
429:and the
427:sun gear
217:Almagest
214:(a.k.a.
193:Almagest
136:gear or
122:sun gear
89:Overview
6159:Cycloid
6133:Helical
6055:Systems
5871:4986932
5851:Bibcode
5722:Gearing
5677:Bibcode
5457:Gearbox
5351:Gallery
5292:removed
5277:sources
5180:During
3671:where:
2232:
2220:
2216:
2204:
2111:
2092:
932:of the
613:
601:
597:
578:
190:in the
182:History
157:coaxial
138:annulus
130:carrier
118:pinions
70:curve.
53:) is a
6744:Portal
6704:Hybrid
6668:Radial
6646:Hubcap
6460:Clutch
6407:Hybrid
6376:series
6228:Cogset
6205:Offset
6106:Shapes
5869:
5808:
5798:
5769:
5760:
5750:
5702:20 May
5695:
5619:
5592:
5223:angle.
4887:where
2754:
2677:
2493:
1957:output
1953:inputs
1890:where
1719:output
1665:
1005:, the
944:, and
859:where
383:where
173:, 1588
114:planet
6780:Gears
6688:Spare
6631:Wheel
6535:Giubo
6190:Train
6123:Crown
6118:Bevel
6048:Gears
5867:S2CID
5725:(PDF)
5693:S2CID
5665:(PDF)
5437:(CVT)
5186:radar
4378:=0,
4177:=0,
4047:=0,
2218:, or
2094:, or
1715:input
580:, or
545:, or
108:is a
59:gears
6683:Snow
6673:Rain
6653:Tire
6113:Spur
5806:OCLC
5796:ISBN
5767:ISBN
5758:OCLC
5748:ISBN
5704:2014
5617:ISBN
5590:ISBN
5275:any
5273:cite
1521:and
496:The
209:The
147:and
134:ring
110:gear
6636:Rim
5894:doi
5890:120
5859:doi
5685:doi
5286:by
4704:or
2213:64
2089:16
1693:...
575:16
220:),
124:or
104:or
45:An
6771::
5888:.
5865:.
5857:.
5847:21
5845:.
5826:.
5804:.
5794:.
5792:69
5756:.
5746:.
5744:19
5712:^
5691:.
5683:.
5673:32
5671:.
5667:.
5639:.
5584:.
5565:.
5539:^
5521:^
5193:.
4603:A
4587:.
4502:so
4447:or
4294:so
4246:or
4096:so
2229:4
2207:16
2108:2
2083:24
940:,
936:,
610:2
594:2
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541:,
537:,
280:.
275:c.
233:.
159:.
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6409:(
6355:e
6348:t
6341:v
6040:e
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5914:.
5900:.
5896::
5873:.
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5830:.
5812:.
5764:.
5706:.
5687::
5679::
5649:.
5625:.
5598:.
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5307:(
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5298:(
5294:.
5280:.
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5114:1
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5105:(
5100:c
5089:=
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5035:(
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4961:=
4956:r
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4915:/
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4898:=
4895:R
4870:s
4857:r
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4846:=
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4821:(
4767:.
4764:)
4759:r
4751:+
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4720:c
4689:,
4686:1
4680:=
4672:c
4659:r
4647:c
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4565:.
4558:r
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4548:s
4544:N
4538:+
4535:1
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4470:c
4460:r
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4438:R
4435:=
4427:c
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4376:s
4357:.
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4346:N
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4336:N
4330:+
4327:1
4324:=
4317:c
4307:s
4288:,
4285:R
4279:1
4276:=
4269:c
4259:s
4240:,
4237:R
4234:=
4226:c
4211:c
4198:s
4175:r
4156:.
4149:s
4145:N
4139:r
4135:N
4126:=
4119:r
4109:s
4090:,
4087:R
4084:=
4077:r
4067:s
4045:c
4025:.
4017:c
4004:r
3992:c
3979:s
3968:=
3965:R
3935:.
3928:s
3924:N
3918:r
3914:N
3905:=
3898:r
3888:s
3878:=
3875:R
3833:0
3830:=
3825:s
3815:s
3807:+
3802:c
3792:c
3784:+
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3769:r
3738:c
3711:s
3684:r
3650:s
3646:N
3642:+
3637:r
3633:N
3626:s
3622:N
3614:c
3603:=
3598:s
3568:r
3564:N
3558:s
3554:N
3546:r
3538:=
3533:s
3503:s
3499:N
3492:s
3488:N
3484:+
3479:r
3475:N
3466:s
3455:=
3450:c
3420:r
3416:N
3409:s
3405:N
3401:+
3396:r
3392:N
3383:r
3372:=
3367:c
3336:s
3332:N
3328:+
3323:r
3319:N
3312:r
3308:N
3300:c
3289:=
3284:r
3254:s
3250:N
3244:r
3240:N
3232:s
3224:=
3219:r
3179:r
3166:r
3161:N
3156:+
3151:s
3146:N
3138:r
3133:N
3126:+
3121:s
3108:r
3103:N
3098:+
3093:s
3088:N
3080:s
3075:N
3068:=
3063:c
3033:s
3021:r
3016:N
3009:s
3004:N
2992:c
2980:r
2975:N
2967:r
2962:N
2957:+
2952:s
2947:N
2939:=
2934:r
2904:r
2892:s
2887:N
2880:r
2875:N
2863:c
2851:s
2846:N
2838:r
2833:N
2828:+
2823:s
2818:N
2810:=
2805:s
2757:.
2746:r
2742:N
2734:r
2730:N
2726:+
2721:s
2717:N
2680:.
2672:r
2668:N
2664:+
2659:s
2655:N
2651::
2646:s
2642:N
2620:,
2609:r
2605:N
2601:+
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2573:=
2569:)
2560:s
2556:N
2548:r
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2532:1
2528:(
2523:/
2519:1
2496:.
2485:s
2481:N
2473:r
2469:N
2465:+
2460:s
2456:N
2447:=
2439:s
2435:N
2427:r
2423:N
2414:+
2411:1
2380:r
2376:N
2368:s
2364:N
2324:r
2320:N
2312:p
2308:N
2272:p
2268:N
2260:s
2256:N
2226:/
2223:1
2210:/
2184:r
2180:N
2172:p
2168:N
2138:r
2134:N
2105:/
2102:3
2098:+
2086:/
2079:+
2063:.
2054:p
2050:N
2042:s
2038:N
2006:p
2002:N
1977:s
1973:N
1929:p
1925:N
1917:s
1913:N
1904:=
1901:n
1875:0
1872:=
1867:c
1858:)
1855:n
1852:+
1849:1
1846:(
1843:2
1835:r
1826:)
1823:n
1820:+
1817:2
1814:(
1811:+
1806:s
1797:n
1774:,
1768:p
1764:N
1759:2
1756:+
1751:s
1747:N
1743:=
1738:r
1734:N
1701:0
1698:=
1668:.
1660:c
1647:r
1614:c
1601:r
1588:c
1575:s
1563:=
1556:s
1552:N
1544:r
1540:N
1504:r
1489:r
1485:N
1481:+
1476:s
1472:N
1464:r
1460:N
1454:+
1449:s
1434:r
1430:N
1426:+
1421:s
1417:N
1409:s
1405:N
1399:=
1394:c
1364:s
1351:r
1347:N
1339:s
1335:N
1322:c
1309:r
1305:N
1297:r
1293:N
1289:+
1284:s
1280:N
1272:=
1267:r
1237:r
1225:s
1221:N
1213:r
1209:N
1196:c
1183:s
1179:N
1171:r
1167:N
1163:+
1158:s
1154:N
1146:=
1141:s
1111:c
1102:)
1097:r
1093:N
1089:+
1084:s
1080:N
1076:(
1073:=
1068:r
1057:r
1053:N
1049:+
1044:s
1033:s
1029:N
987:p
983:N
979:,
974:s
970:N
966:,
961:r
957:N
914:c
906:,
901:p
893:,
888:s
880:,
875:r
840:0
837:=
828:c
818:)
812:p
808:N
799:r
795:N
790:(
781:p
770:p
766:N
757:r
746:r
742:N
734:0
731:=
722:c
712:)
705:p
701:N
697:+
692:s
688:N
683:(
674:p
663:p
659:N
655:+
650:s
639:s
635:N
607:/
604:3
591:/
588:3
584:+
572:/
565:+
472:A
448:p
444:n
411:r
407:N
403:,
398:s
394:N
368:A
365:=
358:p
354:n
347:r
343:N
339:+
334:s
330:N
301:p
297:n
34:.
20:)
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