Screws' motion are quite simple: they are a helical version of a wedge. Hold- ing a nut so it cannot rotate. Element of the screw thread, one can calculate the efficiency when raising or lowering a load1. And the helical gear attached to it against the helical teeth of the other gear? Will this cause backlash. To calculate a worm gear with center distance 100 mm. The worm has 2 teeth, and the worm wheel has 41 teeth. The axial/transverse module is 4. The tolerance for the external diameter of the worm wheel is between 0 and -0.01 and for the active root. Backlash free center distance, allowances (mm).

Where, D1 – Pitch Diameter of Worm D2 – Pitch Diameter of Gear C – Centre to Centre Distance between the Worm and the Gear This worm gear design tutorial will discuss up to the selection of the module and pitch and the calculation of the number of teeth, pitch circle diameter and centre to centre distance between the worm and gear. We will use the AGMA formulae for doing the calculations.

Design calculations of the other aspects of the worm gear will be discussed in a subsequent part of the tutorial. Steps of the Design Calculation • The axial pitch of the worm and the circular pitch of the gear must be same for a mating worm and gear. We will use the term Pitch (P) for both the pitch in this tutorial. • Also, the module of the worm as well as the gear must be equal for a mating worm and gear. • Now, let’s say we have the following design input: Speed of the Worm (N1) = 20 RPM Speed of the Gear (N2) = 4 RPM • And, we have to find out the Module (m), Pitch (P), Number of helix of Worm (T1), Number of teeth of Gear (T2), Pitch circle diameter of Worm (D1), Pitch circle diameter of Gear (D2), Centre to centre distance(C). • Select the suitable module and its corresponding pitch from the following AGMA specified table: Module m (in MM) - Pitch P (in MM) 2 -------------------------6.238 2.5 ---------------------- 7.854 3.15 --------------------- 9.896 4 ------------------------- 12.566 5 ------------------------- 15.708 6.3 ----------------------- 19.792 8 -------------------------- 25.133 10 ------------------------- 31.416 12.5 ----------------------- 39.27 16 -------------------------- 50.625 20 -------------------------- 62.832 • Say, we are going ahead with the Module as 2 and the Pitch as 6.238.

• Use the following gear design equation: N1/N2 = T2/T1 And, we will get: T2 = 5 * T1.Eqn.1 • Now use the following AGMA empirical formula: T1 + T2 >40Eqn.2 • By using the two equations ( Eqn.1 & Eqn.2), we will get the approximate values of. T1 = 7 and T2 = 35 • Calculate the pitch circle diameter of the worm ( D1) by using the below AGMA empirical formula: D1 = 2.4 P + 1.1 = 16.0712 mm • The following AGMA empirical formula to be used for calculating the pitch circle diameter of the gear ( D2): D2 = T2*P/3.14 = 69.53185 mm • Now, we can calculate the centre to centre distance ( C) by the following equation: C = (D1 + D2)/2 = 42.80152 mm • The below empirical formula is the cross check for the correctness of the whole design calculation: (C^0.875)/2.

Multiple reducer gears in microwave oven (ruler for scale) A gear or cogwheel is a part having cut teeth, or cogs, which mesh with another toothed part to transmit. Geared devices can change the speed, torque, and direction of a. Gears almost always produce a change in torque, creating a, through their, and thus may be considered a. The teeth on the two meshing gears all have the same shape.

Two or more meshing gears, working in a sequence, are called a or a. A gear can mesh with a linear toothed part, called a rack, thereby producing instead of rotation. The gears in a transmission are analogous to the wheels in a crossed, belt system. An advantage of gears is that the teeth of a gear prevent slippage. When two gears mesh, if one gear is bigger than the other, a mechanical advantage is produced, with the, and the torques, of the two gears differing in proportion to their diameters. In transmissions with multiple gear ratios—such as bicycles, motorcycles, and cars—the term 'gear' as in 'first gear' refers to a gear ratio rather than an actual physical gear. The term describes similar devices, even when the gear ratio is rather than, or when the device does not actually contain gears, as in a.

Contents • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • History [ ] Early examples of gears date from the 4th century BC in China (Zhan Guo times – Late East ), which have been preserved at the of Henan Province,. The earliest preserved gears in Europe were found in the, an example of a very early and intricate geared device, designed to calculate positions. Its time of construction is now estimated between 150 and 100 BC. Gears appear in works connected to, in circa AD 50, but can be traced back to the mechanics of the in 3rd-century BC, and were greatly developed by the Greek (287–212 BC).

The gear first appeared in the Chinese, dated to the first millennium BC. The segmental gear, which receives/communicates from/to a cogwheel, consisting of a sector of a circular gear/ring having cogs on the periphery, was invented by Arab engineer in 1206. The was invented in the, for use in roller, some time during the 13th–14th centuries. Single-stage gear reducer Examples of early gear applications include: • (c.

200–265 AD) used gears as part of a. • The first geared were built in in 725. Akai Pro Mpd16 Driver Windows 7 here. 1206) invented the segmental gear as part of a water-lifting device.

• The was invented as part of a roller in the (c. 13th–14th centuries). • The 1386 may be the world's oldest still working geared mechanical clock. Comparison with drive mechanisms [ ] The definite ratio that teeth give gears provides an advantage over other drives (such as drives and ) in precision machines such as watches that depend upon an exact velocity ratio. In cases where driver and follower are proximal, gears also have an advantage over other drives in the reduced number of parts required; the downside is that gears are more expensive to manufacture and their lubrication requirements may impose a higher operating cost per hour.

Types [ ] External vs internal gears [ ]. Spur gear Spur gears or straight-cut gears are the simplest type of gear. They consist of a cylinder or disk with teeth projecting radially. Though the teeth are not straight-sided (but usually of special form to achieve a constant drive ratio, mainly but less commonly ), the edge of each tooth is straight and aligned parallel to the axis of rotation. These gears mesh together correctly only if fitted to parallel shafts. No axial thrust is created by the tooth loads. Spur gears are excellent at moderate speeds but tend to be noisy at high speeds.

Herringbone gears Double helical gears and herringbone gears are similar, but the difference is that herringbone gears do not have a groove in the middle like double helical gears do. Double helical gears overcome the problem of axial thrust presented by single helical gears by using two sets of teeth that are set in a V shape. A double helical gear can be thought of as two mirrored helical gears joined together. This arrangement cancels out the net axial thrust, since each half of the gear thrusts in the opposite direction, resulting in a net axial force of zero.

This arrangement can remove the need for thrust bearings. However, double helical gears are more difficult to manufacture due to their more complicated shape. For both possible rotational directions, there exist two possible arrangements for the oppositely-oriented helical gears or gear faces. One arrangement is stable, and the other is unstable. In a stable orientation, the helical gear faces are oriented so that each axial force is directed toward the center of the gear. In an unstable orientation, both axial forces are directed away from the center of the gear. In both arrangements, the total (or net) axial force on each gear is zero when the gears are aligned correctly.

If the gears become misaligned in the axial direction, the unstable arrangement generates a net force that may lead to disassembly of the gear train, while the stable arrangement generates a net corrective force. If the direction of rotation is reversed, the direction of the axial thrusts is also reversed, so a stable configuration becomes unstable, and conversely. Stable double helical gears can be directly interchanged with spur gears without any need for different bearings. Hypoid gear Hypoid gears resemble spiral bevel gears except the shaft axes do not intersect. The pitch surfaces appear conical but, to compensate for the offset shaft, are in fact of revolution. Hypoid gears are almost always designed to operate with shafts at 90 degrees.

Depending on which side the shaft is offset to, relative to the angling of the teeth, contact between hypoid gear teeth may be even smoother and more gradual than with spiral bevel gear teeth, but also have a sliding action along the meshing teeth as it rotates and therefore usually require some of the most viscous types of gear oil to avoid it being extruded from the mating tooth faces, the oil is normally designated HP (for hypoid) followed by a number denoting the viscosity. Also, the can be designed with fewer teeth than a spiral bevel pinion, with the result that gear ratios of 60:1 and higher are feasible using a single set of hypoid gears. This style of gear is most common in motor vehicle drive trains, in concert with a. Whereas a regular (nonhypoid) ring-and-pinion gear set is suitable for many applications, it is not ideal for vehicle drive trains because it generates more noise and vibration than a hypoid does.

Bringing hypoid gears to market for mass-production applications was an engineering improvement of the 1920s. Main articles: and Worms resemble. A worm is meshed with a worm wheel, which looks similar to a. Worm-and-gear sets are a simple and compact way to achieve a high torque, low speed gear ratio. For example, helical gears are normally limited to gear ratios of less than 10:1 while worm-and-gear sets vary from 10:1 to 500:1. A disadvantage is the potential for considerable sliding action, leading to low efficiency.

A worm gear is a species of helical gear, but its helix angle is usually somewhat large (close to 90 degrees) and its body is usually fairly long in the axial direction. These attributes give it screw like qualities.

The distinction between a worm and a helical gear is that at least one tooth persists for a full rotation around the helix. If this occurs, it is a 'worm'; if not, it is a 'helical gear'. A worm may have as few as one tooth. If that tooth persists for several turns around the helix, the worm appears, superficially, to have more than one tooth, but what one in fact sees is the same tooth reappearing at intervals along the length of the worm. The usual screw nomenclature applies: a one-toothed worm is called single thread or single start; a worm with more than one tooth is called multiple thread or multiple start. The helix angle of a worm is not usually specified.

Instead, the lead angle, which is equal to 90 degrees minus the helix angle, is given. In a worm-and-gear set, the worm can always drive the gear. However, if the gear attempts to drive the worm, it may or may not succeed. Particularly if the lead angle is small, the gear's teeth may simply lock against the worm's teeth, because the force component circumferential to the worm is not sufficient to overcome friction. In traditional music boxes, however, the gear drives the worm, which has a large helix angle. This mesh drives the speed-limiter vanes which are mounted on the worm shaft. Worm-and-gear sets that do lock are called self locking, which can be used to advantage, as for instance when it is desired to set the position of a mechanism by turning the worm and then have the mechanism hold that position.

An example is the found on some types of. If the gear in a worm-and-gear set is an ordinary helical gear only a single point of contact is achieved.

If medium to high power transmission is desired, the tooth shape of the gear is modified to achieve more intimate contact by making both gears partially envelop each other. This is done by making both concave and joining them at a; this is called a cone-drive or 'Double enveloping'. Worm gears can be right or left-handed, following the long-established practice for screw threads.

Main article: A rack is a toothed bar or rod that can be thought of as a sector gear with an infinitely large radius of curvature. Torque can be converted to linear force by meshing a rack with a pinion: the pinion turns; the rack moves in a straight line. Such a mechanism is used in automobiles to convert the rotation of the wheel into the left-to-right motion of the tie rod(s). Racks also feature in the theory of gear geometry, where, for instance, the tooth shape of an interchangeable set of gears may be specified for the rack, (infinite radius), and the tooth shapes for gears of particular actual radii are then derived from that. The rack and pinion gear type is employed in a.

Cage gear in Pantigo Windmill, Long Island (with the driving gearwheel disengaged) A cage gear, also called a lantern gear or lantern pinion has cylindrical rods for teeth, parallel to the axle and arranged in a circle around it, much as the bars on a round bird cage or lantern. The assembly is held together by disks at each end, into which the tooth rods and axle are set.

Cage gears are more efficient than solid pinions, [ ] and dirt can fall through the rods rather than becoming trapped and increasing wear. They can be constructed with very simple tools as the teeth are not formed by cutting or milling, but rather by drilling holes and inserting rods. Sometimes used in clocks, the cage gear should always be driven by a gearwheel, not used as the driver. The cage gear was not initially favoured by conservative clock makers.

It became popular in turret clocks where dirty working conditions were most commonplace. Domestic American clock movements often used them. Main article: All cogs of each gear component of magnetic gears act as a constant magnet with periodic alternation of opposite magnetic poles on mating surfaces. Gear components are mounted with a capability similar to other mechanical gearings. Although they cannot exert as much force as a traditional gear, such gears work without touching and so are immune to wear, have very low noise and can slip without damage making them very reliable. They can be used in configurations that are not possible for gears that must be physically touching and can operate with a non-metallic barrier completely separating the driving force from the load. The can transmit force into a enclosure without using a, which may leak.

Nomenclature [ ]. Long and short addendum teeth Circular thickness Length of arc between the two sides of a gear tooth, on the specified. Transverse circular thickness Circular thickness in the transverse plane. Normal circular thickness Circular thickness in the normal plane. In a helical gear it may be considered as the length of arc along a normal helix.

Axial thickness In helical gears and worms, tooth thickness in an axial cross section at the standard pitch diameter. Base circular thickness In involute teeth, length of arc on the base circle between the two involute curves forming the profile of a tooth. Normal chordal thickness Length of the chord that subtends a circular thickness arc in the plane normal to the pitch helix. Any convenient measuring diameter may be selected, not necessarily the standard pitch diameter. Chordal addendum (chordal height) Height from the top of the tooth to the chord subtending the circular thickness arc. Any convenient measuring diameter may be selected, not necessarily the standard pitch diameter.

Profile shift Displacement of the basic rack from the reference cylinder, made non-dimensional by dividing by the normal module. It is used to specify the tooth thickness, often for zero backlash. Rack shift Displacement of the tool datum line from the reference cylinder, made non-dimensional by dividing by the normal module. It is used to specify the tooth thickness. Measurement over pins Measurement of the distance taken over a pin positioned in a tooth space and a reference surface.

The reference surface may be the reference axis of the gear, a or either one or two pins positioned in the tooth space or spaces opposite the first. This measurement is used to determine tooth thickness. Span measurement Measurement of the distance across several teeth in a normal plane.

As long as the measuring device has parallel measuring surfaces that contact on an unmodified portion of the involute, the measurement wis along a line tangent to the base cylinder. It is used to determine tooth thickness.

Modified addendum teeth Teeth of engaging gears, one or both of which have non-standard addendum. Full-depth teeth Teeth in which the working depth equals 2.000 divided by the normal diametral pitch. Stub teeth Teeth in which the working depth is less than 2.000 divided by the normal diametral pitch.

Equal addendum teeth Teeth in which two engaging gears have equal addendums. Long and short-addendum teeth Teeth in which the addendums of two engaging gears are unequal. Pitch nomenclature [ ]. Main article: is the error in motion that occurs when gears change direction.

It exists because there is always some gap between the trailing face of the driving tooth and the leading face of the tooth behind it on the driven gear, and that gap must be closed before force can be transferred in the new direction. The term 'backlash' can also be used to refer to the size of the gap, not just the phenomenon it causes; thus, one could speak of a pair of gears as having, for example, '0.1 mm of backlash.' A pair of gears could be designed to have zero backlash, but this would presuppose perfection in manufacturing, uniform thermal expansion characteristics throughout the system, and no lubricant. Therefore, gear pairs are designed to have some backlash. It is usually provided by reducing the tooth thickness of each gear by half the desired gap distance.

In the case of a large gear and a small pinion, however, the backlash is usually taken entirely off the gear and the pinion is given full sized teeth. Backlash can also be provided by moving the gears further apart. The backlash of a equals the sum of the backlash of each pair of gears, so in long trains backlash can become a problem. For situations that require precision, such as instrumentation and control, backlash can be minimised through one of several techniques. For instance, the gear can be split along a plane perpendicular to the axis, one half fixed to the shaft in the usual manner, the other half placed alongside it, free to rotate about the shaft, but with springs between the two halves providing relative torque between them, so that one achieves, in effect, a single gear with expanding teeth. Another method involves tapering the teeth in the axial direction and letting the gear slide in the axial direction to take up slack. Shifting of gears [ ] In some machines (e.g., automobiles) it is necessary to alter the gear ratio to suit the task, a process known as gear shifting or changing gear.

There are several ways of shifting gears, for example: • • •, which are actually in combination with a • (also called epicyclic gearing or sun-and-planet gears) There are several outcomes of gear shifting in motor vehicles. In the case of, there are higher emitted when the vehicle is engaged in lower gears. The design life of the lower ratio gears is shorter, so cheaper gears may be used, which tend to generate more noise due to smaller overlap ratio and a lower mesh stiffness etc.

Than the helical gears used for the high ratios. This fact has been used to analyze vehicle-generated sound since the late 1960s, and has been incorporated into the simulation of urban roadway noise and corresponding design of urban along roadways. Tooth profile [ ] •. Undercut A profile is one side of a tooth in a cross section between the outside circle and the root circle. Usually a profile is the curve of intersection of a tooth surface and a plane or surface normal to the pitch surface, such as the transverse, normal, or axial plane. The fillet curve (root fillet) is the concave portion of the tooth profile where it joins the bottom of the tooth space.

As mentioned near the beginning of the article, the attainment of a nonfluctuating velocity ratio is dependent on the profile of the teeth. And wear between two gears is also dependent on the tooth profile. There are a great many tooth profiles that provides a constant velocity ratio.

In many cases, given an arbitrary tooth shape, it is possible to develop a tooth profile for the mating gear that provides a constant velocity ratio. However, two constant velocity tooth profiles are the most commonly used in modern times: the and the.

The cycloid was more common until the late 1800s. Since then, the involute has largely superseded it, particularly in drive train applications. The cycloid is in some ways the more interesting and flexible shape; however the involute has two advantages: it is easier to manufacture, and it permits the center-to-center spacing of the gears to vary over some range without ruining the constancy of the velocity ratio.

Cycloidal gears only work properly if the center spacing is exactly right. Cycloidal gears are still used in mechanical clocks. An is a condition in generated gear teeth when any part of the fillet curve lies inside of a line drawn tangent to the working profile at its point of juncture with the fillet. Undercut may be deliberately introduced to facilitate finishing operations. With undercut the fillet curve intersects the working profile.

Without undercut the fillet curve and the working profile have a common tangent. Gear materials [ ].

Wooden gears of a historic Numerous nonferrous alloys, cast irons, powder-metallurgy and plastics are used in the manufacture of gears. However, steels are most commonly used because of their high strength-to-weight ratio and low cost. Plastic is commonly used where cost or weight is a concern. A properly designed plastic gear can replace steel in many cases because it has many desirable properties, including dirt tolerance, low speed meshing, the ability to 'skip' quite well and the ability to be made with materials that don't need additional lubrication.

Manufacturers have used plastic gears to reduce costs in consumer items including copy machines, optical storage devices, cheap dynamos, consumer audio equipment, servo motors, and printers. Another advantage of the use of plastics, formerly (such as in the 1980s), was the reduction of repair costs for certain expensive machines. In cases of severe jamming (as of the paper in a printer), the plastic gear teeth would be torn free of their substrate, allowing the drive mechanism to then spin freely (instead of damaging itself by straining against the jam). This use of 'sacrificial' gear teeth avoided destroying the much more expensive motor and related parts. This method has been superseded, in more recent designs, by the use of clutches and torque- or current-limited motors.

Standard pitches and the module system [ ] Although gears can be made with any pitch, for convenience and interchangeability standard pitches are frequently used. Pitch is a property associated with linear and so differs whether the standard values are in the (inch) or systems. Using inch measurements, standard diametral pitch values with units of 'per inch' are chosen; the diametral pitch is the number of teeth on a gear of one inch pitch diameter. Common standard values for spur gears are 3, 4, 5, 6, 8, 10, 12, 16, 20, 24, 32, 48, 64, 72, 80, 96, 100, 120, and 200. Certain standard pitches such as 1/10 and 1/20 in inch measurements, which mesh with linear rack, are actually (linear) circular pitch values with units of 'inches' When gear dimensions are in the metric system the pitch specification is generally in terms of module or modulus, which is effectively a length measurement across the pitch diameter. The term module is understood to mean the pitch diameter in millimeters divided by the number of teeth.

When the module is based upon inch measurements, it is known as the English module to avoid confusion with the metric module. Module is a direct dimension, unlike diametral pitch, which is an inverse dimension ('threads per inch'). Thus, if the pitch diameter of a gear is 40 mm and the number of teeth 20, the module is 2, which means that there are 2 mm of pitch diameter for each tooth.

The preferred standard module values are 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1.0, 1.25, 1.5, 2.0, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40 and 50. Manufacture [ ]. A functioning gear mechanism discovered in, a planthopper species common in Europe The gear mechanism was previously considered exclusively artificial, but in 2013, scientists from the announced their discovery that the juvenile form of a common insect (species ), found in many European gardens, has a gear-like mechanism in its hind legs. Each leg has joints that form two 180° helix-shaped strips with 12 fully interlocking spur-type gear teeth, including curves at the base of each tooth to reduce the risk of shearing. The joint rotates like mechanical gears and synchronizes Issus's legs when it jumps. Retrieved 2011-01-10.

The Mechanism is thought to date from between 150 and 100 BC •, p. 462 • Lewis, M. 'Gearing in the Ancient World'. 17 (3): 110–115.. Science and Civilization in China: Volume 4, Part 2, page 298. Taipei: Caves Books, Ltd. •, • ^ (2012),, • ^,, • ^; American National Standards Institute, Gear Nomenclature, Definitions of Terms with Symbols (ANSI/AGMA 1012-G05 ed.), American Gear Manufacturers Association • • Machinery's Handbook. New York: Industrial Press.

S., Theory of Machines, S.CHAND • Schunck, Richard, 'Minimizing gearbox noise inside and outside the box',. •, p. 281 • ^, archived from on 26 June 2009, retrieved 15 June 2009. • Canfield, Stephen (1997), 'Gear Types',, Tennessee Tech University, Department of Mechanical Engineering, ME 362 lecture notes, archived from on 29 August 2008. •; (1952), Geometry and the Imagination (2nd ed.), New York: Chelsea, p. 287,. •, pp. 280, 296. •, p. 744 • Kravchenko A.I., Bovda A.M.

Gear with magnetic couple. Of Ukraine N. 2, 2011 – F16H 49/00. • ISO/DIS: 'Gears – Cylindrical Involute Gears and Gear Pairs – Concepts and Geometry', International Organization for Standardization, (2007) • Gunnar Dahlvig, 'Construction elements and machine construction', Konstruktionselement och maskinbyggnad (in Swedish), 7, • Hogan, C. Michael; Latshaw, Gary L.

(21–23 May 1973).. Proceedings of the ASCE, Urban Transportation Division Specialty Conference.

Chicago, Illinois: American Society of Civil Engineers, Urban Transportation Division. • Smith, Zan (2000), 'Plastic gears are more reliable when engineers account for material properties and manufacturing processes during design.' • Oberg, E.; Jones, F. D.; Horton, H. L.; Ryffell, H.

(2000), Machinery's Handbook (26th ed.), Industrial Press, p. 2649,. • Fred Eberle (August 2014).. Gear Solutions: 22. Mehata, Machine Tool Design and Numerical control, Tata McGraw-Hill Publishing Company Limited,, 1996. Machine Design.

• Siegel, Daniel M. Innovation in Maxwell's Electromagnetic Theory: Molecular Vortices, Displacement Current, and Light. Linguatec Personal Translator 2008 Proline. University of Chicago Press.. • MacKinnon, Angus (2002). 'Quantum Gears: A Simple Mechanical System in the Quantum Regime'. 13 (5): 678.:... 14 (2): 113–125..

• Robertson, Adi (September 12, 2013)... Retrieved September 14, 2013. •, Cambridge University, 2013. Bibliography • (2007), (10th ed.), McGraw-Hill Professional,.

• Norton, Robert L. (2004), (3rd ed.), McGraw-Hill Professional,. • Vallance, Alex; Doughtie, Venton Levy (1964), Design of machine members (4th ed.), McGraw-Hill. • Industrial Press (2012), Machinery's Handbook (29th ed.), Further reading [ ] •; American National Standards Institute (2005), Gear Nomenclature: Definitions of Terms with Symbols (ANSI/AGMA 1012-F90 ed.), American Gear Manufacturers Association,. • Buckingham, Earle (1949), Analytical Mechanics of Gears, McGraw-Hill Book Co. • Coy, John J.; Townsend, Dennis P.; Zaretsky, Erwin V.

(1985), (PDF), Scientific and Technical Information Branch, NASA-RP-1152; AVSCOM Technical Report 84-C-15. • Kravchenko A.I., Bovda A.M. Gear with magnetic couple. Of Ukraine N. 2, 2011 – F16H 49/00. • Sclater, Neil. 'Gears: devices, drives and mechanisms.'

Mechanisms and Mechanical Devices Sourcebook. New York: McGraw Hill.

Drawings and designs of various gearings. External links [ ] Wikimedia Commons has media related to. • A place of antique and vintage gears, sprockets, ratchets and other gear-related objects. • Movies and photos of hundreds of working models at Cornell University • • • PDF of gear types and geometries • • • • • • Popular Science, February 1945, pp. 120–125.