Introduction to Gears Engineering Dynamics Lab

Prepared by:

Muhammad Idrees (130501016)

Faraz Khan (130501009)

Tayyab Safwan (130501048)

Junaid Mukhtar (120501026)

Asif Ali (130501043)

Aamir Rafiq (130501037)

Muhammad Ali Zia (130501038)

1 | P a g e

Contents 1.1. Introduction to Gears ...................................................................................................................... 6

1.1.1. Comparison with Drive Mechanism ........................................................................................ 6

1.2. Types of Gears................................................................................................................................. 6

1.2.1. External vs. Internal Gears ...................................................................................................... 6

1.2.2. Spur Gear ................................................................................................................................ 7

1.2.3. Helical Gear ............................................................................................................................. 7

1.2.4. Skew Gear ............................................................................................................................... 8

1.2.5. Double Helical ......................................................................................................................... 9

1.2.6. Bevel Gear ............................................................................................................................. 10

1.2.7. Spiral Bevels .......................................................................................................................... 10

1.2.8. Hypoid Gear .......................................................................................................................... 11

1.2.9. Crown Gear ........................................................................................................................... 11

1.2.10. Worm Gear............................................................................................................................ 12

1.2.11. Non-Circular Gear ................................................................................................................. 13

1.2.12. Rack and pinion ..................................................................................................................... 14

1.2.13. Epicyclic Gears....................................................................................................................... 14

1.2.14. Sun and Planet ...................................................................................................................... 14

1.2.15. Harmonic Gear ...................................................................................................................... 15

1.2.16. Cage Gear .............................................................................................................................. 15

1.2.17. Magnetic Gear....................................................................................................................... 16

1.3. General Nomenclature ................................................................................................................. 17

.............................................................................................................................................................. 17

1.Rotational Frequency ......................................................................................................................... 17

2.Angular frequency ............................................................................................................................. 17

3.Number of Teeth, ............................................................................................................................... 17

4. Gear, wheel ....................................................................................................................................... 17

5. Pinion ................................................................................................................................................ 18

6. Path of contact .................................................................................................................................. 18

7. Line of Action, Pressure Line ............................................................................................................. 18

2 | P a g e

8. Axis .................................................................................................................................................... 18

9. Pitch point ......................................................................................................................................... 18

10. Pitch Circle, Pitch Line ..................................................................................................................... 18

11. Pitch diameter ................................................................................................................................. 18

12. Module ............................................................................................................................................ 18

13. Operating Pitch Diameters .............................................................................................................. 19

14. Pitch Surface ................................................................................................................................... 19

15. Angle of Action ................................................................................................................................ 19

16. Arc of Action ................................................................................................................................... 19

17. Pressure Angle ................................................................................................................................ 19

18. Outside Diameter ............................................................................................................................ 19

19. Root Diameter ................................................................................................................................. 20

20. Addendum ...................................................................................................................................... 20

21. Dedendum ...................................................................................................................................... 20

22. Whole Depth ................................................................................................................................... 20

23. Clearance ........................................................................................................................................ 20

24. Working Depth ................................................................................................................................ 20

28. Base Pitch, Normal Pitch ................................................................................................................ 20

29. Interference .................................................................................................................................... 20

30. Interchangeable Set ........................................................................................................................ 20

1.4. Helical Gear Nomenclature ........................................................................................................... 21

1. Helix Angle ........................................................................................................................................ 21

2. Normal Circular Pitch ........................................................................................................................ 21

3. Transverse Circular Pitch .................................................................................................................. 21

1.5. Worm Gear Nomenclature ........................................................................................................... 21

1. Lead ................................................................................................................................................... 21

2. Linear pitch ....................................................................................................................................... 21

3. Lead angle ......................................................................................................................................... 21

4. Pitch diameter ................................................................................................................................... 21

5. Point of contact ................................................................................................................................. 21

6. Line of Contact .................................................................................................................................. 22

7. Path of action .................................................................................................................................... 22

3 | P a g e

8. Line of action ..................................................................................................................................... 22

9. Surface of action ............................................................................................................................... 22

10. Plane of action ................................................................................................................................ 22

11. Zone of action (contact zone) ......................................................................................................... 22

12. Path of Contact ............................................................................................................................... 22

13. Length of Action .............................................................................................................................. 23

14. Arc of action .................................................................................................................................... 23

15. Arc of Approach .............................................................................................................................. 23

16. Arc of recess .................................................................................................................................... 23

17. Contact Ratio, Mc ........................................................................................................................... 23

18. Transverse Contact Ratio ................................................................................................................ 23

19. Face Contact Ratio .......................................................................................................................... 23

20. Total Contact Ratio ......................................................................................................................... 23

21. Modified Contact Ratio, Mo ........................................................................................................... 23

22. Limit diameter ................................................................................................................................. 24

23. Start of Active Profile (SAP) ............................................................................................................ 24

24. Face Advance .................................................................................................................................. 24

25. Circular Thickness ........................................................................................................................... 24

26. Transverse Circular Thickness ......................................................................................................... 24

27. Normal circular thickness ............................................................................................................... 24

28. Axial Thickness ................................................................................................................................ 25

29. Base Circular Thickness ................................................................................................................... 25

30. Normal Chordal Thickness .............................................................................................................. 25

31. Profile Shift...................................................................................................................................... 25

32. Rack Shift......................................................................................................................................... 25

33. Measurement over Pins ................................................................................................................. 25

34. Span Measurement ......................................................................................................................... 25

35. Modified Addendum Teeth ............................................................................................................. 25

36. Full-Depth Teeth ............................................................................................................................. 26

37. Stub Teeth ....................................................................................................................................... 26

38. Equal Addendum Teeth .................................................................................................................. 26

39. Long and Short-Addendum Teeth ................................................................................................... 26

4 | P a g e

1.6. Pitch Nomenclature ...................................................................................................................... 26

1. Circular Pitch ..................................................................................................................................... 26

2. Transverse Circular Pitch .................................................................................................................. 26

3. Normal Circular Pitch ........................................................................................................................ 26

4. Normal Base Pitch ............................................................................................................................. 27

5. Transverse Base Pitch ....................................................................................................................... 27

6. Diametral Pitch (Transverse)............................................................................................................. 27

7. Normal Diametral Pitch .................................................................................................................... 27

8. Angular Pitch ..................................................................................................................................... 27

1.7. Advantages and Disadvantages of Different Types of Gears ........................................................ 27

1.7.1. Spur Gear .............................................................................................................................. 27

Advantages........................................................................................................................................ 27

Disadvantages ................................................................................................................................... 27

1.7.2. Helical Gear ........................................................................................................................... 28

Advantages........................................................................................................................................ 28

Disadvantages ................................................................................................................................... 28

1.8. Bevel Gear ..................................................................................................................................... 28

Advantages........................................................................................................................................ 28

Disadvantages ................................................................................................................................... 28

1.9. Worm Wheel ................................................................................................................................. 29

Advantages........................................................................................................................................ 29

Disadvantages ................................................................................................................................... 29

1.10. Rack and Pinion ......................................................................................................................... 29

Advantages........................................................................................................................................ 29

Disadvantages ................................................................................................................................... 29

1.11. Backlash .................................................................................................................................... 30

1.12. Design Considerations Related to Gears ................................................................................... 31

Selection of Materials ....................................................................................................................... 31

Gear wheel proportions .................................................................................................................... 32

1.12.1. AGMA Standard of Gear Design ............................................................................................ 33

Design Inputs and Outputs in Gear Design ....................................................................................... 33

Design for space constrains .............................................................................................................. 34

5 | P a g e

Determination of Number of Teeth - Interference ........................................................................... 35

Design for Mechanical Strength - Lewis Equation ............................................................................ 36

A More Realistic Approach - AGMA Strength Equation .................................................................... 37

Design for surface resistance ............................................................................................................ 38

1.13. Gear Train & Types of Gear Train ............................................................................................. 38

Simple Gear Train .............................................................................................................................. 39

Compound Gear Train ....................................................................................................................... 39

Reverted Gear Train: ......................................................................................................................... 40

6 | P a g e

1.1. Introduction to Gears A gear or cogwheel is a rotating machine part having cut teeth, or cogs, which mesh with

another toothed part in order to transmit torque, in most cases with teeth on the one gear

being of identical shape, and often also with that shape on the other gear. Two or more gears

working in tandem are called a transmission and can produce a mechanical advantage through

a gear ratio and thus may be considered a simple machine. Geared devices can change the

speed, torque, and direction of a power source. The most common situation is for a gear to

mesh with another gear; however, a gear can also mesh with a non-rotating toothed part,

called a rack, thereby producing translation instead of rotation.

Gears in a transmission are analogous to the

wheels in a crossed belt pulley system. An advantage of gears is that the teeth of a gear

prevent slippage. When two gears mesh, and one gear is bigger than the other (even though

the size of the teeth must match), a mechanical advantage is produced, with the rotational

speeds and the torques of the two gears differing in an inverse relationship.

In transmissions which offer 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 is

used to describe similar devices even when the gear ratio is continuous rather than discrete,

or when the device does not actually contain any gears, as in a continuously variable

transmission.

1.1.1. Comparison with Drive Mechanism

The definite velocity ratio which results from

having teeth gives gears an advantage over other drives (such as traction drives and V-belts 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.

1.2. Types of Gears

1.2.1. External vs. Internal Gears

An external gear is one with the teeth formed on the

outer surface of a cylinder or cone. Conversely, an internal gear is one with the teeth formed

on the inner surface of a cylinder or cone. For bevel gears, an internal gear is one with the

pitch angle exceeding 90 degrees. Internal gears do not cause output shaft direction reversal.

7 | P a g e

Figure 1 Internal Gear

1.2.2. Spur Gear

Spur gears or straight-cut gears are the simplest type of gear. They consist

of a cylinder or disk with the teeth projecting radially, and although they are not straight-sided

in form (they are usually of special form to achieve constant drive ratio, mainly involute), the

edge of each tooth is straight and aligned parallel to the axis of rotation. These gears can be

meshed together correctly only if they are fitted to parallel shafts.

Figure. 2 Spur

1.2.3. Helical Gear

Helical or "dry fixed" gears offer a refinement over spur gears. The

leading edges of the teeth are not parallel to the axis of rotation, but are set at an angle. Since

the gear is curved, this angling causes the tooth shape to be a segment of a helix. Helical gears

can be meshed in parallel or crossed orientations. The former refers to when the shafts are

parallel to each other; this is the most common orientation. In the latter, the shafts are non-

parallel, and in this configuration the gears are sometimes known as "skew gears".

8 | P a g e

The angled teeth engage more gradually than do spur gear teeth, causing them to run more

smoothly and quietly. With parallel helical gears, each pair of teeth first make contact at a

single point at one side of the gear wheel; a moving curve of contact then grows gradually

across the tooth face to a maximum then recedes until the teeth break contact at a single

point on the opposite side. In skew gears, teeth suddenly meet at a line contact across their

entire width causing stress and noise. Skew gears make a characteristic whine at high speeds.

Whereas spur gears are used for low speed applications and those situations where noise

control is not a problem, the use of helical gears is indicated when the application involves

high speeds, large power transmission, or where noise abatement is important. The speed is

considered to be high when the pitch line velocity exceeds 25 m/s.

A disadvantage of helical gears is a resultant thrust along the axis of the gear, which needs to

be accommodated by appropriate thrust bearings, and a greater degree of sliding friction

between the meshing teeth, often addressed with additives in the lubricant.

Figure 3 Helical gear

1.2.4. Skew Gear

For a 'crossed' or 'skew' configuration, the gears must have the same

pressure angle and normal pitch; however, the helix angle and handedness can be different.

The relationship between the two shafts is actually defined by the helix angle(s) of the two

shafts and the handedness, as defined

1. for gears of the same handedness

2. for gears of opposite handedness

Where is the helix angle for the gear? The crossed configuration is less mechanically sound

because there is only a point contact between the gears, whereas in the parallel configuration

there is a line contact. Quite commonly, helical gears are used with the helix angle of one

9 | P a g e

having the negative of the helix angle of the other; such a pair might also be referred to as

having a right-handed helix and a left-handed helix of equal angles. The two equal but

opposite angles add to zero: the angle between shafts is zero that is, the shafts are parallel.

Where the sum or the difference (as described in the equations above) is not zero the shafts

are crossed. For shafts crossed at right angles, the helix angles are of the same hand because

they must add to 90 degrees.

1.2.5. Double Helical

Double helical gears or herringbone gears overcome the problem of axial thrust presented by

"single" helical gears, by having 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 will generate 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 vice versa.

Stable double helical gears can be directly interchanged with spur gears without any need for

different bearings.

Figure 4 Double Helical Gear

10 | P a g e

1.2.6. Bevel Gear

A bevel gear is shaped like a right circular cone with most of its tip cut off. When two bevel

gears mesh, their imaginary vertices must occupy the same point. Their shaft axes also

intersect at this point, forming an arbitrary non-straight angle between the shafts. The angle

between the shafts can be anything except zero or 180 degrees. Bevel gears with equal

numbers of teeth and shaft axes at 90 degrees are called MITRE gears.

Figure 5 Bevel gear

1.2.7. Spiral Bevels

Spiral bevel gears can be manufactured as Gleason types (circular arc with non-constant tooth

depth), Oerlikon and Cur vex types (circular arc with constant tooth depth), Klingelnberg

Cyclo-Palloid (Epicycloide with constant tooth depth) or Klingelnberg Palloid. Spiral bevel gears

have the same advantages and disadvantages relative to their straight-cut cousins as helical

gears do to spur gears. Straight bevel gears are generally used only at speeds below 5 m/s

(1000 ft/min), or, for small gears, 1000 r.p.m.. The cylindrical gear tooth profile corresponds to

an involute, but the bevel gear tooth profile to an octoid. All traditional bevel gear generators

(like Gleason, Klingelnberg, Heidenreich & Harbeck, WMW Modul) manufactures bevel gears

with an octoidal tooth profile. IMPORTANT: For 5-axis milled bevel gear sets it is important to

choose the same calculation / layout like the conventional manufacturing method. Simplified

calculated bevel gears on the basis of an equivalent cylindrical gear in normal section with an

involute tooth form show a deviant tooth form with reduced tooth strength by 10-28%

without offset and 45% with offset [Diss. Hnecke, TU Dresden]. Furthermore those "involute

bevel gear sets" causes more noise.

11 | P a g e

Figure 6 Spiral Bevel Gears

1.2.8. 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 hyperboloids 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 pinion 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 commonly found driving mechanical differentials;

which are normally straight cut bevel gears; in motor vehicle axles.

Figure 7 Hypoid gear

1.2.9. Crown Gear

Crown gears or contrite gears are a particular form of bevel gear whose teeth project at right

angles to the plane of the wheel; in their orientation the teeth resemble the points on a

crown. A crown gear can only mesh accurately with another bevel gear, although crown gears

are sometimes seen meshing with spur gears. A crown gear is also sometimes meshed with an

escapement such as found in mechanical clocks.

12 | P a g e

Figure 8 Crown Gear

1.2.10. Worm Gear

Worm gears resemble screws. A worm gear is usually meshed with a spur gear or a helical

gear, which is called the gear, wheel, or worm wheel. 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.

Worm gears can be considered 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; and it is

these attributes which give it screw like qualities. The distinction between a worm and a

helical gear is made when 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 will appear, 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 threads

or multiple starts. 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. (The Sunbeam S7 motorcycle had shaft drive, but instead of using a bevel gear in the

rear wheel, the company unwisely specified worm gearing, which proved unreliable and prone

to wear).

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 machine head found on some

types of stringed instruments.

13 | P a g e

If the gear in a worm-and-gear set is an ordinary helical gear only a single point of contact will

be 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 saddle point; this is called a cone-

drive. Double enveloping Worm gears can be right or left-handed, following the long-

established practice for screw threads.

1.2.11. Non-Circular Gear

Non-circular gears are designed for special purposes. While a regular gear is optimized to

transmit torque to another engaged member with minimum noise and wear and maximum

efficiency, a non-circular gear's main objective might be ratio variations, axle displacement

oscillations and more. Common applications include textile machines, potentiometers and

continuously variable transmissions.

Figure 10 Circular Gear

Figure 9 Worm gear

14 | P a g e

1.2.12. Rack and pinion

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 steering 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 rack railway.

Figure 11 Rack and Pinion Gear

1.2.13. Epicyclic Gears

In epicycle gearing one or more of the gear axes moves. Examples are sun and planet gearing

(see below) and mechanical differentials.

Figure 12 Epicyclic Gear

1.2.14. Sun and Planet

Sun and planet gearing was a method of converting reciprocating motion into rotary motion in

steam engines. It was famously used by James Watt on his early steam engines in order to get

around the patent on the crank but also had the advantage of increasing the flywheel speed

so that a lighter flywheel could be used.In the illustration, the sun is yellow, the planet red, the

reciprocating arm is blue, the flywheel is green and the driveshaft is grey.

15 | P a g e

Figure 13

1.2.15. Harmonic Gear

A harmonic gear is a specialized gearing mechanism often used in industrial motion control,

robotics and aerospace for its advantages over traditional gearing systems, including lack of

backlash, compactness and high gear ratios.

Figure 14

1.2.16. Cage Gear

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 either 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.

16 | P a g e

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 favored by conservative clock makers. It became

popular in turret clocks where dirty working conditions were most commonplace. Domestic

American clock movements often used them.

Figure 15

1.2.17. Magnetic Gear

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 backlash 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 magnetic coupling can transmit force into a hermetically sealed enclosure without the use

of a radial shaft seal which may leak.

Figure 16

17 | P a g e

1.3. General Nomenclature

Figure 17

1.Rotational Frequency

Measured in rotation over time, such as RPM.

2.Angular frequency

Measured in radians/second. rad/second

3.Number of Teeth,

How many teeth a gear has, an integer. In the case of worms, it is the number of thread starts

that the worm has.

4. Gear, wheel

The larger of two interacting gears or a gear on its own.

18 | P a g e

5. Pinion

The smaller of two interacting gears.

6. Path of contact

Path followed by the point of contact between two meshing gear teeth.

7. Line of Action, Pressure Line

Line along which the force between two meshing gear teeth is directed. It has the same

direction as the force vector. In general, the line of action changes from moment to moment

during the period of engagement of a pair of teeth. For involute gears, however, the tooth-to-

tooth force is always directed along the same linethat is, the line of action is constant. This

implies that for involute gears the path of contact is also a straight line, coincident with the

line of actionas is indeed the case.

8. Axis

Axis of revolution of the gear; center line of the shaft.

9. Pitch point

Point where the line of action crosses a line joining the two gear axes.

10. Pitch Circle, Pitch Line

Circle centered on and perpendicular to the axis, and passing through the pitch point. A

predefined diametral position on the gear where the circular tooth thickness, pressure angle

and helix angles are defined.

11. Pitch diameter

A predefined diametral position on the gear where the circular tooth thickness, pressure angle

and helix angles are defined. The standard pitch diameter is a basic dimension and cannot be

measured, but is a location where other measurements are made. Its value is based on the

number of teeth, the normal module (or normal diametral pitch), and the helix angle. It is

calculated as: in metric units or in imperial units.

12. Module

Since it is unpractical to calculate with Irrational numbers, mechanical engineers usually use a

scaling factor that replaces the circular pitch, p, with a regular value instead. This is known as

the module of the wheels and is simply defined as where m is the module and p the circular

pitch. The distance between the two axis becomes

19 | P a g e

where a is the axis distance, z1 and z2 are the number of cogs (teeth) for each of the two

wheels (gears). These numbers (or at least one of them) is often chosen among primes in

order to make an even contact between every cog of both wheels, and thereby avoid

unnecessary wear and damage. An even uniform gear wear is achieved by ensuring the tooth

counts of the two gears meshing together are Relatively Prime to each other; this occurs when

the Greatest Common Divisor (GCD) of each gear tooth count equals 1, e.g. GCD(16,25)=1; If a

1:1 gear ratio is desired a relatively prime gear may be inserted in between the two gears; this

maintains the 1:1 ratio but reverses the gear direction; a second relatively prime gear could

also be inserted to restore the original rotational direction while maintaining uniform wear

with all 4 gears in this case. Mechanic engineers at least in continental Europe use the module

instead of circular pitch. The module, just like the circular pitch, can be used for all types of

cogs, not just evolving based straight cogs.

13. Operating Pitch Diameters

Diameters determined from the number of teeth and the center distance at which gears

operate. Example for pinion:

14. Pitch Surface

In cylindrical gears, cylinder formed by projecting a pitch circle in the

axial direction. More generally, the surface formed by the sum of all the

pitch circles as one moves along the axis. For bevel gears it is a cone.

15. Angle of Action

Angle with vertex at the gear center, one leg on the point where mating

teeth first make contact, the other leg on the point where they

disengage.

16. Arc of Action

Segment of a pitch circle subtended by the angle of action.

17. Pressure Angle

The complement of the angle between the direction that the teeth exert force on each other,

and the line joining the centers of the two gears. For involute gears, the teeth always exert

force along the line of action, which, for involute gears, is a straight line; and thus, for involute

gears, the pressure angle is constant.

18. Outside Diameter

Diameter of the gear, measured from the tops of the teeth.

Figure 18

20 | P a g e

19. Root Diameter

Diameter of the gear, measured at the base of the tooth.

20. Addendum

Radial distance from the pitch surface to the outermost point of the tooth.

21. Dedendum

Radial distance from the depth of the tooth trough to the pitch surface.

22. Whole Depth

The distance from the top of the tooth to the root; it is equal to addendum plus dedendum or

to working depth plus clearance.

23. Clearance

Distance between the root circle of a gear and the dedendum circle of its mate.

24. Working Depth

Depth of engagement of two gears, that is, the sum of their operating addendums.

25. Circular Pitch

Distance from one face of a tooth to the corresponding face of an adjacent tooth on the same

gear, measured along the pitch circle.

26. Diametral Pitch

Ratio of the number of teeth to the pitch diameter. Could be measured in teeth per inch or

teeth per centimeter.

27. Base Circle

In involute gears, where the tooth profile is the involute of the base circle. The radius of the

base circle is somewhat smaller than that of the pitch circle.

28. Base Pitch, Normal Pitch

In involute gears, distance from one face of a tooth to the corresponding face of an adjacent

tooth on the same gear, measured along the base circle.

29. Interference

Contact between teeth other than at the intended parts of their surfaces.

30. Interchangeable Set

A set of gears, any of which will mate properly with any other.

21 | P a g e

1.4. Helical Gear Nomenclature

1. Helix Angle

Angle between a tangent to the helix and the gear axis. It is zero in the limiting case of a spur

gear, albeit it can considered as the hypotenuse angle as well.

2. Normal Circular Pitch

Circular pitch in the plane normal to the teeth.

3. Transverse Circular Pitch

Circular pitch in the plane of rotation of the gear. Sometimes just called "circular pitch".

Several other helix parameters can be viewed either in the normal or transverse planes. The

subscript n usually indicates the normal.

1.5. Worm Gear Nomenclature

1. Lead

Distance from any point on a thread to the corresponding point on the next turn of the same

thread, measured parallel to the axis.

2. Linear pitch

Distance from any point on a thread to the corresponding point on the adjacent thread,

measured parallel to the axis. For a single-thread worm, lead and linear pitch are the same.

3. Lead angle

Angle between a tangent to the helix and a plane perpendicular to the axis. Note that it is the

complement of the helix angle which is usually given for helical gears.

4. Pitch diameter

Same as described earlier in this list. Note that for a worm it is still measured in a plane

perpendicular to the gear axis, not a tilted plane.subscript w denotes the worm, subscript g

denotes the gear.

5. Point of contact

Any point at which two tooth profiles touch each other.

22 | P a g e

6. Line of Contact

A line or curve along which two tooth surfaces are tangent to each other.

7. Path of action

The locus of successive contact points between a pair of gear teeth, during the phase of

engagement. For conjugate gear teeth, the path of action passes through the pitch point. It is

the trace of the surface of action in the plane of rotation.

8. Line of action

The path of action for involute gears. It is the straight line passing through the pitch point and

tangent to both base circles.

9. Surface of action

The imaginary surface in which contact occurs between two engaging tooth surfaces. It is the

summation of the paths of action in all sections of the engaging teeth.

10. Plane of action

The surface of action for involute, parallel axis gears with either spur or helical teeth. It is

tangent to the base cylinders.

11. Zone of action (contact zone)

For involute, parallel-axis gears with either spur or helical teeth, is the rectangular area in the

plane of action bounded by the length of action and the effective face width.

Figure 19

12. Path of Contact

The curve on either tooth surface along which theoretical single point contact occurs during

the engagement of gears with crowned tooth surfaces or gears that normally engage with only

single point contact.

23 | P a g e

13. Length of Action

The distance on the line of action through which the point of contact moves during the action

of the tooth profile.

14. Arc of action

The arc of the pitch circle through which a tooth profile moves from the beginning to the end

of contact with a mating profile.

15. Arc of Approach

The arc of the pitch circle through which a tooth profile moves from its beginning of contact

until the point of contact arrives at the pitch point.

16. Arc of recess

The arc of the pitch circle through which a tooth profile moves from contact at the pitch point

until contact ends.

17. Contact Ratio, Mc

The number of angular pitches through which a tooth surface rotates from the beginning to

the end of contact. In a simple way, it can be defined as a measure of the average number of

teeth in contact during the period in which a tooth comes and goes out of contact with the

mating gear.

18. Transverse Contact Ratio

The contact ratio in a transverse plane. It is the ratio of the angle of action to the angular

pitch. For involute gears it is most directly obtained as the ratio of the length of action to the

base pitch.

19. Face Contact Ratio

The contact ratio in an axial plane, or the ratio of the face width to the axial pitch. For bevel

and hypoid gears it is the ratio of face advance to circular pitch.

20. Total Contact Ratio

The sum of the transverse contact ratio and the face contact ratio.

21. Modified Contact Ratio, Mo

For bevel gears, the square root of the sum of the squares of the transverse and face contact

ratios.

24 | P a g e

22. Limit diameter

Diameter on a gear at which the line of action intersects the maximum (or minimum for

internal pinion) addendum circle of the mating gear. This is also referred to as the start of

active profile, the start of contact, the end of contact, or the end of active profile.

23. Start of Active Profile (SAP)

Intersection of the limit diameter and the involute profile.

24. Face Advance

Distance on a pitch circle through which a helical or spiral tooth moves from the position at

which contact begins at one end of the tooth trace on the pitch surface to the position where

contact ceases at the other end.

Figure 20

25. Circular Thickness

Length of arc between the two sides of a gear tooth, on the specified datum circle.

26. Transverse Circular Thickness

Circular thickness in the transverse plane.

27. 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.

25 | P a g e

28. Axial Thickness

In helical gears and worms, tooth thickness in an axial cross section at the standard pitch

diameter.

29. Base Circular Thickness

In involute teeth, length of arc on the base circle between the two involute curves forming the

profile of a tooth.

30. 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.

31. Profile Shift

Displacement of the basic rack datum line 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.

32. 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.

33. 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 datum surface or

either one or two pins positioned in the tooth space or spaces opposite the first. This

measurement is used to determine tooth thickness.

34. 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 will be along a line tangent to the base cylinder. It is used to determine

tooth thickness.

35. Modified Addendum Teeth

Teeth of engaging gears, one or both of which have non-standard addendum.

26 | P a g e

36. Full-Depth Teeth

Teeth in which the working depth equals 2.000 divided by the normal diametral pitch.

37. Stub Teeth

Teeth in which the working depth is less than 2.000 divided by the normal diametral pitch.

38. Equal Addendum Teeth

Teeth in which two engaging gears have equal addendums.

39. Long and Short-Addendum Teeth

Teeth in which the addendums of two engaging gears are unequal.

1.6. Pitch Nomenclature Pitch is the distance between a point on one tooth and the

corresponding point on an adjacent tooth. It is a dimension

measured along a line or curve in the transverse, normal, or

axial directions. The use of the single word pitch without

qualification may be ambiguous, and for this reason it is

preferable to use specific designations such as transverse

circular pitch, normal base pitch, axial pitch.

1. Circular Pitch

Arc distance along a specified pitch circle or pitch line between corresponding profiles of

adjacent teeth.

2. Transverse Circular Pitch

Circular pitch in the transverse plane.

3. Normal Circular Pitch

Circular pitch in the normal plane, and also the length of the arc along the normal pitch helix

between helical teeth or threads.Axial pitch, Linear pitch in an axial plane and in a pitch

surface. In helical gears and worms, axial pitch has the same value at all diameters. In gearing

of other types, axial pitch may be confined to the pitch surface and may be a circular

measurement. The term axial pitch is preferred to the term linear pitch. The axial pitch of a

helical worm and the circular pitch of its worm gear are the same.

Figure 21

27 | P a g e

4. Normal Base Pitch

An involute helical gear is the base pitch in the normal plane. It is the normal distance

between parallel helical involute surfaces on the plane of action in the normal plane, or is the

length of arc on the normal base helix. It is a constant distance in any helical involute gear.

5. Transverse Base Pitch

In an involute gear, the pitch on the base circle or along the line of action. Corresponding sides

of involute gear teeth are parallel curves, and the base pitch is the constant and fundamental

distance between them along a common normal in a transverse plane.

6. Diametral Pitch (Transverse)

Ratio of the number of teeth to the standard pitch diameter in inches.

7. Normal Diametral Pitch

Value of diametral pitch in a normal plane of a helical gear or worm.

8. Angular Pitch

Angle subtended by the circular pitch, usually expressed in radians.

degrees or radians

1.7. Advantages and Disadvantages of Different Types of Gears

1.7.1. Spur Gear

Advantages

They offer constant velocity ratio

Spur gears are highly reliable

Spur gears are simplest, hence easiest to design and manufacture

A spur gear is more efficient if you compare it with helical gear of same size

Spur gear teeth are parallel to its axis. Hence, spur gear train does not produce axial

thrust. So the gear shafts can be mounted easily using ball bearings.

They can be used to transmit large amount of power (of the order of 50,000 kW)

Disadvantages

Spur gear are slow-speed gears

Gear teeth experience a large amount of stress

They cannot transfer power between non-parallel shafts

28 | P a g e

They cannot be used for long distance power transmission.

Spur gears produce a lot of noise when operating at high speeds.

when compared with other types of gears, they are not as strong as them

1.7.2. Helical Gear

Advantages

The angled teeth engage more gradually than do spur gear teeth causing them to run

more smoothly and quietly

Helical gears are highly durable and are ideal for high load applications.

At any given time their load is distributed over several teeth, resulting in less wear

Can transmit motion and power between either parallel or right angle shafts

Disadvantages

An obvious disadvantage of the helical gears is a resultant thrust along the axis of the

gear, which needs to be accommodated by appropriate thrust bearings, and a greater

degree of sliding friction between the meshing teeth, often addressed with additives in

the lubricant. Thus we can say that helical gears cause losses due to the unique

geometry along the axis of the helical gears shaft.

Efficiency of helical gear is less because helical gear trains have sliding contacts

between the teeth which in turns produce axial thrust of gear shafts and generate

more heat. So, more power loss and less efficiency

1.8. Bevel Gear

Advantages

This gear makes it possible to change the operating angle.

Differing of the number of teeth (effectively diameter) on each wheel

allows mechanical advantage to be changed. By increasing or decreasing the ratio of

teeth between the drive and driven wheels one may change the ratio of rotations

between the two, meaning that the rotational drive and torque of the second wheel

can be changed in relation to the first, with speed increasing and torque decreasing, or

speed decreasing and torque increasing.

Disadvantages

One wheel of such gear is designed to work with its complementary wheel and no

other.

Must be precisely mounted.

The shafts' bearings must be capable of supporting significant forces.

29 | P a g e

1.9. Worm Wheel

Advantages

Worm gear drives operate silently and smoothly.

They are self-locking.

They occupy less space.

They have good meshing effectiveness.

They can be used for reducing speed and increasing torque.

High velocity ratio of the order of 100 can be obtained in a single step

Disadvantages

Worm gear materials are expensive.

Worm drives have high power losses

A disadvantage is the potential for considerable sliding action, leading to low efficiency

They produce a lot of heat.

1.10. Rack and Pinion

Advantages

Cheap

Compact

Robust

Easiest way to convert rotation motion into linear motion

Rack and pinion gives easier and more compact control over the vehicle

Disadvantages

Since being the most ancient, the wheel is also the most convenient and somewhat

more extensive in terms of energy too. Due to the apparent friction, you would already

have guessed just how much of the power being input gives in terms of output, a lot of

the force applied to the mechanism is burned up in overcoming friction, to be more

precise somewhat around 80% of the overall force is burned to overcome one.

The rack and pinion can only work with certain levels of friction. Too high a friction and

the mechanism will be subject to wear more than usual and will require more force to

operate.

The most adverse disadvantage of rack and pinion would also be due to the inherent

friction, the same force that actually makes things work in the mechanism. Due to the

friction, it is under a constant wear, possibly needing replacement after a certain time

30 | P a g e

1.11. Backlash Backlash 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 gear train equals the sum of

the backlash of each pair of gears, so in long trains backlash can become a problem.

Figure 22

For situations in which precision is important, such as instrumentation and control, backlash

can be minimized 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 providing for the

gear to be slid in the axial direction to take up slack.

Shifting of gears

31 | P a g e

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:

1. Manual transmission

2. Automatic transmission

Derailleur gears which are actually sprockets in combination with a roller chain

Hub gears (also called epicycle gearing or sun-and-planet gears)

There are several outcomes of gear shifting in motor vehicles. In the case of vehicle noise

emissions, there are higher sound levels 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 utilized in analyzing vehicle generated

sound since the late 1960s, and has been incorporated into the simulation of urban roadway

noise and corresponding design of urban noise barriers along roadways.

1.12. Design Considerations Related to Gears

The accuracy of the output of a gear depends on the accuracy of its design and manufacturing.

The correct manufacturing of a gear requires a number of prerequisite calculations and design

considerations. The design considerations taken into account before manufacturing of gears

are:

Strength of the gear in order to avoid failure at starting torques or under dynamic

loading during running conditions.

Gear teeth must have good wear characteristics.

Proper alignment and compactness of drive.

Provision of adequate and proper lubrication arrangement.

Selection of material combination.

Gear wheel proportions.

Selection of Materials

The gear material should have the following properties:

High tensile strength to prevent failure against static loads

High endurance strength to withstand dynamic loads

Low coefficient of friction

Good manufacturability

32 | P a g e

Gear wheel proportions

A gear has three important parts

Hub

Web or arms

Rim

Hubs of gears are of two types, solid or split. The advantage of split hub is that it reduces the

cooling stresses in the gear and facilitates the mounting of the gear on the shaft. The solid hub

gear is to be mounted overhung on the shaft. The key is placed under the arm in case of solid

hub while in case of split hub; the key is placed at right angles to the hub joint. Small gears up

to 250 mm pitch circle diameter are built with a web, which joins the hub and the rim. The

thickness of the web of the gear should be such that it is capable of transmitting the torque

without shearing off at the hub where it joins. The gear is designed such that the thickness of

its web is equal to half the circular pitch. Gears of larger diameter are provided with arms. The

number of arms depends on the pitch circle diameter of the gear. Following are the prevailing

practices of the number of arms and gear diameters

Gear diameter (mm) Arms

300-500 4-5

500-1500 6

1500-2400 8

>2400 10-12

While calculating the dimensions of the arms it is assumed that they transmit the stalling

torque safely. Elliptical cross sections are preferred for lighter loads while remaining cross

sections are used for large and heavy gears.

The following aspects are considered while determining cross sectional diameter of the arm.

Empirical formulas are used to determine the rim thickness.

.......... Equation 1

33 | P a g e

Where is the number of teeth and are the number of arms.

A good design is a one in which the rim has a central rib of thickness equal to half the circular

pitch.

If the layout of the shaft is known, the diameter of the gear shaft can be calculated. Toothed

wheels fixed on the shaft are fitted by interference-for example, press or light press fit. For

impact load or speeds above 2000 RPM. Press fit is employed. If the wheel is to be removed

from the shaft medium fit are used.

1.12.1. AGMA Standard of Gear Design

A designed gear should meet following design criteria conforming to AGMA standards. It

should have

Enough mechanical strength to withstand force transmitted

Enough surface resistance to overcome pitting failure

Enough dynamic resistance to carry fluctuating loads

Design Inputs and Outputs in Gear Design

Following figure shows design inputs and outputs of a gear design

Figure 23 (Input and output parameters for a gear design)

Various design output parameters are pictorially represented in following figure.

34 | P a g e

Figure 24 (Various design output parameters )

Design for space constrains

The designed gear system should fit within a space limit. So the designer could say if he sums

pitch diameters of the mating gears, it should be less than or equal to allowable space limit as

shown in figure below.

Figure 25 (Space constrain of gear design)

The rectangle represents space on which gear should get fit. One can take 80% of width of this

space as allowable width for gear design. So following is the relation obtained by this

condition.

.......... Equation 2

We also know speed ratio of gears, this will lead to one more relation in terms of pitch circle

diameters.

.......... Equation 3

35 | P a g e

By solving above 2 equations simultaneously we can obtain pitch circle diameters of both the

gears.

Determination of Number of Teeth - Interference

Here we will understand how to determine number of teeth on both the gears. To do this we

have to assume number of teeth on one gear ( ), say the smaller gear. Now using the relation

given below we can determine number of teeth on other gear ( .

.......... Equation 4

So we got number of teeth on both the gears, but one should also check for a phenomenon

called interference if gear system has to have a smooth operation. Interference happens when

gear teeth has got profile below base circle. This will result high noise and material removal

problem. This phenomenon is shown in following figure.

Figure 26 (A pair of gear teeth under interference)

If one has to remove interference, the pinion should have a minimum number of teeth

specified by following relation.

(

)

.......... Equation 5

Where represents addendum of tooth. For 20 degree pressure angle (which is normally

taken by designers) = 1 m. Module m, and pitch circle diameter Pd are defined as follows.

.......... Equation 6

.......... Equation 7

If this relation does not hold for a given case, then one has to increase number of teeth T1,

and redo the calculation. The algorithm for deciding number of teeth T1 and T2 is shown

below.

36 | P a g e

Figure 27 (Flow chart to determine number of teeth on each gears)

Design for Mechanical Strength - Lewis Equation

Now the major parameter remaining in gear design is width of the gear teeth, b. This is

determined by checking whether maximum bending stress induced by tangential component

of transmitted load, at the root of gear is greater than allowable stress. As we know power

transmitted, P and pitch line velocity V of the gear can be determined using following

relation.

.......... Equation 8

Here we consider gear tooth like a cantilever which is under static equilibrium. Gear forces

and detailed geometry of the tooth is shown in figure below.

Figure 28 (Gear tooth under load)

37 | P a g e

One can easily find out maximum value of bending stress induced if all geometrical

parameters shown in above figure are known. But the quantities t and l are not easy to

determine, so we use an alternate approach to find out maximum bending stress value using

Lewis approach. Maximum bending stress induced is given by Lewis bending equation as

follows.

.......... Equation 9

Where Y is Lewis form factor, which is a function of pressure angle, number of teeth and

addendum and dedendum. Value of Y is available as in form of table or graph. Using above

relation one can determine value of b, by substituting maximum allowable stress value of

material in LHS of equation.

A More Realistic Approach - AGMA Strength Equation

When a pair of gear rotates we often hear noise from this, this is due to collision happening

between gear teeth due to small clearance in between them. Such collisions will raise load on

the gear more than the previously calculated value. This effect is incorporated in dynamic

loading factor, value of which is a function of pitch line velocity.

At root of the gear there could be fatigue failure due to stress concentration effect. Effect of

which is incorporated in a factor called value of which is more than 1.

There will be factors to check for overload ( ) and load distribution on gear tooth ( ).

While incorporating all these factors Lewis stregth equation will be modified like this

.......... Equation 10

The above equation can also be represented in an alternating form (AGMA Strength equation)

like shown below

.......... Equation 11

Where is

.......... Equation 12

Using above equation we can solve for value of b, so we have obtained all the output

parameters required for gear design.

But such a gear does not guarantee a peaceful operation unless it does not a have enough

surface resistance.

38 | P a g e

Design for surface resistance

Usually failure happens in gears due to lack of surface resistance, this is also known as pitting

failure. Here when 2 mating surfaces come in contact under a specified load a contact stress is

developed at contact area and surfaces get deformed. A simple case of contact stress

development is depicted below, where two cylinders come in contact under a load F.

Figure 29 (Surface deformation and development of surface stress due to load applied)

For a gear tooth problem one can determine contact stress as function of following

parameters

.......... Equation 13

If contact stress developed in a gear interface is more than a critical value (specified by AGMA

standard), then pitting failure occurs. So designer has to make sure that this condition does

not arise.

1.13. Gear Train & Types of Gear Train A gear train is formed by mounting gears on a frame so that the teeth of the gears engage.

Gear teeth are designed to ensure the pitch circles of engaging gears roll on each other

without slipping, providing a smooth transmission of rotation from one gear to the next

The transmission of rotation between contacting toothed wheels can be traced back to the

Antikythera mechanism of Greece and the south-pointing chariot of China. Illustrations by the

renaissance scientist Georgius Agricola show gear trains with cylindrical teeth. The

implementation of the involute tooth yielded a standard gear design that provides a constant

speed ratio.

following are the different types of gear trains, depending upon the arrangement of wheels:-

Simple Gear Train

Compound Gear Train

Reverted Gear Train

Epicyclic Gear Train

39 | P a g e

Simple Gear Train

The simple gear train is used where there is a large distance to be covered between the input

shaft and the output shaft. Each gear in a simple gear train is mounted on its own shaft.

When examining simple gear trains, it is necessary to decide whether the output gear will turn

faster, slower, or the same speed as the input gear. The circumference (distance around the

outside edge) of these two gears will determine their relative speeds.

Figure 30 Simple Gear Train

Compound Gear Train

In a compound gear train at least one of the shafts in the train must hold two gears.

Compound gear trains are used when large changes in speed or power output are needed and there is

only a small space between the input and output shafts.

The number of shafts and direction of rotation of the input gear determine the direction of rotation of

the output gear in a compound gear train. The train in Figure has two gears in between the input and

output gears. These two gears are on one shaft. They rotate in the same direction and act like one

gear. There are an odd number of gear shafts in this example. As a result, the input gear and output

gear rotate in the same direction.

Figure 31

40 | P a g e

Reverted Gear Train:

When the axes of the first gear (i.e. first driver) and the last gear (i.e. last driven or follower)

are co-axial, then the gear train is known as reverted gear train as shown in Fig.

Figure 32

Epicyclic Gear Train:

Epicyclic gear trains are powerful when used correctly, but are often misunderstood.

Illustrated below is a typical epicyclic gear train. Notice how the planet gears roll on and

revolve about the sun gear. The ring gear rolls on the planet gears. Such a gear configuration

has useful applications, but the overall gear ratio is quite difficult to intuitively calculate.

Please select "Epicyclic Ratio Calc'n" to learn about an effective yet simple method for

calculating the overall gear ratio.

Figure 33

41 | P a g e

References

http://my.safaribooksonline.com/9789332503489/chap1_sub10_xhtml

http://www.engineeringtoolbox.com/mechanics-t_52.html

http://www.splung.com/content/sid/2/

https://www.clear.rice.edu/elec201/Book/basic_mech.html