Gears an introduction

The topics which we discussed in the class is given in nutshell. Students are here by asked to go through all the terminologies , and understand the concepts in gears.
Gears
Gears are machine elements that transmit motion by means of successively engaging teeth. The gear teeth act like small levers.
1 Gear Classification
Gears may be classified according to the relative position of the axes of revolution. The axes may be
1. parallel,
2. intersecting,
3. neither parallel nor intersecting.
Here is a brief list of the common forms. We will discuss each in more detail later.
• Gears for connecting parallel shafts
• Gears for connecting intersecting shafts
• Neither parallel nor intersecting shafts
Gears for connecting parallel shafts
1. Spur gears
2. Parallel helical gears
3. Herringbone gears (or double-helical gears)
4. Rack and pinion (The rack is like a gear whose axis is at infinity.)

Gears for connecting intersecting shafts
1. Straight bevel gears
2. Spiral bevel gears

Neither parallel nor intersecting shafts
1. Crossed-helical gears
2. Hypoid gears
3. Worm and wormgear

The fundamental law of gear-tooth action may now also be stated as follow (for gears with fixed center distance)
The common normal to the tooth profiles at the point of contact must always pass through a fixed point (the pitch point) on the line of centers (to get a constant velocity ratio).

The Involute Curve

The curve most commonly used for gear-tooth profiles is the involute of a circle. This involute curve is the path traced by a point on a line as the line rolls without slipping on the circumference of a circle. It may also be defined as a path traced by the end of a string which is originally wrapped on a circle when the string is unwrapped from the circle. The circle from which the involute is derived is called the base circle.

Terminology for Spur Gears

In the following section, we define many of the terms used in the analysis of spur gears. Some of the terminology has been defined previously but we include them here for completeness.
Pitch surface : The surface of the imaginary rolling cylinder (cone, etc.) that the toothed gear may be considered to replace.
• Pitch circle: A right section of the pitch surface.
• Addendum circle: A circle bounding the ends of the teeth, in a right section of the gear.
• Root (or dedendum) circle: The circle bounding the spaces between the teeth, in a right section of the gear.
• Addendum: The radial distance between the pitch circle and the addendum circle.
• Dedendum: The radial distance between the pitch circle and the root circle.
• Clearance: The difference between the dedendum of one gear and the addendum of the mating gear.
• Face of a tooth: That part of the tooth surface lying outside the pitch surface.
• Flank of a tooth: The part of the tooth surface lying inside the pitch surface.
• Circular thickness (also called the tooth thickness) : The thickness of the tooth measured on the pitch circle. It is the length of an arc and not the length of a straight line.
• Tooth space: The distance between adjacent teeth measured on the pitch circle.
• Backlash: The difference between the circle thickness of one gear and the tooth space of the mating gear.
• Circular pitch p: The width of a tooth and a space, measured on the pitch circle.
• Diametral pitch P: The number of teeth of a gear per inch of its pitch diameter. A toothed gear must have an integral number of teeth. The circular pitch, therefore, equals the pitch circumference divided by the number of teeth. The diametral pitch is, by definition, the number of teeth divided by the pitch diameter. That is,

That is, the product of the diametral pitch and the circular pitch equals .
• Module m: Pitch diameter divided by number of teeth. The pitch diameter is usually specified in inches or millimeters; in the former case the module is the inverse of diametral pitch.
• Fillet : The small radius that connects the profile of a tooth to the root circle.
• Pinion: The smaller of any pair of mating gears. The larger of the pair is called simply the gear.
• Velocity ratio: The ratio of the number of revolutions of the driving (or input) gear to the number of revolutions of the driven (or output) gear, in a unit of time.
• Pitch point: The point of tangency of the pitch circles of a pair of mating gears.
• Common tangent: The line tangent to the pitch circle at the pitch point.
• Line of action: A line normal to a pair of mating tooth profiles at their point of contact.
• Path of contact: The path traced by the contact point of a pair of tooth profiles.
• Pressure angle : The angle between the common normal at the point of tooth contact and the common tangent to the pitch circles. It is also the angle between the line of action and the common tangent.