# Theory of Machines: Gear Basics & Terminologies

## Gear Definition

A Gear is a rotating machine part having cut teeth, or cogs, that meshes with another toothed part in order to transmit torque.

Gears are the most common source used for power transmission.

Two or more gears working in tandem is called a transmission and can produce a mechanical advantage through a Gear ratio and thus may be considered a simple machine.

The gears in a transmission are analogous to the wheels in a pulley.

The advantage of using gears is that the teeth of a gear do not slip or it prevents slipping.

When two gears of unequal number of teeth are combined, a mechanical advantage is produced, with both the rotational speeds and the torques of the two gears differing in a simple relationship.

You can see small gears for devices like wrist watch etc., and large or huge gears in big ships, vehicles etc. The gear is a very important element of any mechanism.

Toothed gears are also used to change the speed, power, and direction between an input and output shaft.

Gears are the most common source used for power transmission.

Gears can be applied to two shafts which are in the following arrangements (position of shaft axes)-

• Parallel
• Collinear
• Perpendicular and Intersecting
• Perpendicular and Non-Intersecting
• Inclined at an Arbitrary Angle

## Gear Terminologies

Terms used in Gears

### Pitch Surface –

The surface of the imaginary rolling cylinder (cone, etc.) that the toothed gear may be considered to replace at the pitch circle.

### Base Circle –

An imaginary circle used in involute gearing to generate the involutes that form the tooth profiles.

### Pitch Circle –

It is an imaginary circle which by pure rolling action, would give the same motion as the actual gear.

A circle bounding the ends of the teeth, in a right section of the gear.

### Dedendum circle –

It is the circle drawn through the bottom of the teeth. This is also called
root circle.

It is the radial distance of a tooth from the pitch circle to the top of the tooth.

### Dedendum –

The radial distance between the pitch circle and the root circle (bottom of the tooth).

### Clearance –

It is the radial distance from the top of the tooth to the bottom of the tooth, in
a meshing gear.

### Clearance Circle –

A circle passing through the top of the meshing gear is known as clearance circle.

### Face of a tooth –

That part of the tooth surface lying outside the pitch surface or above the pitch surface.

### Top land –

It is the surface of the top of the tooth.

### Profile –

It is the curve formed by the face and flank of the tooth.

### Flank of a tooth –

The part of the tooth surface lying inside the pitch surface or below the pitch surface.

### Circular thickness (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 along the pitch circle.

### Backlash –

The difference between the circle thickness of one gear and the tooth space of the mating gear. Zero backlash is preferred but actually some backlash is allowed to prevent jamming of teeth due to teeth errors and thermal expansion.

Backlash = Space width – Tooth thickness

### Circular Pitch (Pc) –

The width of a tooth and a space, measured on the pitch circle.

Pc = [(Π × D)/T]

D = diameter of pitch circle

T = No. of teeth on the Wheel

### Diametral Pitch –

It is the ratio of number of teeth to the pitch circle diameter in millimeters. It is denoted by Pd.

Pd = T/D

### Module (m) –

Pitch circle diameter (in mm) divided by number of teeth, or inverse of diametral pitch.

m = D/T

The small radius that connects the profile of the tooth to the root circle.

### Pinion –

It is the smaller of any pair of mating gears. The larger of the pairs is called the ‘Gear‘.

### Velocity ratio –

It is 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 unit of time.

### Pitch point –

It is a common point of contact between two pitch circles.

### Common tangent –

The line tangent to the pitch circle at the pitch point.

Line of Action or Pressure Line –

The force which the driving tooth exerts at point of contact of the two teeth. This line is also the common tangent at the point of contact of the mating gears and is known as the line of action or the pressure line. The component of the force along the common tangent at the pitch point is responsible for the power transmission.

The component of the force perpendicular to the common tangent through the pitch point produces the required thrust.

### Pressure Angle or Angle of Obliquity (φ) –

The angle between pressure line and the common tangent to the pitch circles is known as the pressure angle or the angle of obliquity. It is denoted by φ

For more power ‘transmission and lesser pressure on the bearing pressure angle must be kept small.

### Path of Contact –

It is the path traced by the point of contact of two teeth from the beginning to the end of engagement.

### Length of the path of contact –

The length of the common normal cut-off by the addendum circles of the wheel and pinion.

### Arc of contact –

The path traced by a point on the pitch circle from the beginning to the end of engagement of a given pair of teeth. It (Arc of contact) consists of two parts, namely-

1. Path of Approach – Portion of the path of contact from the beginning of engagement to the pitch point.
2. Path of Recess – Portion of the path of contact from the pitch point to the end of engagement.

### Contact Ratio –

The ratio of the length of “arc of contact” to the “circular pitch” is known as contact ratio i.e. number of pairs of teeth in contact.

### Angle of Action (δ) –

It is the angle turned by a gear from the beginning of engagement to the end of engagement of a pair of teeth i.e. the angle turned by arcs of contact of respective gear wheels.

Similarly, Angle of approach (a) and angle of recess (β) can be defined as-

S=a+ β

Source – Theory of Machine (RS Khurmi)

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