Basic Terminology and Classification of Toothed Gearing

Definition

Toothed gearing refers to a mechanical system consisting of rotating machine elements provided with teeth that mesh with each other to transmit motion and power from one shaft to another. It ensures a positive drive, meaning there is no slippage, allowing for exact velocity ratios.

Main Content

1. Fundamental Geometric Terminology

Pitch Circle: An imaginary circle that rolls without slipping with a pitch circle of a mating gear. It represents the "effective" size of the gear.
Addendum and Dedendum: Addendum is the radial distance from the pitch circle to the top of the tooth. Dedendum is the radial distance from the pitch circle to the bottom (root) of the tooth.

2. Gear Tooth Dimensions

Circular Pitch ($p$): The distance measured along the circumference of the pitch circle from a point on one tooth to the corresponding point on the adjacent tooth.
Module ($m$): The ratio of the pitch circle diameter to the number of teeth. It is a standard index of tooth size ($m = D/T$).
Pressure Angle: The angle between the common normal at the point of tooth contact and the common tangent to the pitch circles. A standard angle is often 20°.

3. Classification of Gears

According to Shaft Position:
Parallel shafts (Spur and Helical gears).
Intersecting shafts (Bevel gears).
Non-parallel, non-intersecting shafts (Worm and Worm wheels).
According to Peripheral Velocity:
Low velocity, medium velocity, and high velocity gears.

       Spur Gear Profile
      ___________________
     /   |     |     |   \  <-- Addendum Circle
    |    |  (Tooth)  |    |
    |____|___________|____| <-- Pitch Circle
    |    |           |    |
     \___|___________|___/  <-- Dedendum/Root Circle

Working / Process

1. Determining the Gear Ratio

Identify the number of teeth on the driver gear ($T_1$) and the driven gear ($T_2$).
Calculate the ratio as $N_1/N_2 = T_2/T_1$. This determines how much the speed is multiplied or reduced.

2. Meshing and Engagement

The gears are mounted on shafts so that the pitch circles are exactly tangent to each other.
As the driver rotates, the teeth exert a force on the teeth of the driven gear, transmitting torque through the contact point along the pressure line.

3. Power Transmission

The input power from the prime mover (motor) rotates the driving gear.
The tooth-to-tooth contact transfers the load directly to the driven gear, ensuring the mechanical energy is passed through the shaft assembly.

Advantages / Applications

Positive Drive: Unlike belt drives, gears never slip, ensuring a constant speed ratio.
High Efficiency: Because they operate through rolling/sliding contact, they are highly efficient at transmitting high power.
Compactness: Gears can transmit large amounts of power in a relatively small physical space, making them ideal for automotive transmissions, clocks, and heavy industrial machinery.

Summary

Toothed gearing is the science of using meshed teeth to transmit mechanical power reliably. By understanding the geometric parameters like the pitch circle, module, and pressure angle, engineers can design systems that rotate at precise speeds. Important terms to remember include Module, Pitch Circle, Addendum, Dedendum, and Pressure Angle.