Which of the following is the correct relation for gear?

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  1. Circular pitch = π× Module
  2. Circular pitch = 2× Module
  3. Circular pitch = 2π× Module
  4. Circular pitch = Module

Answer (Detailed Solution Below)

Option 1 : Circular pitch = π× Module
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Explanation:

Circular Pitch in Gears

  • Circular pitch is a term used in gear design that refers to the distance along the pitch circle between corresponding points on adjacent teeth. It is an essential parameter that helps in the analysis and design of gears, ensuring proper meshing and smooth transmission of motion and power between gears.

Formula: Circular pitch is mathematically defined as:

Circular Pitch (Pc) = π × Module

Here,

  • π is a constant (approximately 3.14159).
  • Module is the ratio of the pitch diameter to the number of teeth in the gear. It is a measure of the size of the teeth in a gear.

Working Principle:

  • In gears, the pitch circle is an imaginary circle that represents the point of contact where two gears mesh. The circular pitch is the arc length of this pitch circle, measured between corresponding points on adjacent teeth. It plays a crucial role in determining the spacing and size of gear teeth to ensure proper meshing and efficient transmission of motion. The relationship Circular Pitch = π × Module is derived from the geometry of the pitch circle and the definition of the module.
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