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12.2. Solved Examples: Transmitting rotational motion through gears

Example 1.

Consider the system of gears below. Find the speed of gear 6 (in rpm).

A six-gear system with compound gears, showing directions of rotation and a table of gear teeth and RPMs to find gear 6 speed.
A side view of the gear system, displaying the gear shafts and their arrangement.
Gear 1 Gear 2 Gear 3 Gear 4 Gear 5 Gear 6
Number of teeth 41 23 37 19 29 17
Rotational Speed [rpm] 85 rpm ?

Solution:

To apply equation (7) in solving the system, we need to decide which gears are drivers and which are driven.

Drivers: 1, 3, 5

Driven: 2, 4, 6

The equation becomes:

[latex]N \times T_1 \times T_3 \times T_5 = n \times t_2 \times t_4 \times t_6[/latex]

Rearranging for n, we get:

[latex]n = {\frac{n \times T_1 \times T_3 \times T_5}{t_2 \times t_4 \times t_6}} = {\frac{85 \times 41 \times 37 \times 29}{23 \times 19 \times 17}} = 503.35 \text{ rpm}[/latex]


Example 2.

Consider the system below, for which gear A has 45 teeth and rotates at 200 rpm, gear B has 51 teeth, and gear C rotates at 150 rpm. Find the number of teeth for gear C.

Three interconnected gears labeled A, B, and C. Gear A rotates counterclockwise, driving gear B clockwise, which in turn drives gear C counterclockwise.

Solution:

To apply equation (7) in solving the system, we need to decide which gears are drivers and which are driven.

Drivers: A, B

Driven: B, C

Note: In this situation gear B has both driver and driven functions.

The equation becomes:

[latex]N \times T_A \times T_B = n \times t_B \times t_C[/latex]

Rearranging for [latex]t_c[/latex], we get:

[latex]t_C = {\frac{n \times T_A}{n}} = 60 \text{ teeth}[/latex]

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College Physics – Fundamentals and Applications Copyright © by Daniela Stanescu, Centennial College is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.