Question

structures & mechanical systems and control
grade 8
velocity ratio vs force ratio
ch if the speed/velocity ratio decreases the force ratio will increase, and vice versa
when we work with gears this relationship is as follows:

• if a small driver gear drives a larger driven gear, the driven gear turns slower, but with greater force.
• if a large driver gear drives a smaller driven gear, the driven gear turns with less force, but faster.

answer the following question on gears
2.4.1 study the gear train below and answer the questions that follow. the small gear is the driver and has 15 teeth. the big gear is the driven gear and has 45 teeth.
which gear will turn the slowest?
2.4.2 calculate the gear ratio of this gear train.
gear ratio = (number of teeth driven gear) / (number of teeth driver gear)
2.4.3 does this gear train provide a force advantage or a speed advantage? explain your answer.
2.4.4 what is the mechanical advantage of this gear train?
2.4.5 does this gear train increase or decrease the rotation speed. explain your answer.
compiled by ilze j. van rensburg
ratp - 2023
page 16 of 52
january 2024

Explanation:

2.4.1

From the text, a small driver gear (15 teeth) drives a larger driven gear (45 teeth). A larger driven gear turns slower. So the big (driven) gear with 45 teeth turns slowest.

Step1: Identify teeth counts

Driver gear teeth: \( 15 \), Driven gear teeth: \( 45 \)

Step2: Apply gear ratio formula

Gear ratio \( = \frac{\text{Number of teeth driven gear}}{\text{Number of teeth driver gear}} = \frac{45}{15} \)

Step3: Simplify the fraction

\( \frac{45}{15} = 3 \)

A small driver (15 teeth) drives a larger driven (45 teeth) gear. From the text, a small driver driving a larger driven gear gives the driven gear greater force (force advantage) as it turns slower. So this gear train provides a force advantage.

Answer:

The big (driven) gear (with 45 teeth)

2.4.2