Question

calculate the gear ratio of this compound gear.
show your work to receive full credit.

Explanation:

Step1: Calculate gear ratio \( GR_{AB} \)

Gear ratio formula: \( GR=\frac{\text{Number of teeth on driven gear}}{\text{Number of teeth on driving gear}}\).
For \( GR_{AB} \), driving gear is \( A \) (\( 40 \) teeth) and driven gear is \( B \) (\( 120 \) teeth).
\( GR_{AB}=\frac{120}{40}=3 \)

Step2: Calculate gear ratio \( GR_{CD} \)

For \( GR_{CD} \), driving gear is \( C \) (\( 16 \) teeth) and driven gear is \( D \) (\( 80 \) teeth).
\( GR_{CD}=\frac{80}{16}=5 \)

Step3: Calculate compound gear ratio \( GR_{total} \)

Compound gear ratio formula: \( GR_{total}=GR_{AB}\times GR_{CD} \)
\( GR_{total}=3\times5 = 15 \)

Answer:

\( GR_{AB} = 3 \), \( GR_{CD}=5 \), compound gear ratio \(= 15\)