Question

what is the compound gear reduction shown here? 5/1 and 3/1 15/1 torque 12/60 x 12/36

Explanation:

Step1: Recall compound gear reduction formula

Compound gear reduction \(R = \frac{N_{d1}}{N_{d2}}\times\frac{N_{d3}}{N_{d4}}\) (where \(N_{d}\) are number of teeth on driven gears and \(N_{d}\) on driving gears).

Step2: Analyze given options

• Option \(5/1\) and \(3/1\) is not a single value for compound reduction.
• Option “Torque” is a physical quantity, not a gear - reduction ratio.
• For compound gear reduction, if we assume first - pair driving gear has \(N_{1}=12\) teeth and driven has \(N_{2} = 60\) teeth, second - pair driving gear has \(N_{3}=12\) teeth and driven has \(N_{4}=36\) teeth. The formula \(R=\frac{N_{2}}{N_{1}}\times\frac{N_{4}}{N_{3}}\) (since gear - reduction ratio is \(\frac{\text{Number of teeth on driven gear}}{\text{Number of teeth on driving gear}}\) for each pair). But the expression \(12/60\times12/36\) is in the form of \(\frac{\text{Number of teeth on driving gear}}{\text{Number of teeth on driven gear}}\times\frac{\text{Number of teeth on driving gear}}{\text{Number of teeth on driven gear}}\) which is wrong for reduction ratio calculation. However, if we consider it as a mis - written form of the product of two gear - ratio terms (where each term is driving/driven, and then take reciprocal for reduction), but among the given options, the most relevant in form (as compound gear reduction is a product of two gear - ratio terms) is \(12/60\times12/36\).
• Option \(15/1\) is a single value, but without knowing the number of teeth on gears, if we calculate \(12/60\times12/36=\frac{12\times12}{60\times36}=\frac{144}{2160}=\frac{1}{15}\) (if we consider reduction ratio as \(\frac{\text{driven}}{\text{driving}}\) for each pair \(\frac{60}{12}\times\frac{36}{12}= 5\times3 = 15/1\)). But the option \(12/60\times12/36\) is in the form of writing the ratio of driving to driven for each pair (and then when we take the product and then reciprocal for reduction, but the problem may be just asking for the form of compound - gear - ratio expression.

Answer:

\(12/60\times12/36\)