Final answer:
To solve for output velocity in a compound gear train, identify the input velocity and gear ratios, then multiply the input velocity by the product of the gear ratios to obtain the final output velocity.
Step-by-step explanation:
To solve for output velocity in a compound gear train, given an input velocity, follow these steps:
- Identify the known values: The input velocity (Vi) and the gear ratios for the gear train.
- Determine the gear ratios for each pair of gears in the gear train. This is the ratio of the number of teeth on the output gear (To) to the number of teeth on the input gear (Ti).
- Multiply the input velocity by the product of all the gear ratios to find the final output velocity (Vf): Vf = Vi x (To1/Ti1) x (To2/Ti2) x …
Make sure all the units are consistent, and convert as necessary. Use the formula Vf = Vi + at if acceleration is also involved.