Referring to the mower cutter bar schematic shown in the accompanying diagram, the knife guard spacing is $76.2\text{ mm}$ ($3\text{ inches}$). For proper knife register, the stroke length of the knife section must equal the guard spacing. If the pitman crank rotates at $900\text{ rpm}$, the mean linear knife cutting speed is ________ $\text{m/s}$ (round off to two decimal places).
Answer Key:
2.29
Step-by-Step Solution & Explanation
1. Stroke length $S = 76.2\text{ mm} = 0.0762\text{ m}$.
2. In one revolution of the crank, the knife travels two complete strokes (forward and backward): $2S = 2 \times 0.0762 = 0.1524\text{ m}$.
3. Crank speed $N = 900\text{ rpm} = 900 / 60 = 15\text{ rev/s}$.
4. Mean linear knife speed:
$v_m = 2S \times \frac{N}{60} = 0.1524 \times 15 = 2.286\text{ m/s} \approx 2.29\text{ m/s}$.