The RPM of "D" is 700 and hobbed with 38 teeth. If gears "A", "B", and "C" have 82, 62, and 20 teeth respectively, the RPM of "A" in the gear train illustration is __________. See illustration MO-0088.
• Relationship between gear speed and number of teeth (driver RPM × driver teeth = driven RPM × driven teeth) • How to handle a compound gear train where two gears (B and C) are rigid on the same shaft and therefore turn at the same RPM • Overall speed ratio for multiple meshing gears is the product of the individual gear-pair ratios
• Start from the known gear D (700 RPM and 38 teeth) and work backward through the train to find the RPM of the shaft that carries gear C, then B, then finally A • Write the gear relation for each mesh separately (C with D, and A with B), then combine them into one equation linking RPM of A to RPM of D • Think about whether the intermediate shaft with gears B and C changes the RPM between them, or only the torque and direction
• Confirm you’ve used the correct basic formula: N₁ × T₁ = N₂ × T₂ for each meshing pair (N = RPM, T = teeth) • Be sure B and C are treated as having the same RPM because they are on the same shaft in the illustration • After calculating, check that your final RPM for gear A is reasonable in magnitude and direction (more teeth generally means lower speed when meshed with a smaller gear, and vice versa)
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