The RPM of "D" is 500 and hobbed with 36 teeth. If gears "A", "B", and "C" have 72, 64, and 24 teeth respectively, the RPM of "A" in the gear train illustration is __________. See illustration MO-0088.
• Use the basic gear relation (speed₁ × teeth₁ = speed₂ × teeth₂) for each pair of meshing gears. • Identify which gears are meshing and which gears are rigidly mounted on the same shaft (same RPM). • Work the problem step-by-step from gear D (given RPM) back to gear A, keeping track of the direction of speed change at each stage.
• From the illustration, which gears are in direct mesh with each other, and which two gears appear to be on the same shaft (compound gear)? • Starting with gear D at 500 RPM and 36 teeth, what is the RPM of the gear it meshes with, using the teeth-speed relation? • Once you know the RPM of the compound gear, how does that RPM transfer through the next meshing pair to give you the RPM of gear A?
• Be sure you have correctly identified the compound pair (two gears sharing the same shaft and RPM). • For each mesh, check that you are applying speed₁ × teeth₁ = speed₂ × teeth₂ in the correct direction (driver vs. driven). • After finding the RPM of gear A, compare with the choices and confirm the overall ratio from D to A matches the sequence of tooth ratios you used.
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