Project ForgeTheory of Machines
Kinematics of Mechanisms
GATE 2023
Medium
Two meshing spur gears 1 and 2 with diametral pitch of 8 teeth per mm and an angular velocity ratio |ω2|/|ω1| = 1/4, have their centers 30 mm apart. The number of teeth on the driver (gear 1) is ______.
96(± 0.5 accepted)
Explanation
For meshing gears, ω2/ω1=N1/N2, so N2=4N1. Diametral pitch Pd=N/D gives D1=N1/Pd=N1/8 and D2=N2/Pd=4N1/8=N1/2. Center distance=(D1+D2)/2=30 → (N1/8+N1/2)/2=30 → 5N1/16=30 → N1=96.
Source: GATE ME 2023 Official Paper (2023)
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