Project ForgeTheory of Machines
Kinematics of Mechanisms
GATE 2012
Medium
Two crossed helical gears are used for speed reduction: Gear I has pitch circle diameter 80 mm in the plane of rotation and helix angle 30°; Gear II has pitch circle diameter 120 mm and helix angle 22.5°. If the input speed is 1440 rpm, the output speed in rpm is
- A1200
- 900
- C875
- D720
Explanation
For crossed helical gears sharing a common normal module mn, teeth count T=d·cosψ/mn, so T1/T2=(d1cosψ1)/(d2cosψ2). By the standard meshing relation N1T1=N2T2: N2=N1·T1/T2=N1·(d1cosψ1)/(d2cosψ2)=1440×(80×cos30°)/(120×cos22.5°)=1440×69.28/110.87≈900 rpm.
Source: GATE ME 2012 (Booklet Code A) (2012)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.