Topic: Theory of Machines
A gear train comprises of 4 spur gears - the driven gear G1, two idlers G2, G3 and the driving gear G4. The radii of G1, G2, G3 and G4 are r, r/2, r/3 and 2r, respectively. What is the ratio of angular velocities of G1 to G4 and their direction of rotation?
- A. Ratio 1, opposite direction
- B. Ratio = 1/6, same direction
- C. Ratio = 2, Opposite direction
- D. Ratio = 1/2, same direction
Answer: C. Ratio = 2, Opposite direction
Explanation: In a simple gear train with idlers, the speed ratio only depends on the driving and driven gears. Ratio = omega_1 / omega_4 = Radius_4 / Radius_1 = 2r / r = 2. With 4 gears (1 driver, 2 idlers, 1 driven), there are 3 meshes. Each mesh reverses rotation. Therefore, G4 and G1 will rotate in opposite directions.