Question

The axes of the two shafts are intersecting and are at 35° to each other. These two shafts are connected by Hook’s joint. At which position of the drives shaft velocity ratio will not be unity?

(a) 42.145°

(b) 222.145°

(c) 317.85°

(d) 141.52°

I had been asked this question by my school principal while I was bunking the class.

My question is taken from Universal Joints and Differential topic in chapter Chassis & Transmission System of Automobile Engineering

Answer 1

Correct answer is (d) 141.52°

The explanation: (ωB / ωA) = (cos α) / (1 – cos^2θ sin^2α) where A = driving shaft and B = driven shaft and α is the angle between shaft  A and shaft B. θ is the angle through which the shaft A rotates. Velocity ratio is unity when tanθ = ± \(\sqrt{cos\alpha} = ± \sqrt{cos35}\) = ± 0.90 i.e. θ = 42.145°, 222.145°, 317.85°, and 137.85°.