Question

A double universal joint is used to connect two shafts in the same plane. The intermediate shaft is inclined at an angle of 20° to the driving shaft as well as the driven shaft. Find the minimum speed of the driven shaft if the driving shaft has a constant speed of 500 r.p.m.

(a) 532.1 r.p.m

(b) 469.85 r.p.m.

(c) 566.25 r.p.m.

(d) 441.5 r.p.m.

The question was asked in an international level competition.

This intriguing question comes from Straight Line Mechanism in section Mechanisms with Lower Pairs of Machine Kinematics

Answer 1

Correct option is (d) 441.5 r.p.m.

Best explanation: Given α = 20° ; NA = 500 r.p.m.

Let A, B and C are the driving shaft, intermediate shaft and driven shaft respectively. We know that for the driving shaft (A) and intermediate shaft (B),

minimum speed of the driven shaft,

NC(min) = NB(min)× cos α = NAcos^2α = 441.5 r.p.m.