Question

The bell crank fits over a 100-mm-diameter shaft which is fixed and cannot rotate. The horizontal force T is applied to maintain equilibrium of the crank under the action of the vertical force P 100 N. Determine the maximum and minimum values which T may have without causing the crank to rotate in either direction. The coefficient of static frietion between the shaft and the bearing surface of the crank is 0.20.

Answer 1

Friction angle tan 1tan 10.20 11.31 Radius of friction eircle r r sin 50 sin 11.31 9.81 mm Angle tan-1 120-33.7 180 9.81 Angle B sin =sin 1 - 2.60 (120)(180)

(a) Impending counterclockwise motion. The equilibrium triangle of forces
is drawn and gives

T₁ = P cot ( θ - β ) = 100 cot (33.7 2.60)

T₁ = T_max = 165.8 N

(b) Impending clockwise motion. The equilibrium triangle of forces for this
case gives

T₂ = P cot ( θ +β) = 100 cot (33.7 + 2.60)

T₂ = T_max = 136.2 N