Machine Kinematics MCQ – Friction and Double Hooke’s Joint

The angle of inclination of the plane, at which the body begins to move down the plane, is called
a) angle of friction
b) angle of repose
c) angle of projection
d) none of the mentioned

Answer: a
Explanation: Consider that a body A of weight (W) is resting on a horizontal plane B. If a horizontal force P is applied to the body, no relative motion will take place until the applied force P is equal to the force of friction F, acting opposite to the direction of motion. The magnitude of this force of friction is F = μ.W = μ.RN, where RN is the normal reaction.

In a screw jack, the effort required to lift the load W is given by
a) P = W tan (α – φ)
b) P = W tan (α + φ)
c) P = W cos (α – φ)
d) P = W cos (α + φ)

Answer: b
Explanation: If one complete turn of a screw thread by imagined to be unwound, from the body of the screw and developed, it will form an inclined plane. P = W tan (α + φ)
where α = Helix angle, and
φ = Angle of friction.

The efficiency of a screw jack is given by
a) tan (α + φ)/tan α
b) tan α / tan (α + φ)
c) tan (α − φ)/ tan α
d) tan α/ tan (α − φ)

Answer: b
Explanation: Efficiency, η = Ideal effort/ Actual effort
= P0 / P
= W tanα/ W tan(α + φ)
= tan α / tan (α + φ).

The radius of a friction circle for a shaft of radius r rotating inside a bearing is
a) r sin φ
b) r cos φ
c) r tan φ
d) r cot φ

Answer: a
Explanation: If a circle is drawn with centre O and radius OC = r sin φ, then this circle is called the friction circle of a bearing. The force R exerted by one element of a turning pair on the other element acts along a tangent to the friction circle.

The efficiency of a screw jack is maximum, when
a) α = 45º + φ/2
b) α = 45º – φ/2
c) α = 90º + φ
d) α = 90º − φ

Answer: b
Explanation: The efficiency of a screw jack is maximum when sin (2α + φ) is maximum, i.e. when
α = 45º – φ/2.

The maximum efficiency of a screw jack is
a) 1 – sinφ/ 1 + sinφ
b) 1 + sinφ/ 1 – sinφ
c) 1 – tanφ/ 1 + tanφ
d) 1 + tanφ/ 1 – tanφ

Answer: a
Explanation: Maximum efficiency, ηmax = sin (90º – φ + φ) – sinφ/sin (90º – φ + φ) + sinφ
= sin 90º – sin φ/sin 90º + sin φ
= 1 – sinφ/ 1 + sinφ.

The frictional torque transmitted in a flat pivot bearing, considering uniform pressure, is
a) 1/2 × μ.W. R
b) 2/3 × μ.W. R
c) 3/4 × μ.W. R
d) μ.W.R

Answer: b
Explanation: Total frictional force = 2/3 × μ.W. R
where μ = Coefficient of friction,
W = Load over the bearing, and
R = Radius of the bearing surface.

The frictional torque transmitted in a conical pivot bearing, considering uniform wear, is
a) 1/2 × μ.W. R cosec α
b) 2/3 × μ.W. R cosec α
c) 3/4 × μ.W. R cosec α
d) μ.W.R cosec α

Answer: a
Explanation: Total frictional torqur = 1/2 × μ.W. R cosec α
where R = Radius of the shaft, and
α = Semi-angle of the cone.

The frictional torque transmitted by a disc or plate clutch is same as that of
a) flat pivot bearing
b) flat collar bearing
c) conical pivot bearing
d) trapezoidal pivot bearing

Answer: b
Explanation: None.

The frictional torque transmitted by a cone clutch is same as that of
a) flat pivot bearing
b) flat collar bearing
c) conical pivot bearing
d) trapezoidal pivot bearing

Answer: d
Explanation: None.

In automobiles, Hooke’s joint is used between which of the following?
a) Clutch and gear box
b) Gear box and differential
c) Differential and wheels
d) Flywheel and clutch

Answer: b
Explanation: The main application of the universal or Hooke’s coupling is found in the transmission from the gear box to the differential or back axle of the automobiles. In such a case, we use two Hooke’s coupling, one at each end of the propeller shaft, connecting the gear box at one end and the differential on the other end.

Which of the following statements is not correct?
a) Hooke’s joint is used to connect two rotating co-planar, non-intersecting shafts
b) Hooke’s joint is used to connect two rotating co-planar, intersecting shafts
c) Oldham’s coupling is used to connect two parallel rotating shafts
d) Hooke’s joint is used in the steering mechanism for automobiles

Answer: a
Explanation: None.

A Hooke’s joint is used to connect two
a) coplanar and non-parallel shafts
b) non-coplanar and non-parallel shafts
c) coplanar and parallel shafts
d) non-coplanar and parallel shafts

Answer: b
Explanation: A Hooke’s joint is used to connect two shafts, which are intersecting at a small angle.