This set of Machine Kinematics Multiple Choice Questions & Answers (MCQs) focuses on “Friction and Double Hooke’s Joint”.

1. 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

View Answer

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.R

_{N}, where RN is the normal reaction.

2. 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)

View Answer

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.

3. 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)

View Answer

Explanation: Efficiency, η = Ideal effort/ Actual effort

= P

_{0}/ P

= W tanα/ W tan(α + φ)

= tan α / tan (α + φ).

4. 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

View Answer

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.

5. 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

View Answer

Explanation: The efficiency of a screw jack is maximum when sin (2α + φ) is maximum, i.e. when

α = 45º – φ/2.

6. 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

View Answer

Explanation: Maximum efficiency, η

_{max}= sin (90º – φ + φ) – sinφ/sin (90º – φ + φ) + sinφ

= sin 90º – sin φ/sin 90º + sin φ

= 1 – sinφ/ 1 + sinφ.

7. 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

View Answer

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.

8. 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

View Answer

Explanation: Total frictional torqur = 1/2 × μ.W. R cosec α

where R = Radius of the shaft, and

α = Semi-angle of the cone.

9. 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

View Answer

Explanation: None.

10. 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

View Answer

Explanation: None.

11. 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

View Answer

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.

12. 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

View Answer

Explanation: None.

13. 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

View Answer

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

14. Two shafts with an included angle of 160° are connected by a Hooke’s joint. The driving shaft runs at a uniform speed of 1500 r.p.m. The driven shaft carries a flywheel of mass 12 kg and 100 mm radius of gyration. Find the maximum angular acceleration of the driven shaft.

a) 3090 rad/s^{2}

b) 4090 rad/s^{2}

c) 5090 rad/s^{2}

d) 6090 rad/s^{2}

View Answer

Explanation: Given : α = 180° – 160° = 20°; N = 1500 r.p.m.; m = 12 kg ; k = 100 mm = 0.1 m

We know that angular speed of the driving shaft,

ω = 2 π × 1500 / 60 = 157 rad/s

and mass moment of inertia of the driven shaft,

I = m.k

^{2}= 12(0.1)

^{2}= 0.12 kg – m

^{2}

Let dω_{1} / dt = Maximum angular acceleration of the driven shaft, and

θ = Angle through which the driving shaft turns.

We know that, for maximum angular acceleration of the driven shaft,

cos 2θ = 2sin^{2}α/2 – sin^{2}α = 2sin^{2}20°/2 – sin^{2}20° = 0.124

2θ = 82.9° or θ = 41.45°

and dω_{1} / dt = ω^{2}cosα sin2θsin^{2}α/(1 – cos^{2}θsin^{2}α)^{2}

= 3090 rad/s^{2}.

15. The angle between the axes of two shafts connected by Hooke’s joint is 18°. Determine the angle turned through by the driving shaft when the velocity ratio is maximum.

a) 90°

b) 180°

c) 270°

d) 360°

View Answer

Explanation: Given : α = 98°

Let θ = Angle turned through by the driving shaft.

We know that velocity ratio,

ω

_{1}/ω = cosα/1 – cos

^{2}θsin

^{2}α

The velocity ratio will be maximum when cos^{2} θ is minimum, i.e. when

cos^{2} θ = 1 or when θ = 0° or 180°.

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