GATE Theory of Machines

Theory of Machines: Mechanism & Machines

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Here you get the short notes of some the important topics of “Theory of Machines”.

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Mechanism and Machines

1. Mechanism

If the number of bodies assembled in such a way that the motion of one body causes the motion of other constrained or predictable. This is called Mechanism.

2. Machine

A machine is basically a mechanism or combination of mechanisms, which apart from imparting motion to the part, also transmits and modifies the available mechanical energy into some kind of a desired work.

(It may also be called as a combination of rigid or resistant bodies).

3. Constrained Motion types

  • Completely Constrained Motion
  • Incompletely Constrained Motion
  • Successfully Constrained Motion

4. Rigid Body/Resistant Body

  • Rigid body doesn’t suffer any type of distortion under the action of a force.
  • In real life no body is a rigid body, so for engineering application concept of resistant body comes to play.
  • A resistant body doesn’t deform for the purpose it is used. It means if a body is designed to withstand a force of 50 N, and under this amount of force if the body doesn’t deform then it is called a resistant body; however it may deform if a force of 51 N or more is applied.

5. Link

A member of mechanism that connects other members and having a relative motion.

6. Classification of Kinematic Pair

i. According to nature of Contact

  • Lower Pair – having surface or area contact. Ex- Shaft rotating in a bearing
  • Higher Pair – having point or line contact. Ex- Cam & Follower

ii. According to Nature of Mechanical Constraint

  • Closed pair – held mechanically (direct even without application of external force)
  • Open pair – held due to force of gravity or spring force (external forces)

iii. According to Nature of Relative of Motion

  • Sliding pair
  • Rolling pair
  • Turning pair
  • Screw pair
  • Cylindrical pair
  • Spherical pair

7. Degrees of Freedom –

Degrees of Freedom = 6 – no. of restraints

Remember no. of restraints can never be zero (means joint disconnected), and can never be 6 (means joint becomes rigid).

Formula to find D.O.F of Space Mechanism (3-D)

F = 6(L – 1) – 5d1 – 4d2 – 3d3 – 2d4 – d5

Where, L = total number of links in a Mechanism

F = Degrees of Freedom

d1 = Pairs having 1 D.O.F

d2 = Pairs having 2 D.O.F

d3 = Pairs having 3 D.O.F

d4 = Pairs having 4 D.O.F

d5 = Pairs having 5 D.O.F

Formula to find D.O.F of Plane Mechanism (2-D)

F = 3(L – 1) – 2d1 – d2

Kutzback’s Criterion

F = 3(L – 1) – 2j – h

j = binary joints (lower pair)

h = no. of higher joints (higher pairs)

Gruebler’s Criterion

If h = 0, then formula reduced to

F = 3(L – 1) – 2j

Note – If F = 0 (Frame)

F < 0 (Redundant frame)

F > 0 (Constrained/Unconstrained frame)

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8. Simple Mechanism/Compound Mechanism

In simple words, mechanisms having four links are called simple mechanism.

i. Four bar mechanism

ii. Slider crank mechanism

iii. Double slider crank mechanism

Mechanisms having more than four links are called compound mechanisms.


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