Test: Mechanism - 1 - Mechanical Engineering MCQ

• If there is all pairs are lower pair of a kinematic chain then 4 pairs required to make a chain.
• But, if there is atleast one higher pair involved then minimum 3 pairs required to make a kinematic chain. Cam and follower is example of a kinematic chain and it includes total 3pairs.

One higher pair = two lower pair.

• Flexible Link: A flexible link is one that while transmitting motion is partly deformed in a manner not to affect the transmission of motion, for example, belts, ropes, chains, springs, etc.
• Fluid Link: A fluid link is one that is deformed by having an incompressible fluid in a closed vessel and the motion is transmitted through the fluid by pressure, as in the case of a hydraulic press, hydraulic jack, and hydraulic brake.
• Rigid Link: A rigid link is one that does not undergo any deformation while transmitting motion. Links in general are elastic in nature.
  They are considered rigid if they do not undergo appreciable deformation while transmitting motion, for example connecting rod, crank, tappet rod, etc.
• Resistant Link: A link that is rigid for the purposes it serves.
  Apart from rigid links, there are some semi-rigid links that are normally flexible, but under certain loading conditions act as a rigid link for limited purposes and thus are resistant links.
  These days resistant links are usually referred to as rigid links.
• Floating Link: This is a link that is not connected to the frame.

A kinematic chain is a group of links either joined together or arranged in a manner that permits them to move relative to one another. 

Now, let's take an example of such a mechanism

The above-shown figure is a cam and follower mechanism. 

In this mechanism, there are 2 lower pairs i.e. between links (1,2 and 3,1) and 1 higher pair which is between link (2,3). 

Hence, the minimum number of links that can make a mechanism is 3.

Whatever may be the number of links and joints Grubler's criterion applies to mechanism with only single degree freedom. Subject to the condition 3l-2j-4=0 and it satisfy this condition.
Degree of freedom is given by
 

1. Dynamic-static analysis → D` Alembert‘s principal
2. Mobility (for plane mechanism) → Grubler’s criterion
3. Continuous relative rotation → Grashoff’s law
4. Velocity and acceleratio → Kennedy’s theorem

Kinematic pairs are classified under three headings namely, lower pair, higher pair and wrapping pair.

Lower Pair: 

A pair is said to be a lower pair when the connection between two elements is through the area of contact. Some of the types of Lower pair are:

• Revolute Pair
• Prismatic Pair
• Screw Pair
• Cylindrical Pair
• Planar Pair

Higher Pair: 

A pair is said to be higher pair when the connection between two elements has only a point or line of contact. Examples of higher pairs are:

• A point contact takes place when spheres rest on plane or curved surfaces (in case of ball bearings).
• Contact between teeth of a skew-helical gears.
• Contact made by roller bearings
• Contact between teeth of most of the gears.
• Contact between cam-follower
• Spherical Pair.

Wrapping Pairs:

In a higher pair, the contact between the two bodies has only a line contact or a point contact. Whereas in a wrapping pair, one body completely wraps over the other. The typical example is of a belt and a pulley or a chain and a sprocket where the belt completely wraps around the pulley or the chain completely wraps around the sp.

Mechanism: A mechanism is a set of machine elements or components or parts arranged in a specific order to produce a specified motion.

When one of the links of a kinematic chain is fixed, the chain is called a mechanism.

Mechanisms are of the following types:

Simple mechanism

• This is a mechanism which has four links.

Compound mechanism

• This is a mechanism which has more than four links.

Complex mechanism

• This is formed by the inclusion of ternary or higher-order floating link to a simple mechanism.

Planar mechanism

• This is formed when all the links of the mechanism lie in the same plane.

Spatial mechanism

• This is formed when all the links of the mechanism lie in the different plane.

Equivalent mechanism

• Turning pairs of plane mechanisms may be replaced by other types of pairs such as sliding pairs or cam pairs. The new mechanism thus obtained having the same number of degrees of freedom as the original mechanism is called the equivalent mechanism.

It should be lesser or equal, i.e. S + L ≤ P + Q (where S and L are length of shortest and longest link, respectively).

Crank and slotted lever mechanism is mostly used in shaping machines, which is the inversion of a single slider-crank chain.

The correct option is D an inversion of the single slider-crank chain.

• If one of the links is fixed in a kinematic chain, it is called a mechanism.
• So, we can obtain as many mechanisms as the number of links (n inversions from a kinematic chain having ‘n’ number of links) in a kinematic chain.
• A slider-crank is a kinematic chain having four links so four inversions.
• It has one sliding pair and three turning pairs.
• Link 1 is a frame (fixed).
• Link 2 has rotary motion and is called a crank.
• Link 3 has got combined rotary and reciprocating motion and is called a connecting rod.
• Link 4 has reciprocating motion and is called a slider.
• This mechanism is used to convert rotary motion to reciprocating and vice versa. 

Inversions of the slider-crank mechanism are obtained by fixing links 1, 2, 3, and 4.

• First inversion: This inversion is obtained when link 1 (ground body) is fixed.
  Application-  Reciprocating engine, reciprocating compressor, etc.
• Second inversion: This inversion is obtained when link 2 (crank) is fixed.
  Application- Whitworth quick returns mechanism, Rotary engine, etc.
• Third inversion: This inversion is obtained when link 3 (connecting rod) is fixed.
  Application - Slotted crank mechanism, Oscillatory engine, etc.
• Fourth inversion: This inversion is obtained when link 4 (slider) is fixed.
  Application- A hand pump, pendulum pump or Bull engine, etc.

The extreme position of the crank (O1P) are shown in figure.
From right triangle O2O1P1, we find that sin 

According to Grashoff’s Law for a four bar mechanism, the sum of shortest and longest link lengths should not be greater than the sum of the remaining two link length.

i.e. S + L ≤ P + Q

For Double crank mechanism Shortest link is fixed.Here shortest link is ‘P’.

• A machine is a tool containing one or more parts that use energy to perform an intended action.
• A simple machine is a device that simply transforms the direction or magnitude of a force, but a large number of more complex machines exist.
• Examples include Levers, Screw Jack, Wheel and axle, Pulleys, Wedge, Inclined plane, etc.
• Spring stores and releases energy. it neither’s changed direction or magnitude of the force. To qualify as a simple machine, a device must exchange the magnitude of a Force.

Crank and lever mechanism:

This is the first inversion of four bar chain.

It is used to convert rotary motion of input link into oscillatory motion of output link.

Beam engine mechanism is an example of this inversion and it consists of four links.

The crank rotates about a fixed centre and the lever oscillates at another fixed centre.

• When link 4 is moved upwards, it will push link 3 upwards but since link 3&4 are joined by a revolute joint, the link will have to rotate in anticlockwise direction to move upwards.
• Since link 2&3 are joined, link 2 will show the same motion as link 3. So link will rotate in counter clockwise direction.

• This is a case of rolling with sliding on a stationary curved surface, so the instantaneous centre of the body will lie on the common normal at the point of contact, it means line joining two extreme cases.

Important Points

• Instantaneous centre of a body rolling without sliding on a stationary curved surface will lie at the point of contact surface.
• Instantaneous centre of a body in case of pure sliding on a stationary curved surface at the point where it is centred at the curved surface.