Degree of Freedom MCQ Quiz in தமிழ் - Objective Question with Answer for Degree of Freedom - இலவச PDF ஐப் பதிவிறக்கவும்

Explanation:

Degree of Freedom:

• The DOF of a mechanism refers to the number of independent parameters required to completely specify the configuration of the mechanism in space.
• According to Kutzback's equation of DOF

DOF = 3(n - 1) - 2j - h

where, n = Number of links, j = Number of joints, h = Number of higher pairs in mechanism.

The physical interpretation of DOF:

• DOF < 0, Overstructure/Superstructure
• DOF = 0, structure /Frame/Truss
• DOF > 0, Mechanism

• DOF of a mechanism predicts the possible number of output with respect to a given input.
• DOF also predicts the number of inputs required in order to obtain a constrained mechanism or number of links that should be controlled as input in order to have a single output.

Concept:

Oldham’s coupling mechanism:

• It is the third inversion of the double slider crank chain.  

• Double Slider Crank Chain consists of four pairs out of which two are turning pairs and two others are sliding pairs.
• Link 1 and link 4 is sliding pair, link 1 and link 2 is turning pair, link 2 and link 3 is second turning pair, link 3 and link 4 is second sliding pair.

Lower kinematic pairs:

• If there is area contact between mating elements, the pair formed is known as lower kinematic pair.
• On the basis of the degree of freedom lower pairs are divided into two groups:
• Linear motion pairs: DOF = 1, Ex. P, R, H pairs.
• Surface motion pairs: DOF > 1, Ex. C, G, E  pairs.
• Therefore, lower kinematic pairs have one or more than one DOF possible.
• In a planar mechanism, each linear motion pairs will restrict two DOF(i.e. Permit only one DOF).

Spherical pair

• Two elements of a pair are connected in such a way that one element (with the spherical shape) turns or swivels about the other fixed element.
• e.g. the ball and socket joint, attachment of a car mirror, pen stand etc.
• Spherical joint or pair has three degrees of freedom.
• And due to more than one degree of freedom, it is surface motion pairs results in a lower pair.
• Each revolute joint has one degree of freedom and introduces five constraints, while each spherical joint has three degrees of freedom and introduces three constraints.`

Concept:

Degree of Freedom: The degree of freedom (DOF) of a mechanical system is the number of independent variables required to define the position or motion of the system. 

For a simple mechanism, the degree of freedom (F) is given by the Grubler’s criterion:

F = 3 (n - 1) - 2j - h

Where j = number of revolute joints

n = number of links

h = number of higher pairs

Calculation:

Given, n = 8, j = 9, h = 0

F = 3 (8 - 1) - 2 × 9 - 0

F = 21 - 18 = 3

Explanation:

Degrees of freedom/mobility of a mechanism is the number of inputs (number of independent coordinates) required to describe the configuration or position of all the links of the mechanism, with respect to the fixed link at any given instant.

According to Kutzbach criterion:

D.O.F = 3(L - 1) – 2j – h where L is the number of links, j is the number of binary joints or lower pairs and h is the number of higher pairs.

Revolute pair and prismatic pair are lower pairs.

Additional Information

Grubler's Equation: 

• For those mechanisms which have a single degree of freedom and zero higher pair.

​3L - 2j - 4 = 0

where, L = Number of links, j = Number of binary joints

Degree of freedom

• F = 0 (Frame)
• F < 0 (Redundent frame/Super structure)
• F > 0 (Constrained/Un-constrained frame)

Concept:

• For a pure rolling of a cylinder, only two kinds of movement are possible
  • CW or CCW rotation about an axis
  • Linear movement
• A rigid body in space is six degrees of freedom system.
  • A free rigid body in space without any constraints typically has six degrees of freedom.
  • These include three translational movements along the x, y, and z axes and three rotational movements about each of these axes.

• The vibrating engine is also having more than two degrees of freedom.
• Vibration absorber: Generally, a vibrating absorber, or more specifically, a tuned mass damper, has a single degree of freedom as it primarily moves in one direction to counteract vibrations. The system's design is to provide a specific frequency at which it effectively absorbs energy.

A rigid body in space is correct because a rigid body in space has multiple degrees of freedom, specifically six, allowing it to move and rotate freely in three-dimensional space, which qualifies as having multiple degrees of freedom.

Concept:

Kutzback equation for DOF is given by

DOF = 3(n - 1) - 2j - h

where n = Number of links, j = Number of joints, h = Number of higher pairs.

Calculation:

Given:

Here, there are 5 links, 5 binary joints 

⇒ L = 5, j = 5, h = 0

⇒ n = 3(5 – 1) - 2 (5)

⇒ n = 2

Explanation:

In kinematics:

Degree of Freedom: The degree of freedom (DOF) of a mechanical system is the minimum number of independent variables required to define the position or motion of the system. 

For a simple mechanism, the degree of freedom (F) is given by Kutzback’s equation:

F = 3 (n - 1) - 2j - h

Where, j = number of revolute joints, n = number of links, h = number of higher pairs

Grubler's equation: It is for those mechanisms having F = 1 and h = 0

From Kutzback equation

F = 3 (n - 1) - 2j - h

1 = 3 (n - 1) - 2j - 0

3l - 2j - 4 = 0

Additional Information

If F > 1 ⇒ more than 1 input required to obtain a definite motion of links

if F = 1 ⇒ Only 1 input required to obtain a definite motion of links ⇒ Kinematic chain

If F = 0 ⇒ It has zero mobility ⇒ Frame

If F < 0 ⇒ It is a redundant frame.

Concept:

Gruebler's criteria for planar mechanism:

DOF = 3(n - 1) - 2P

where n = no of links, P = No of lower pairs(turning pairs)

Calculation:

Given:

n = 4, P =4

DOF = 3(4 - 1) - 2 × 4 = 1

Explanation:

The general expression for the number of degree of freedom in a plane mechanism having n links, j simple hinge joints, h number of higher pair and F_r redundant degree of freedom is:

Concept:

The degree of freedom is equal to the number of independent coordinates require to specify its configuration, i.e., the relative positions of all the links.

According to Kulzbeck law,

F = 3 (L - 1) - 2 j - h

where, L = no. of links, j = no. of joints, h = no. of higher pairs

Calculation:

Given:

L = 5, j = 5, h = 0