3n 6 Degrees Of Freedom

Degree of Freedom is defined as the minimum number of independent variables required to define the position of a rigid trunk in space. In other words, DOF defines the number of directions a body can movement. The degree of freedom concept is used in kinematics to summate the dynamics of a body.

If DOF > 0 Information technology's a Machinery

If DOF = 0 It'south a Structure

and If DOF < 0 It's a Pre-Loaded Construction

Examples of DOF

Hither are the examples of the use of DOF in diverse conditions:

Degree of Liberty of a Point in 2D Aeroplane

To define the position of indicate "P" in 2-dimensional space just its distance from the origin in the 10 and y-axis is required. Therefore point P has ii DOF in 2-D space.

Degree of Freedom of a Line in second Aeroplane

To constraint, the position of a line (L) or rigid trunk in 2-Dimensional space, its distance from the origin in the X and Y-axis and bending from 10-centrality is required. Therefore line (50) or rigid body has 3 DOF in second space.

Degree of Freedom of a Rigid Body in 3D Plane

To define/constraint the position of a rigid trunk in iii-dimensional space. Its distance from the origin in the X, Y, Z-axis and angle from XY, XZ, YZ planes are required. Therefore a rigid torso has half dozen DOF in 3D space.

Degree of Freedom of Kinematic Links

Kinematic links are used to transfer move from ane point to another point. 1 link is joined to another link by joints. These joints add kinematic constraints to the link.

Kinematic constraints between rigid bodies/Links result in the decrease of the degrees of liberty of the arrangement.

Calculation of Degree of Freedom for a Kinematic Links

DOF of a kinematic link can be calculated using Grubler's Dominion.

Grubler'southward Rule ( Degree of Freedom Formula )

DOF = 3 × (n-1) – 2×fifty – h

Where

n = Total Number of links

fifty = Number of lower pairs.

h = Number of college pairs (If more one input is required to constraint a link)

4 Link Mechanism DOF

Number of Links (n) = 4

Lower Pair (l) = 4, Higher Pair (h) = 0

As per Grubler's equation :

DOF = 3(northward-1)-2l-h

DOF = 3(iv-1)-ii(4) = 1

Therefore input to whatsoever one link will issue in the motion of all links.

Five Link Mechanism

Number of Links (n) = 5

Lower Pair (fifty) = 5, College Pair (h) = 0

Equally per Grubler's equation :

DOF = three(northward-i)-2l-h

DOF = iii(v-ane)-two(five) = 2

Therefore two inputs are required to completely control the motility.

3 Link Mechanism with 1 higher pair Link

Number of Links (n) = iv

Lower Pair (l) = 3, Higher Pair (h) = 1

As per Grubler's equation:

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

DOF = iii(4-i)-2(3)-1 = two

Therefore ii inputs are required to completely command the move.

Why we require Degree of Freedom of a Rigid Body

DOF of a trunk or a production is used to ascertain its motion in free space. For instance, if you are going to buy a new choice and identify robot. Beginning affair you look for DOF of a robot. Information technology will help you in agreement what tasks this robot tin perform for y'all.

The above Robotic arm can rotate about an axis and can take horizontal move. Therefore it has 2-DOF.

The above Robotic arm tin can rotate about five different axis. Therefore it has 5-DOF.

Normally asked Questions on DOF

Yes, it is possible when a trunk is over constraint. For example in a truss structure, Extra links are added to reduce stress on existing truss members.

Writing on a paper or movement on carrom board are example of 2 DOF.

DOF in robotics defines, in how many directions a robot can move. For instance robotic arm that can pick and place objects should take 4 DOF. Because it requires 4 motions:

three axis motions to reach anywhere in 3D space.
1 axis gripper to pick and place object.

Higher the DOF of a robot. Higher volition be the flexibility it will offer to control motions.

Grubler'south Rule can be used to summate the DOF for a kinemetic link. According to Grubler's Rule

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

Where

north = Total Number of links, fifty = Number of lower pairs, h = Number of higher pairs

In a lower pair joint two elements of a pair are joined together with the surface contact between them

Whereas In a higher pair, just one point or line is responsible to form a joint between ii links.

In a layman language. Only one input is required to constraint the motion of the lower pair joint. whereas more than one inputs are required to constraint the motion of higher pair joints.

A quadcopter exhibits half-dozen degrees of liberty considering to control its motion we need to control six motions.

Linear motion in X y and Z direction.
Rotational Motion : Yaw, Scroll and Pitch

To sum up, the DOF of a body or a production is used to define its motion in complimentary space. To reduce the DOF of a body, kinematic restrictions are added to a body. We propose you also read this article on the free body diagram.

We volition keep calculation more information on the degree of freedom in mechanics . Please add your suggestions comments or questions in the comment box.