## 20 May 2017

### Degree of freedom in kinematics

Degree of freedom :

Degree of freedom is related to motion possibilities of rigid bodies.

An unconstrained rigid body moving in space can describe the following independent motions :

• Translational motion along any three manual perpendicular axis x y and Z.
Thus, rigid body processes 6 degrees of freedom.

The concept of degree of freedom in the kinematics of machines is used in three ways :
• A body is relative to a reference frame.
• Kinematic joints
• A mechanism.

The connection of a link with another imposes certain constraints on their relative motion.
The number of restraint can never be zero or six.

Degree of freedom of a pair is defined as the number of independent relative motions, both translational and rotational a pair can have.

Degree of freedom = 6 -  Number of restraints

The general equation to find out degrees of freedom of a planar mechanism is given below. This equation is also known as Kuthbach equation.
D.O.F = 3 ( N-1 ) - 2Lp - Hp

Here N = Total number of links in the mechanism.
LP and HP = Number of lower pairs and higher pairs respectively.

If the mechanism is 3 dimensional in nature, you could easily derive an equation for mobility using the same concept. So the equation for the degree of freedom would be following below :
D.O.F = 6 ( N-1 ) - 5P5 - 4P4 - 3P3 - 2P2 - 1P1

Where Pn = number of pairs which block 'n' degrees of freedom.
The main thing here will be the determination of nature of the kinematic pair.