Degrees of freedom (DOF)/ Mobility of a Mechanism:
It is the number of independent Spatial coordinates required to describe the position of a body in space.”
A free body in space (fig.) can have six degrees of freedom.
i.e. linear positions along x, y and z axes and rotational/angular positions with respect to x, y and z axes.
* In a kinematic pair, depending on the constraints imposed on the motion, the links may loose some of the six degrees of freedom.
* DOF = 6 - No. of Restraints (Restraints never be Zero or Six)
Gruebler’s Criterion, F = 3 (L-1) – 2P (Single D.O.F only and Lower Pairs)
Kutzbach’s Criterion, F= 3(L-1)-2P1-1P2 (Two D.O.F)
Where , F = Degree of freedom L = No. of Links
P = No. of pairs 0r P=No. of links+Loops-1
h = No. of higher Pair
Here, L=4, P=4,
So, F = 3(4-1)-2(4)
i.e. Fon=e1input to any one link will result in definite motion of all links.
Here, L=6, P=7
So, F = 3(6-1)-2(7)
F = 1
Here, L=5, P=5,
So, F = 3(5-1)-2(5)
F = 2
i.e. two inputs to any one link will result in definite motion of all links.
