Degrees of freedom

The connection of a link with another imposes certain constraints on their relative motion thus,

Degrees of freedom = 6 – number of restraints

Degree of Freedom of Space Mechanism (3-D)

F = 6(L – 1) – 5P₁ – 4P₂ – 3P₃ – 2P₄ – P₅

Here,      F = Degree of freedom (D.O.F.)
L = Total number of links in mechanism
P₁ = Number of pairs having one D.O.F.
P₂ = Number of pairs having two D.O.F.
P₃ = Number of pairs having three D.O.F.
P₄ = Number of pairs having four D.O.F.
P₅ = Number of pairs having five D.O.F.

• Degree of freedom of plane (2D) mechanism (Gruebler’s Criterion)

F = 3(L– 1) – 2P₁ – P₂
Here, L = Number of links in a mechanism
P₁ = Number of pairs having one degree of freedom
P₂ = Number of pairs having two degree of freedom

• Kutzback’s equation

F = 3(L  – 1) – 2j – h
Here,         L = Number of link, j = Number of lower joints,
h = Number of higher joints

• Grubler’s Equation: For those mechanisms which have single degree of freedom and zero higher pair.

3l – 2j – 4 = 0
Here, l = Number of links, j = Number of binary joints

• Degree of Freedom: F = 0 (Frame), F < 0 (Redundant frame)

F > 0 (constrained/unconstrained frame)
All mechanisms have minimum 4 number of links.

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