Question

Identify the current expression for Kutzbach's criterion of mobility, given n is the number of links, j₁ is the number of low-pair joints and j₂ is the number of high-pair joints.
1. m = 2 (n - 1) - j₁ - j₂
2. m = 3 (n - 1) - j₁ - 2j₂
3. m = 3 (n - 1) - 2j₁ - j₂
4. m = 3 (n - 1) + j₁ - j₂

Answer 1

Correct Answer - Option 3 : m = 3 (n - 1) - 2j₁ - j₂

Explanation:

Degree of freedom(DOF)/Mobility of linkage –

• Degree of freedom of plane mechanism is defined as the number of inputs or independent coordinates needed to define the configuration or
• position of all the links of mechanism with respect to a fixed link.

Kutzback equation of degree of freedom,

F = 3 × (n – 1) – 2j₁ – j₂

Where, n = number of links in the mechanism, j₁ = Binary joint or lower pair, j2 = higher Pair and F = Degree of freedom

Grubler's criterial applies to planar mechanism having no higher pairs (h = 0) and completely constraint (F = 1).

1 = 3 × (n – 1) – 2j  

∴ 1 = 3n – 3 –  2j

∴ 2j  – 3n + 4 = 0