Mobility / Grashof's Condition and Barker's Classification

Mobility of Mechanism

Degrees of freedom for planar linkages joined with common joints can be calculated through Gruebler’s equation.

Gruebler’s equation is given by the formula:

M = 3(L-1) - 2J₁ - J₂

where:

• M is degree of freedom or Mobility
• L is number of links
• J₁ is number of full joints
• J₂ is number of half joints

Grashof Condition

Grashof’s Law states that for a four-bar linkage system, if the sum of length of shortest and longest of a planar quadrilateral linkage is less than or equal to the sum of the remaining two links , then the shortest link can rotate freely with respect to neighbouring link.

Let denote the smallest link of four bar linkage with S and the longest link by L and the other two links by P and Q.

The necessary condition to satisfy Grashof’s Law is :

S + L ≤ P + Q

Barker's Classification

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