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Mechanical Engineering QUESTION #2475
Question 1
The Grübler–Dobrovolski formula for the mobility (DOF) \(M\) of a general spatial mechanism of family \(f\) with \(n\) movable links and kinematic pairs of class \(j\) is:
  • \(M = 3n - 2c_5 - c_4\)
  • \(M = 6n - \sum_{j=f+1}^{5}(j-f)c_j\)
  • \(M = (6-f)n - \sum_{j=f+1}^{5}(j-f)c_j\)✔️
  • \(M = 6n - 5c_5 - 4c_4\)
Correct Answer Explanation
The Dobrovolski formula is \(M=(6-f)n-\sum_{j=f+1}^{5}(j-f)c_j\), where \(f\) is the family number, \(n\) is the number of movable links, and \(c_j\) is the number of kinematic pairs of class \(j\). For planar mechanisms \(f=3\), this reduces to \(M=3n-2c_5-c_4\).