Grübler’s formula

Every mechanism consists in links connected by joints which have got certain degrees of freedom.

For planar mechanism, the number of degrees of freedom can be obtain by the Grübler’s formula;

G.D.L= 3 (n-1) – 2P(I) – P(II)

It is important to take into account that the contact zone between two gear’s teeth is considered a cam joint; Second class joint.

being:

n= number of links.
P(I)= number of first class joints.
P(II)= number of second class joints.

P(II)= número de pares cinemáticos de segunda clase.

Cases:

  1.     G<0     Hyperstatic structure.
  2.     G=0     Isostatic structure.
  3.     G=1     Desmodromic mechanism: Given the position of one element, the rest are known.
  4.     G=2     Differential mechanism.
  5.     G>2     ‘n’ degrees of freedom mechanism.