The correction to Grubler criterion for calculating the Degrees of Freedoms of Mechanisms

It is well known that the widely used Chybychev-Grubler Kutzbach’s criterion does not give the correct mobility for many mechanisms. In this paper we will show that if we add to the known Grubler equation the number of inner forces existing in the mechanism, termed self-stresses, we will derive the correct answer. The unique contribution of this paper is that it enables to find this correction on the given mechanism without any need to write the corresponding matrices or any equations. It should be noted that the correct mobility is obtained from the given configuration of the mechanism; that is the instantaneous mobility and not the global mobility.Copyright © 2011 by ASME