Chebychev–Grübler–Kutzbachʹs criterion for mobility calculation of multi-loop mechanisms revisited via theory of linear transformations

The paper presents a critical review of the well known Chebychev–Grübler–Kutzbachʹs criterion for global mobility calculation of multi-loop mechanisms. We emphasize on the limits of this criterion by applying it to three parallel robots and ascertaining that the results are erroneous. In fact, this criterion does not fit for many classical mechanisms or modern parallel robots. We explain why this criterion does not work for certain mechanisms and we accurately limit its applicability. We found our proof on the theory of linear transformations. As far as we are aware this paper presents for the first time an accurate applicability limitation of this well known criterion with huge and long-time utilisation in analysis and synthesis of mechanisms.