AbstractWe propose to analyse some classical overconstrained mechanisms by using explicitely the relations of singularity and not only the closure equation A1ˆ...ˆAn = e. Using the fact that their configuration space manifold is such that the constraint jacobian is permanently not of full rank, we apply our earlier developed analysis strategy for singularities to analyse overconstrained mechanisms. By theorem 1, the holonomic constraints A1ˆ...ˆAn = e are linearized and formulated in an appropriate form on the Lie algebra ... This gives a redundant set of linear equations which is solved. The used method is coordinate‐free and the solution of the Bennett and Bricard mechanisms is given as illustration of the method.