Isostaticity or hyperstaticity
Tree couplings

The choice of a rigid connection is reserved for special cases. Two shafts joined by a rigid connection lose all relative movement.

This absence of relative movement can be functional (figure 1 ) when one of the shafts is not guided. The linkage allows this shaft to be guided, as it becomes integral with the other, whose movements are correctly defined. The assembly is then isostatic, i.e. it is guided by the minimum number of links.

On the other hand, when the shafts are guided in rotation, their rigid connection causes the assembly to be hyperstatic (i.e. an overabundance of connections guiding the line of shafts).