Simulation of mechanisms - Freedom, mobility and hyperstatistics

We've already had occasion to use the expressions degree of mobility and degree of freedom. They are frequently used in Mechanics, but are not always precisely defined. In particular, it's not always clear whether they refer to the whole mechanism or just some of its links.

Clarification of these notions is particularly important for the use of mechanism simulation software. We have seen, for example, at the end of the dossier , with regard to the Koenig joint, that the number of these freedoms or mobilities could change during operation. In this case, it increased transiently in a given position. In the case of chains open in certain positions, it can decrease. These are known as singular positions, and they can cause a number of problems in the simulation.

We have also seen, in , that hyperstatism was closely linked to kinematics, and that mechanism simulation software selected a certain number of independent linkage equations and, consequently, a set of principal dynamic unknowns and a set of hyperstatic unknowns taken arbitrarily equal to 0. This selection results from the choice made in these software programs of an automatic method (Gauss, pivot...) and the user has no possibility of influencing this choice. It may well be that this choice does not correspond to the one we would have liked. The only way for the user to impose his will in this area is to make the mechanism isostatic according to his own criteria. In fact, some software programs require the mechanism to be isostatic in order to function. We'll show you how to achieve this.

Finally, following on from the initial comments made along these lines in , this dossier will enable us to explore in greater depth the correspondence between the two questions raised above.