Mechanical models and the mobility of robots and mechanisms

Mobility is a fundamental parameter of mechanisms expressing in a qualitative manner their kinematic and dynamic properties. The mobility formulae presented in literature take into consideration some of the structural entities, such as bodies, joints, constraints, closed loops, and space characteristics; however, the specific mechanical model that has traditionally been at the origin of the mobility criteria themselves is incompletely specified and, even then, only implicitly. In this paper, we propose a classification of the mobility criteria based on the known dynamic models. While all known mobility criteria have been associated with a specific dynamic model, some particular, less used dynamic models (like natural coordinates and multi-particle models) suggested new mobility criteria models. The associated mechanical model for each category of mobility criteria allows a qualitative assessment of the kinematic and dynamic sets of equations to be formulated in later stages of analysis. A simple multi-loop mechanism is taken as an example just to illustrate the mobility calculation and qualitative assessment of the kinematic and dynamic models in each case. Based on the proposed classification of the mobility formulae, an assessment is made with particular regard to their applicability to overconstrained mechanisms.