Mechanical models and the mobility of robots and mechanisms

SUMMARY 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. 1. Introduction Mechanism structure is traditionally presented as being defined by entities such as bodies (called sometimes kinematic elements) and joints. 1,14,15 This is a structural representation that is fundamental to many of the well known mobility formulae thoroughly and critically presented by Gogu in ref. [2]. The structure of mechanisms has been studied in the past, especially from the synthesis point-of-view, with the goal of identifying methods for composing mechanisms capable of performing various prescribed functions. The structure based on the classification of planar kinematic groups proposed by Assur in ref. [3] is still a valuable tool for the structural synthesis of mechanisms; however, it is not directly applicable for mobility calculation. One interesting feature in applying Assur's kinematic groups is that the composition of mechanisms has to be made by successively adding groups to the driving elements, although not simultaneously, to avoid errors in defining the closed loops. This principle is useful in the particular case of multi-loop mechanisms, which are addressed by the method proposed in the present paper as well. According to Gogu, 2 mobility (M) is used to verify the existence of a mechanism (M > 0), to indicate the number of independent parameters in both kinematic and dynamic models and to …