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ABSTRACT
In general mechanics, binding equations illustrate the constraints on generalized coordinates caused by contacts between solids. Together with the equations of dynamics, they belong to movement equations. A certain systematic process used in most simulation software allows for writing these binding equations. This article presents the unfolding of the process and the implementation of these equations. Forces in binding are then detailed (in particular contact force torsors, absolute parameterization and relative parameterization).
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Michel FAYET: Emeritus University Professor - INSA (Lyon)
INTRODUCTION
We have seen , referring to the general form of the equations of motion, states that in addition to the equations of dynamics, it is also necessary to know the equations of linkage. This is what we do here, keeping the two options used in the software: absolute parameterization or relative parameterization, and examining the linking equations of a geometric nature (which only concern the generalized coordinates themselves), those derived to order 1, then to order 2.
The way to write these equations in their first- and second-order derivative forms is based on a systematic procedure used in virtually all simulation software . This procedure has the advantage of giving a directly usable physical meaning to the Lagrange multipliers associated with these equations. The latter represent, in effect, the components of the force torsor in the links. This is why their analysis is considered immediately afterwards.
Before turning to the developments proposed in this presentation, we advise the reader to consult the dossier : "Simulation of mechanisms – Topology, geometry, kinematics", in which the basic principles concerning the particular form of the equations of motion, as well as the geometry and kinematics of multi-body systems, are developed.
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