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Proceedings/Recueil Des Communications Année : 2008

Stability of Singularities of a Kinematical Chain

Résumé

Since few years, the geometry of singularities of kinematical chains is better known. Using both Lie group theory and concepts of differential or analytic geometry, we already classified these singularities according to the nature of the function f associated to the chain (f is a product of exponential mappings of a Lie group). In the most general case, the tangent cone at a singularity has been explicitely given. Here, a different (and more difficult) aspect of the problem is studied. The concrete realisation of a kinematical chain is never perfect. That means that the vectors of the Lie agebra defining the function f are not exactly those of the chain: they are deformed. What happens for the singularities in this case? Are they remaining or do they disappear during the deformation? First, the mechanical problem is analysed as this of the stability of the fuction f and mathematical tools concerning stable mappings are given. Stability of a mapping means that the orbit of f under the action of diffeomorphisms in the source and in the target is an open set and its infinitesimal equivalent formulation is noted the inf-stability. Then we prove that the set of singularities of first class itself is a sbmanifold and we analyse a condition of normal crossing of the restriction of f to its manifold of singularities. Applying a result of the general theory, the stability of f is analysed.
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Dates et versions

hal-04367123 , version 1 (29-12-2023)

Identifiants

Citer

Jean Lerbet. Stability of Singularities of a Kinematical Chain. ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, ASMEDC, pp.611-616, 2008, ⟨10.1115/DETC2005-84126⟩. ⟨hal-04367123⟩
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