Analytic geometry and singularities of mechanisms. (English) Zbl 0910.70004
Summary: We analyze the geometrical structure of the set \(M\) of configurations of a mechanism. Using Lie groups language and without any hypothesis of regularity, one can attach to this set a structure of an analytic variety. We then compute the tangent cone at each point of this set without introducing any coordinates, and we describe the structure of \(M\) whatever the singularity may be. Finally, some examples are presented.
MSC:
70B15 | Kinematics of mechanisms and robots |
70G45 | Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics |