Abstract
The configuration spaces (c-space) of mechanisms and robots can in many cases be presented as an algebraic variety. Different motion modes of mechanisms and robots are usually irreducible components of the c-space and their union the whole c-space. Singularities of the variety correspond usually (but not necessarily) to intersections of irreducible components/motion modes of the configuration space. If the mechanisms purpose is to perform several tasks and it contains closed kinematical loops then the tasks are usually different motion modes of the mechanism connected by singularities in c-space. This means that in order to switch the mechanism from one task to an other the mechanism needs to go through a singularity in c-space. Now there are different kinds of singularities and our main purpose here is introduce concepts and tools which allows to investigate and design the properties of these singularities. The concepts related to singularities and their properties are well understood in algebraic geometry and the advances in computational algebraic geometry and commutative algebra allows us actually investigate and design these properties if necessary.
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