Mechanical linkages, basic objects of mechanical engineering, are a beautiful source of geometric problems. Mathematically one may study a linkage's configuration space, a topological space encoding the totality of all its admissible positions, see 3 or the very readable books 1 and 2. A recent survey of configuration spaces of planar linkages is found in 5. Sossinsky further studies configuration spaces of planar mechanical linkages with one degree of freedom in 4 and he points out that a purely topological approach is not enough but a finer geometric approach is needed.
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