We define planar linkages and present a class of spider-like planar linkages. We define the configuration space of robotic devices and characterize the configuration space for symmetric spider-like linkages. We show that the space is connected and, using the implicit function theorem and cellular decompositions, we prove that it is a closed surface for generic parameters and calculate its genus.
We generalize spider-like linkages to asymmetric leg configurations and present their configuration space. We give a general (combinatorial) formula for the genus in regular cases, which nicely recovers the known symmetric case.
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