Abstract
We present a theoretical and algorithmic method for describing the singularity locus for the endpoint map of any serial manipulator with revolute joints. As a surface of revolution around the first joint, the singularity locus is determined by its intersection with a fixed plane through the first joint. The resulting plane curve is part of an algebraic curve called the singularity curve. Its degree can be computed from the specialized case of all pairs of consecutive joints coplanar, when the singularity curve is a union of circles, counted with multiplicity two. Knowledge of the degree and a simple iterative procedure for obtaining sample points on the singularity curve lead to the precise equation of the curve.
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