Singularities (cont.) • Two classes of singularities: – Workspace boundary singularities – Workspace interior singularities • Robot in singular configuration: it has lost one or more degrees of freedom in Cartesian space

Classifying Singular Points Our goal is to extend the method already developed for solving P ( x) y Q( x) y R ( x) y 0 near an ordinary point so that it applies to the neighborhood of a singular point x0. To do so, we restrict ourselves to cases in which singularities in Q/P and R/P at x0 are not too severe, that is, to what might be called “weak singularities.” It turns out that the appropriate conditions to distinguish weak Q( x) 2 R( x) singularities lim x x are is finite and lim x x is finite. x x0 0 P( x) x x0 0 P( x)