A broadly applicable formulation for determining the crossability of singul
ar surfaces and curves in the workspace of serial robotic manipulators is p
resented. Singular surfaces and curves al-e analytically determined using n
ullspace rank-deficiency criteria of the mechanism's constraint position Ja
cobian. Imposed joint limits in terms of inequality constraints are taken i
nto account in the formulation. Directions of admissible normal movements o
n a surface or curve are established from the analysis of the normal curvat
ure of singular surfaces. The normal curvature of a parametric surface used
in this formulation, is determined from the first and second fundamental f
orms adapted from differential geometry. Definiteness properties of a quadr
atic form developed from the acceleration analysis determine admissible nor
mal movements. For singular surfaces resulting from active joint constraint
s, definiteness properties are not enough and supplementary criteria are ne
cessary. Two additional criteria are derived. This paper is a complete trea
tment of the problem of determining whether a singular surface/curve in the
workspace is crossable. Planar and spatial numerical examples are presente
d to illustrate the formulation. [S1050-0472(00)01301-5].