Barriers to output control of manipulators, both in the interior and at the boundary of accessible output sets, are analyzed using first and second order Taylor approximations of the output in selected directions as functions of manipulator input. The formulation is valid for both planar and spatial manipulators, with open chain and closed loop structures, and accounts for the effects of unilateral constraints on the range of admissible control inputs. Criteria defining curves and surfaces associated with singular output control of manipulators are extended to define normals to such curves and surfaces. It is shown that output velocity in the direction normal to such curves and surfaces must be zero, so they arc barriers to velocity control in the associated manipulator configuration. Second order Taylor expansion of normal output with respect to input parameters yields quantitative information regarding barriers to output position control. Definiteness properties of the resulting quadratic approximation define directions of admissible and inadmissible outputs. Algorithms for automatically computing the associated quadratic forms and eigenvalues that determine their definiteness properties are presented and illustrated using planar examples.