This paper demonstrates fundamental problems with dexterity measures f
ound throughout the robotics literature and offers a methodology for c
orrecting those problems. Measures of robot dexterity derived from eig
envalues, eigenvectors, similarity transformations, singular-value dec
ompositions and the Moore-Penrose inverse of the manipulator Jacobian
do not have invariant physical meaning. The paper presents manipulabil
ity ellipsoids and manipulability screw-subspaces for both redundant a
nd nonredundant manipulators.