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This paper deals with the application of Lie Algebra to the mobility analysis of kinematic chains. It develops an algebraic formulation of a group‐theoretic mobility criterion developed recently by two of the authors of this publication. The instantaneous form of the mobility criterion presented here is based on the theory of subspaces and subalgebras of the Lie Algebra of the Euclidean group and their possible intersections. It is shown using this theory that certain results on mobility of over‐constraint linkages derived previously using screw theory are not complete and accurate. The theory presented provides for a computational approach that would allow efficient automation of the new group‐theoretic mobility criterion. The theory is illustrated using several examples. © 2003 Wiley Periodicals, Inc.