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This paper addresses the problem of determining the instantaneous state of mobility and constraint of a general mechanism or assembly using screw theory. This problem has been attacked before by different methods with varying success. The method presented here is very simple and applies to many types of mechanisms, with one interesting exception. This exception also eludes the Griibler/Kutzbach criterion. The method presented here also improves the accuracy and scope of a method presented by Konkar and Cutkosky. Note to Practitioners - This paper permits an engineer to analyze the state of constraint of an assembly, mechanism, or fixture in order to see if it is properly constrained or whether it contains unwanted overconstraints. Overconstraint can lead to locked-in stress, incorrect tolerance analysis, and lack of robustness in a design. Very small changes in the sizes of parts or positions of locators in fixtures can have large effects on locations of parts, deformation, or internal stresses. Proper constraint is desirable because it provides for only one way to assemble parts. Operator dependency is eliminated, assembly is quick and repeatable, and special skin is not needed.