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In this paper a new method for the dynamic analysis of three-dimensional mechanisms is presented. This method is based on the use, as mechanism coordinates, of Cartesian coordinates and components of some points and vectors rigidly attached to every element. With these coordinates the constraint equations are very easily formulated. A constant mass matrix has been derived for an element with two points and two vectors. Two simple and efficient methods to establish the dynamic equilibrium equations are presented. The use of the singular value decomposition is also included. Finally some comparative results are presented.