Computer aided design of modular fixtures for machining, assembly and inspection processes strongly depends on software tools to ensure correct location of parts in the workspace. From a geometric viewpoint, the analysis of deterministic positioning checks that a fixture is able to correctly align a part to the machine reference frame. Several methodologies among those proposed in literature use results of the screw theory previously applied to the kinematic study of mechanisms. In this work, further properties of the screw theory formalism are highlighted so that its information content could be better exploited. This is accomplished by applying the singular value decomposition to the matrix defining the configuration of the geometric constraints acting on a part. This paper shows how the results of the decomposition can be interpreted.