Abstract: In order to achieve the automation of dimensioning completeness testing with cyclic constraints, determination of the cyclic constraints is converted into the recognition problem of rigid solid(RS), and a method of three-dimensional dimensioning completeness testing based on rigid body recognition is proposed. Firstly, a concept of located primitive(LP) is introduced, and the selection mechanism of LP group is established based on the intersection of LP's degree of invariance. Subsequently, on the basis of LP group, the recognition method of RSs is proposed based on the method of locus intersection. And then, the RSs are merged by using the fixation of the equivalent group of LPs, with the addition of virtual dimensions. Four types of dimensions completeness states are analyzed according to the merged status of RS and the used status of dimensions. Finally, a model with cyclic constraints and redundant dimensions is taken as an example to demonstrate the completeness testing of dimensions, and verify the effectiveness and stability of the approach.