The absence of constraints is one of the major limitations in current Virtual Reality (VR) systems for precise 3D interactions and precise solid modelling in VR environments. In this paper, constraints are incorporated into the VR environment for acquiring precise constraint-based manipulations that are used to perform precise solid modelling in an intuitive manner. Constraint-based manipulations are accompanied with automatic constraint recognition and precise constraint satisfaction and are realized by allowable motions for precise 3D interactions in the VR environment. The allowable motions are represented as a mathematical matrix for conveniently deriving allowable motions from constraints. A procedure-based degree-of-freedom incorporation approach for 3D constraint solving is presented for deriving the allowable motions. A rule-based constraint recognition engine is developed for both constraint-based manipulations and implicitly incorporating constraints into the VR environment.