This research combines physics-based and constraint-based approaches for virtual assembly simulations where geometric constraints are created or deleted within the virtual environment at runtime. In addition, this research provides a solution to low clearance assembly by utilizing B-Rep data representation of complex CAD models for accurate collision/physics results. These techniques are demonstrated in the SHARP software (System for Haptic Assembly and Realistic Prototyping). Combining physics-based and constraint-based techniques and operating on accurate B-rep data, SHARP can now assemble parts with 0.001% clearance and can accurately detect collision responses with 0.0001mm accuracy. Case studies are presented which can be used to identify the suitable combination of methods capable of best simulating intricate interactions and environment behavior during manual assembly.