This paper introduces horizontal shaft of vertical mill is changed into statically indeterminate beam supported by three points used of virtual constraint in the reforming process of RE1 vertical mill transmission device of 500mm hot strip mill production line in Laiwu iron and steel general works,thus the strength,rigidity and transmission stability of this mill are increased.

The concepts of “dynamic substructure method”and “virtual constraint”are applied to get the dynamic response of this kind of mechanic model.

The paper discusses the criterion for deciding virtual constraint and the sufficient and necessary conditions for the constraint existing in mechanisms.

The analysis and calculation of virtual restraint;

According to definition of virtual restraint,this paper analyses several forms and necessary and sufficient conditions of the existence of virtual restraints in mechanism,and presents the procedures for the judgment of virtual restraint and the calculating methods for the number of virtual restraints.

Establishes a force model for the internal parallel move gear transmission with mulriple redundant constraints.

Finally, a new approach for solving the deformation constraint graph is given, which is based on compound node and virtual constraint.

Furthermore, the restriction index Ri, the ratio between real and theoretical averaged cross-sectional solid holdups in the particle back-mixing region section, was defined to quantitatively show the restric.