In this paper the topological structure of multi-body system and their low-order body arrays,and basic concepts of characteristic matrixes and their composing methods are presented,basic rules of having-error kinematics of multi-body system are analyzed,891E gear measurement center taken as an example,volumetric geometirc errors of gear measurement center based on characteristic matrixes are researched,it provides a kind of ideal method of model building for the precision analysis and geometric errors of gear measurement center.