The matching relationship between the number of link of assur group and the number of prismatic pair for the mechanism with all prismatic pair is introduced

and the configuration of assur group for the mechanism with all prismatic pair is determined.The relationship between the number of connecting rod for each element

the number of exterior shift pair and the ring number for assur group are studied by using numerical calculation method of combination of linkage

and one concept of characteristic value of assur group is introduced.The theory foundation for expanding the configuration of assur group of mechanism with all prismatic pair is established

and 15 types of configurations

from 1 to 4 assur group and its special configuration are determined by using the topological graphs of assur group rapidly

and the method for determining configurations is useful for constructing n-assur group.