According to the geometric apollonius’theorem

the new concept of "auxiliary circle" is presented.The fact that the falling area of hydraulic-pipe fixed-hinge center is the "circle" is discovered

under the conditions of l3

Ψ

λ and μ.The concepts of typeⅠ

type O and type Ⅱ and their structural characteristics as well as ordinary graphic synthesis method are diven

and the changing law of beginning center-distance lO1C1

beginning length l12（0）

offset distance e

frame length l4

beginning assembling angle σ and other parameters relative to O1 is discussed.