This paper introduces a new analytical formula for designing a planar rank and rocker mechanism according to travel velocity-ratio coefficient.

Via introducing the "Auxiliary Circle Ⅰ" and "Auxiliary Circle Ⅱ" , the paper contributes a new way to improving the traditional graphic method for designing the crank-rocker mechanism in according with the travel velocity-ratio coefficient K , and makes the design process more simple and direct.

This paper makes deep and systematic researches on the theoretical task according to travel velocity-ratio coefficient K and allowable transmission angle,and draws some conclusions of guiding significance for the analysis and synthesis of type Ⅰ as well as type Ⅱ planar crank and rocker mechanisms.

The mechanism offset double crank slider not only has the characteristic of super quick-return (k>3),but also has variety time ratio.

The time ratio of this mechanism is changed only the setting position is changed, when the sizes of all links are determined.

By means of assistant circles, this paper solved the problem of designing planar crank slide block mechanism on the condition of time ratio, additional with the crank length L 1 or the connecting rod length L 2 .

Tha paper discusses how to design crank and rocker machanism on exilary circled graphic solution with the given travel velocity ratio coefficient K,angle between extreme positions of the rocher ψ,the length of the rocher l_3(or the length of the rack l_4),the length of the crank l_1(or the length of the link pole l_2),and so on.

Adopting the differential method,taking the allowable minimum transmission angle[γ] of the mechanism as the foundation of design and using the travel speed ratio coefficient of mechanism as the functi.

Based on literature,this article has deduced the calculation formula of the maximum value K_(max) of travel speed ratio coefficient in the crank and rocker mechanism with the characteristic of the swift-return movement,when a given minimum driving angle value of is allowed.

That is a method in accordance with the minimum transmission angle γmin and other known conditions(travel speed ratio coefficient k,rocker swinging angle φ and one of the rod lengths among the linkage) and adopting the analytical geometry method to establish a series of relationship formula and to determine the lengths of other rods of this mechanism.

A method to design the planar linkage mechanism according to the coefficient of travel speed variation K and the allowable drive angle[γ] was established based on a combination of diagrammatic method and analysis method.

In the diagram,the relation among minimum transmission angle,the coefficient of travel speed variation,the oscillating angle of the rocker and the length of the bars is shown,concisely,conveniently and directly.

As an example , the innovative design of full hinge large advance-to return-time ratio mechanism is elaborated, and which has important application value.