NOVEL METHOD OF REALIZING THE OPTIMAL TRANSMISSION OF THE CRANK-AND-ROCKER MECHANISM DESIGN
Abstract: A novel method of realizing the optimal transmission of the crank-and-rocker mechanism is presented. The optimal combination design is made by finding the related optimal transmission parameters. The diagram of the optimal transmission is drawn. 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. The method possesses the main characteristic. That it is to achieve the optimal transmission parameters under the transmission angle by directly choosing in the diagram, according to the given requirements. The characteristics of the mechanical transmission can be improved to gain the optimal transmission effect by the method. Especially, the method is simple and convenient in practical use.
Keywords：Crank-and-rocker mechanism, Optimal transmission angle, Coefficient of travel speed variation
INTRODUCTION
By conventional method of the crank-and-rocker design, it is very difficult to realize the optimal combination between the various parameters for optimal transmission. The figure-table design method introduced in this paper can help achieve this goal. With given conditions, we can, by only consulting the designing figures and tables, get the relations between every parameter and another of the designed crank-and-rocker mechanism. Thus the optimal transmission can be realized.
The concerned designing theory and method, as well as the real cases of its application will be introduced later respectively.
ESTABLISHMENT OF DIAGRAM FOR OPTIMAL TRANSMISSION DESIGN
It is always one of the most important indexes that designers pursue to improve the efficiency and property of the transmission. The crank-and-rocker mechanism is widely used in the mechanical transmission. How to improve work ability and reduce unnecessary power losses is directly related to the coefficient of travel speed variation, the oscillating angle of the rocker and the ratio of the crank and rocker. The reasonable combination of these parameters takes an important effect on the efficiency and property of the mechanism, which mainly indicates in the evaluation of the minimum transmission angle.
The aim realizing the optimal transmission of the mechanism is how to find the maximum of the minimum transmission angle. The design parameters are reasonably combined by the method of lessening constraints gradually and optimizing separately. Consequently, the complete constraint field realizing the optimal transmission is established.
The following steps are taken in the usual design method. Firstly, the initial values of the length of rocker and the oscillating angle of rocker are given. Then the value of the coefficient of travel speed variation is chosen in the permitted range. Meanwhile, the coordinate of the fixed hinge of crank possibly realized is calculated corresponding to value .
-
- Length of bars of crank and rocker mechanism
As shown in Fig.1, left arc is the permitted field of point . The coordinates of point are chosen by small step from point to point .
The coordinates of point are
(1)
(2)
where , the step, is increased by small increment within range(0,). If the smaller the chosen step is, the higher the computational precision will be. is the radius of the design circle. is the distance from to .
(3)
Calculating the length of arc and , the length of the bars of the mechanism corresponding to point is obtained[1,2].
1.2 Minimum transmission angle
Minimum transmission angle (see Fig.2) is determined by the equations[3]
(4)
(5)
(6)
where ——Length of crank(mm)
——Length of connecting bar(mm)
——Length of rocker(mm)
——Length of machine frame(mm)
Firstly, we choose minimum comparing with . And then we record all values of greater than or equal to and choose the maximum of them.
Secondly, we find the maximum of corresponding to any oscillating angle which is chosen by small step in the permitted range (maximum of is different oscillating angle and the coefficient of travel speed variation ).
Finally, we change the length of rocker by small step similarly. Thus we may obtain the maximum of corresponding to the different length of bars, different oscillating angle and the coefficient of travel speed variation .
Fig.3 is accomplished from Table for the purpose of diagram design.
It is worth pointing out that whatever the length of rocker is evaluated, the location that the maximum of arises is only related to the ratio of the length of rocker and the length of machine frame /, while independent of .
DESIGN METHOD
-
- Realizing the optimal transmission design given the coefficient of travel speed variation and the maximum oscillating angle of the rocker
The design procedure is as follows.
(1) According to given and , taken account to the formula the extreme included angle is found. The corresponding ratio of the length of bars / is obtained consulting Fig.3.
(7)
(2) Choose the length of rocker according to the work requirement, the length of the machine frame is obtained fr
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英文原文：
NOVEL METHOD OF REALIZING THE OPTIMAL TRANSMISSION
OF THE CRANK-AND-ROCKER MECHANISM DESIGN
Abstract: A novel method of realizing the optimal transmission of the crank-and-rocker mechanism is presented. The optimal combination design is made by finding the related optimal transmission parameters. The diagram of the optimal transmission is drawn. 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. The method possesses the main characteristic. That it is to achieve the optimal transmission parameters under the transmission angle by directly choosing in the diagram, according to the given requirements. The characteristics of the mechanical transmission can be improved to gain the optimal transmission effect by the method. Especially, the method is simple and convenient in practical use.
Keywords：Crank-and-rocker mechanism, Optimal transmission angle, Coefficient of travel speed variation
INTRODUCTION
By conventional method of the crank-and-rocker design, it is very difficult to realize the optimal combination between the various parameters for optimal transmission. The figure-table design method introduced in this paper can help achieve this goal. With given conditions, we can, by only consulting the designing figures and tables, get the relations between every parameter and another of the designed crank-and-rocker mechanism. Thus the optimal transmission can be realized.
The concerned designing theory and method, as well as the real cases of its application will be introduced later respectively.
ESTABLISHMENT OF DIAGRAM FOR OPTIMAL TRANSMISSION DESIGN
It is always one of the most important indexes that designers pursue to improve the efficiency and property of the transmission. The crank-and-rocker mechanism is widely used in the mechanical transmission. How to improve work ability and reduce unnecessary power losses is directly related to the coefficient of travel speed variation, the oscillating angle of the rocker and the ratio of the crank and rocker. The reasonable combination of these parameters takes an important effect on the efficiency and property of the mechanism, which mainly indicates in the evaluation of the minimum transmission angle.
The aim realizing the optimal transmission of the mechanism is how to find the maximum of the minimum transmission angle. The design parameters are reasonably combined by the method of lessening constraints gradually and optimizing separately. Consequently, the complete constraint field realizing the optimal transmission is established.
The following steps are taken in the usual design method. Firstly, the initial values of the length of rocker and the oscillating angle of rocker are given. Then the value of the coefficient of travel speed variation is chosen in the permitted range. Meanwhile, the coordinate of the fixed hinge of crank possibly realized is calculated corresponding to value .
-
- Length of bars of crank and rocker mechanism
As shown in Fig.1, left arc is the permitted field of point . The coordinates of point are chosen by small step from point to point .
The coordinates of point are
(1)
(2)
where , the step, is increased by small increment within range(0,). If the smaller the chosen step is, the higher the computational precision will be. is the radius of the design circle. is the distance from to .
(3)
Calculating the length of arc and , the length of the bars of the mechanism corresponding to point is obtained[1,2].
1.2 Minimum transmission angle
Minimum transmission angle (see Fig.2) is determined by the equations[3]
(4)
(5)
(6)
where ——Length of crank(mm)
——Length of connecting bar(mm)
——Length of rocker(mm)
——Length of machine frame(mm)
Firstly, we choose minimum comparing with . And then we record all values of greater than or equal to and choose the maximum of them.
Secondly, we find the maximum of corresponding to any oscillating angle which is chosen by small step in the permitted range (maximum of is different oscillating angle and the coefficient of travel speed variation ).
Finally, we change the length of rocker by small step similarly. Thus we may obtain the maximum of corresponding to the different length of bars, different oscillating angle and the coefficient of travel speed variation .
Fig.3 is accomplished from Table for the purpose of diagram design.
It is worth pointing out that whatever the length of rocker is evaluated, the location that the maximum of arises is only related to the ratio of the length of rocker and the length o
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