Motion Analysis of Elliptical Gear-Link Mechanism

A single basic mechanism has certain limitations. By using the mechanism combination principle, it is possible to construct a mechanism that satisfies the work requirements and has good motion and dynamic characteristics in order to make full use of the good characteristics of various mechanisms.
A non-circular gear is a variant of a circular gear, that is, its rolling pitch circle has become non-circular, called a pitch curve. Since the radius of curvature of the non-circular gear is a variable, the radial direction from the center of rotation to the meshing point is also a variable. In the process of a pair of non-circular gears, if the center distance of the two gears is kept unchanged, the gear ratio changes according to the position of the meshing node, and the change ratio of the gear ratio is connected by the meshing node at the center. The law of change is determined. This makes it possible to achieve a gear ratio movement using a non-circular gear.
Elliptical gears are the most common form of non-circular gears. By utilizing the above properties and connecting a link mechanism thereon, the time ratio of the working stroke and the idle stroke of the actuator can be changed. It has better rushback characteristics, which greatly improves the work efficiency, and can make the moving speed of the actuator in the working stroke approximately constant speed, reducing shock and vibration.
1 The elliptical gear-link combination mechanism motion analysis is a series combined elliptical gear-link mechanism. The structural dimensions of the two elliptical gears are exactly the same, their center of rotation 1, 2 are respectively set at one focus, and the other focus is represented by Fi, F2, respectively, and a and bc are respectively the long semi-axes of the ellipse. , short semi-axle and half focal length, then the eccentricity of the ellipse = c / a two-wheel meshing node is P. the link mechanism is a crank slider mechanism, the guide of the slider is at the same horizontal line as the center 2 of the wheel 2 Upper, the activity of the link is hinged at the focus of the non-swirl center of the wheel 2.
When the driving wheel 1 rotates through the 0 angle, the driven wheel 2 rotates through the corner.
Using the geometric properties of the ellipse and the basic law of gear meshing, the instantaneous gear ratio of the pair of elliptical gears is determined/21. Where 1 is the driving wheel angular velocity and 2 is the driven wheel angular velocity.
Because any point on the ellipse is equal to the two focal points of the major axis of the first: Male, born in 1977, Master cos 0, can be obtained in AO2PF2 the instantaneous transmission ratio, the crank angle obtained from the law of sines to the positive horizontal direction Similarly, the angle equations of other positions can be obtained, where L1 is the crank length; 2 is the link length; sin can be used to determine the displacement according to the conditions and needs, and then select the appropriate eccentricity, and then the angular velocity A of the driving wheel 1) Determine the angular velocity c2 of the driven wheel, and then obtain the velocity v at each instantaneous position of the slider according to the equation (7), and then calculate the acceleration ac by the numerical differentiation method to draw a graph.
Therefore, the rapid reversal ratio factor k is obtained: and the quick reciprocating ratio of the simple crank slider mechanism is 4k=180.+ If the quick return effect is equivalent to the quick return effect of the elliptical gear-link combination mechanism, That is, k (ellipse) = k (general), a ("general" = ka (ellipse), when a (ellipse X: r / 3 - general) = a (ellipse) = / 3, visible elliptical gear mechanism can be in a In the smaller case, a larger k is achieved, and a=7t/3 is difficult in practical engineering. In addition, in the elliptical gear mechanism, as a decreases, k increases continuously. In the general organization, as a increases, k increases.
Take the elliptical gear-link mechanism of the two ellipse, the semi-major axis length and the half focal length are 50mm, 15mm respectively, the angular velocity A of the driving wheel 1 is 12rad/s, the crank length is 30mm, and the connecting rod length is 70mm. According to the above analysis and The derivation process easily calculates the velocity Vc and acceleration a of the slider corresponding to each instantaneous motion position of the mechanism and fits the calculated data into a curve, as shown.
As can be seen from (a), the speed change and the quick return effect of the member slider C are performed. It can also be seen from (b) that the acceleration value is particularly small in the range of the near-180 range of the driving gear angle 0, that is, the slider C is approximately constant-speed motion. From the previous derivation, the pole angle can be found as a = 56. 60. From this, the rapid recovery ratio is obtained. 2 The characteristics of the quick return characteristic are analyzed. The conclusion and example analysis can be obtained from the elliptical gear linkage mechanism. Make full use of the advantages of the elliptical gear and the linkage mechanism, so that it has better motion characteristics and a larger emergency speed ratio than the linkage mechanism.

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