We are an __folding umbrellas factory__, here is a brief introduction to the mechanics of umbrellas.

The umbrella structure may seem simple, but in fact it contains ingenious mechanical principles. The specific analysis is as follows.

The umbrella has a radially symmetrical structure around the handle. We draw a longitudinal section of the umbrella along a pair of ribs, as shown in Figure 2. The points marked by letters in the figure are connected by hinges. Assuming that the equivalent total weight of the umbrella surface, rib and spring is G, if the umbrella has n ribs, the pressure on each rib is equivalent to hanging a weight of G at the M and N points in the figure. /n heavy objects.

In order to facilitate analysis, the above figure is further simplified, as shown in Figure 3. Move the assumed weight to points A and B, so that only the longitudinal force of the umbrella rib can be considered, without considering the transverse stress of the umbrella rib.

Hanging a weight of G/n at point M is equivalent to hanging a weight of G'/n at point A. This change is equivalent to the spring force. At this time, the spring is in a compressed state, and the elastic force is set as F. F acts on both points C and D, and the directions are shown in Figure 3. F is decomposed into two forces F1 and F2 along the direction of rib CA and CB at point C, and two forces of F3 and F4 are decomposed along the direction of rib AD and BD at point D.

Since α > β, F1 > F3.

F1 and F3 are transmitted to point A along the ribs CA and DA, and F2 and F4 are transmitted to point B along the ribs CB and DB. The force analysis of point A is carried out first, and the force of point A is shown in Figure 4. (In the figure, F0 is the pulling force of the OA segment rib to point A.)

The four forces at point A are decomposed orthogonally along the horizontal and vertical directions, respectively. (Assume that the horizontal direction to the left is the positive direction, and the vertical direction upward is the positive direction.)

In order to open the umbrella, point A must move to the upper left, so the horizontal and vertical forces of point A are required to be greater than zero.

The force analysis of point B is the same as that of point A.

In the process of opening the umbrella, the spring gradually elongates, the two points C and D move upward along the umbrella handle, and the umbrella ribs AC and BC change from vertical to horizontal.

The range of variation in spring length, initially (AD-AC), and finally:

Therefore, it is required that the spring must have an expansion and contraction amount S, and its stubborn coefficient must be large enough.

Theoretically, after the umbrella is closed, all the ribs are vertical, and α, β, and γ are all 0. At this point, F cannot open the umbrella no matter how big it is. In fact, although the umbrella is closed, the two points A and B cannot completely fall on the handle OD, so the umbrella rib cannot be completely vertical. As long as the initial value of F is large enough, the umbrella can be opened.

It can be seen from the above analysis that the special structure composed of the umbrella rib and the spring is the key for the spring to bootstrap and the umbrella to open. Although the rib and umbrella surface exert pressure on the spring, they also support the spring. As long as the spring's elasticity is large enough, it can lift itself up and open the umbrella.

We have many types of umbrellas, such as the __compact travel umbrella__. Welcome to our website!