Tumbler is a toy with a long history, especially loved by children of all ages. Song Wei, a scholar in the Qing Dynasty, wrote in "One is the beginning of the era": "The tumbler began in the Tang Dynasty." According to the records, a long poem "Wine Beard" was presented to show the moral, and in the preface, it was said, "Hu Zhi's patrol, its rotation is also a talent." "This is the prototype of the tumbler. Then it gradually spread to this day and evolved into a toy to amuse children, adding endless fun to children and even adults. Then after studying theoretical mechanics, we can analyze the principle of "tumbler" from the perspective of mechanics and understand its related applications in daily life and production.

First, the principle of mechanics

The most common wine glasses are paper and mud bottom, that is, molded with paper pulp or glued with waste paper, and then made into a semicircular base with mud. After the two are bonded, put paper on the outside and color it. Others use wood as the bottom, and iron blocks and pebbles are fixed in the center of the bottom; There is also a "gourd" made by digging out the inner marrow with a small gourd and filling it with lead; Today, there is a little tumbler made of egg shells and old table tennis balls. All these wine glasses have a common feature: the upper body is a hollow shell, the lower body is a solid hemisphere, and the bottom is round. These characteristics make them have the same basic mechanical structure and can achieve the effect of "not falling down".

1. The main structure of the tumbler

A tumbler is a lightweight hollow shell; The lower body is a solid hemisphere, which is relatively heavy, and the center of gravity of the tumbler is in the hemisphere. There is a contact point between the lower hemisphere and the bearing surface. When the hemisphere rolls on the bearing surface, the position of the contact point will change. A tumbler will always stand on a supporting surface with contact points, and will always be a monopod.

2. Stability of tumbler balance

When the external force acts on the tumbler, it will lose its balance, but after the external force is removed, the tumbler can return to the balance state by itself, which shows that the tumbler has the ability to resist external interference and maintain balance, which is the stability of balance. The formation of this anti-interference and balance-keeping ability depends on the stress of the tumbler.

3. There are three kinds of forces on the tumbler.

First, the stress of tumbler balance. On the desktop, the tumbler is affected by two external forces: one is gravity G, the attraction of the earth to the tumbler; The other is the supporting force, the reaction force of the desktop to the bovine sphere. According to the equilibrium condition of an object, as long as the two forces are equal in magnitude and opposite in direction and act on a straight line, the tumbler can maintain a state of balance.

Second, the stress of tumbler tilt. When the tumbler leans, it is acted by two moments. We call the action of external force interference, and external force forms interference torque. The other is called resistance moment, which is formed by its own gravity. Originally, the tumbler was upright, but due to the action of external force, the external force produced a moment at the contact point between the tumbler and the finished surface, which made the tumbler tilt and broke the original balance. In addition, gravity does not produce moment, because the tumbler is upright, the line of action of gravity and the fulcrum are on the same line, and the moment is zero. Due to the external force, the tumbler leans, the hemisphere rolls to one side, and the contact point moves with it, forming a new contact point, that is, a new fulcrum. At this time, the line of action of gravity and the original fulcrum are not in a straight line, thus forming a moment, which is the resistance moment. It is precisely because of the formation and development of resistance moment that the interference of external force is resisted and prevented. The direction of resistance moment is just opposite to that of disturbance moment. At the same time, with the increase of the tilt angle of the tumbler, the offset of the center of gravity line of action is also increasing, and the magnitude of the resistance moment is also increasing. When the resistance moment is equal to the disturbance moment, the tumbler will enter a new equilibrium state-inclined equilibrium state, and the interference of external forces will stop. Therefore, after the tumbler is disturbed by external forces, the original balance is destroyed, but a new balance is formed, and the tumbler can keep the balance one after another. Although the ways of balance are different, the essence of balance remains unchanged, that is, dynamic balance.

Third, the pressure of tumbler recovery. From the perspective of potential energy, an object with low potential energy is relatively stable, and this object will definitely become a state with low potential energy. When the tumbler falls, most of the base with concentrated center of gravity rises, which leads to the increase of potential energy, so the tumbler should return to its original position. From the lever principle, when a tumbler falls, the center of gravity is always at the end. No matter where the fulcrum is, although the arm of the base is short, the moment = force * arm of force, and the tumbler will still return to its original position because of the large moment at the other end of the base. In addition, the bottom of the tumbler is round, so the friction is small, which is convenient for the tumbler to return to its original position.

In the whole process above, establishing a new balance is the main problem, because only in this way can we resist the interference of external forces, while restoring some balance is a secondary problem, because the interference of external forces has been removed at this time. In the whole process, the tumbler always maintains the nature of balance, that is, "the stability of balance"

4. Summary of mechanical principles

To sum up, the main point of this principle lies in: making the line of action of gravity deviate from the fulcrum, and making gravity produce a moment on the fulcrum, that is, the resistance distance. With the increasing tilt angle of the tumbler, the offset of the line of gravity action increases, and the resistance moment also increases, finally achieving the balance with the external force moment. This is how the tumbler's ability to resist external interference and maintain balance is formed.

Second, the application of the tumbler principle

The principle of tumbler mechanics is widely used in people's production and life. The tumbler principle not only brings fun to people in architectural design, toy manufacturing, daily necessities, automobile structural design, physical fitness, etc., but also makes full use of the fact that "light and heavy objects are more stable because of their lower center of gravity", greatly improving the common tumbler toy sandbags in various facilities.

As for toys, daily necessities and sports equipment, as shown in the above picture, the tumbler cup is a cup-shaped container, which is characterized by a hollow and thickened round bottom, with the weight concentrated in the center of the cup bottom and a small contact surface at the bottom, so that the cup can shake when moving. Tumbler sandbag is a common physical exercise equipment, which relies on its iron chassis to stabilize the center of gravity, so that most of the weight is concentrated in a very low position, and the upper part is only soft foam or other substances, even if it is subjected to strong external force, the sandbag will not topple. There are also electric fan bases, microphone stands, bus stop signs and so on. Using tumbler principle to improve the maneuverability of Xi Little Wild Goose Pagoda.

In terms of architectural design and automobile structure, as shown in the above figure, the Little Wild Goose Pagoda in Xi 'an, which has a history of 1300 years, has experienced dozens of earthquakes, and the historical earthquake caused it to crack and recombine three times, especially in an earthquake in 1556, which changed its complete height from 56 meters to its current height of 43 meters, but so far its tower has not tilted, which is surprising. What is the reason for it? Around the tower foundation of Little Wild Goose Pagoda, the underground with a diameter of about 60 meters gradually deepens from the outside to the center of the tower foundation. There are several layers of bluestone in the middle, and the tower foundation is built with bricks. At the same time, there is a three-meter-high platform foundation on the ground, and the tower body is directly above it. This makes the tower look like a tumbler as a whole, so it has not been seriously ill for thousands of years. When designing and manufacturing a car, by increasing the proportion of the chassis to the weight of the whole car body, the center of gravity of the car is lowered, so that the car can maintain a balanced state when braking or turning in an emergency, avoiding the occurrence of traffic accidents that endanger life safety, and improving the handling performance of the car by using the tumbler principle.

Besides, the experiment of "Rolling on a Cone" that we saw in the Science and Technology Museum, the tightrope walker with a balance bar and Tai Ji Chuan's semi-squat posture all used the tumbler principle.