Modeling of “Concentric Drum” Tilt Angle Model Based on Mechanical Analysis

Abstract

“Concentric drums” is a group cooperation project, which requires better tacit understanding between the team members. At the same time, the force exerted on the rope can be accurately controlled, which contains a more complex mechanical relationship. In reality, it is impossible for the players to make force synchronously and the force is difficult to control accurately, which can be attributed to the following two situations: first, there is no situation in which the team has no force in advance but the size is not uniform when the force is applied, so the drum surface is at the level position at the moment when the players start to make force; second, there are individual players who make force in advance, and the strength of each player is different, resulting in the tilted of the drum surface when the players are exerting force. In the first case, the vertical component forces of two opposite members in the same straight line are combined into one force, then the moment of each resultant force is calculated and the vector sum is performed, the angular acceleration is solved according to the rigid body mechanics formula, and finally the tilt angle is calculated by using the time brought in by double integration. In the second case, firstly, consider that some members of the team will start the force ahead of time, and those members who do not start the force will be brought into the model of case I according to the force value of 0 to obtain tilt angle 1, Secondly, the force of the remaining team members is considered. At this time, based on the inclined plane, the force of each member after treatment is brought into the model of case I again to get the inclined angle tilt angle 2 caused by different forces. After two inclinations, three planes with different angles can be obtained. The angle between the final plane and the original plane can be calculated by using the space coordinate normal vector, that is, the bevel angle of horizontal inclination of the drum surface.