CN110910704B - Training system for concentric drums - Google Patents
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- CN110910704B CN110910704B CN201911243137.9A CN201911243137A CN110910704B CN 110910704 B CN110910704 B CN 110910704B CN 201911243137 A CN201911243137 A CN 201911243137A CN 110910704 B CN110910704 B CN 110910704B
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- G09B9/00—Simulators for teaching or training purposes
Abstract
The invention discloses a training system of concentric drums, which adopts the technical scheme that: the device comprises a concentric drum and a ball, wherein the concentric drum is provided with a force sensor for detecting the force of the ball impacting the surface of the concentric drum; the concentric drums are uniformly connected with a plurality of traction ropes at intervals in the circumferential direction, and tension sensors are mounted on the traction ropes; the force sensor and the tension sensor send detected data to computer equipment; the computer equipment is used for simulating the training process and analyzing an optimal guidance scheme. According to the invention, by guiding the action of the team member, the training time can be shortened, and a good training effect can be obtained.
Description
Technical Field
The invention relates to the field of practical training systems, in particular to a practical training system of a concentric drum.
Background
The "concentric drums" are a common group exercise program. This project mainly is the two-sided drum of application one side cow hide, and fixed many ropes in the middle of the drum body, the fixed point of rope on the drum body is evenly distributed along the circumference, and the length of every rope is the same. Each team member pulls one rope to keep the drumhead level. At the beginning of the project, the ball falls vertically from above the center of the drumhead, and players work in tandem to pitch the ball over the drumhead in a rhythmic manner. In the process of bumping, players can only grasp the tail end of the rope and cannot touch the drum or other positions of the rope.
The mass of volleyball and double-sided drum used in the project is constant and cannot be changed randomly, the number of people participating in the project is not less than 8, and the minimum distance between players is not less than 60 cm. When the event starts, the ball must be no less than 40cm from the drumhead and the game can continue. The goal of the game is to make the number of successive ball kicks as large as possible.
Currently, concentric drum program training is usually a number of attempts between players to achieve as many pitch numbers as possible. This method is time consuming and is susceptible to factors such as the timing and strength of force exerted by the team members. The player is after carrying out the action of running top the ball many times, and the slope of certain degree can appear in the drumhead, needs the player to adjust the stay cord mode, if training time is shorter between the player, then can be because of the inexperience does not know the condition of how to adjust, lead to the ball to fall to the ground to make training time extension. Moreover, the concentric drum project has high requirement on the cooperation capability among the team members, and the effect of simple repeated training is not obvious.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a concentric drum training system which guides the actions of team members, can shorten the training time and obtains a good training effect.
The invention adopts the following technical scheme:
a training system of a concentric drum comprises the concentric drum and a ball, wherein the concentric drum is provided with a force sensor for detecting the force of the ball impacting the surface of the concentric drum; the concentric drums are uniformly connected with a plurality of traction ropes at intervals in the circumferential direction, and tension sensors are mounted on the traction ropes; the force sensor and the tension sensor send detected data to computer equipment; the computer equipment is used for simulating the training process and analyzing an optimal guidance scheme.
Further, the simulation method of the computer device comprises the following steps:
(1) establishing an optimal cooperation model by taking the constraint conditions that the friction force and the mass of the traction rope are ignored and the traction rope does not have elasticity; solving the optimal cooperation model to obtain the optimal height of the concentric drum;
(2) establishing a force application time and force model of the inclination angle of the concentric drum by taking the position of the gravity center of the concentric drum not to change as a constraint condition; solving the inclination angle of the concentric drum about the force application opportunity and the force model to obtain the minimum inclination angle;
(3) establishing a concentric drum inclination angle adjustment model by taking the fact that the position of the concentric drum cannot move left and right in the training process as a constraint condition; and solving the concentric drum inclination angle adjustment model to obtain the optimal component force applied to each traction rope.
Further, in the step (1), a stress analysis is performed by taking the vertical direction of the center point of the concentric drum as an axis and the center point of the concentric drum as a stress point to establish an optimal cooperation model for preventing the ball from falling.
Further, in the step (2), a global coordinate system and a local coordinate system are established, and coordinate transformation is performed; representing the attitude angle of the concentric drum by the included angle of the global coordinate system and the local coordinate system, wherein the attitude angle comprises a deflection angle
Pitch angle
Roll angle
Further, the inclination angle of the concentric drums with respect to the moment of exertion and the force model is:
wherein, FiRepresenting the tension of each pull-cord, M representing the rigid body turning moment, theta0Representing the initial drumhead inclination angle and R the concentric drum radius.
Furthermore, firstly, the inclination angle and the falling direction of the ball in the movement process are obtained according to the movement track of the ball, and then the deflection angle of the concentric drum to be adjusted is obtained.
Further, in the step (3), the concentric drum inclination angle adjustment model is:
γ2＝γ1+β；
wherein, the included angle between the rebound track of the ball and the vertical direction, and beta represents the deflection angle between the ball and the vertical direction after the last collision.
Further, the tension applied to each of the pulling ropes is found using the parallelogram rule.
Compared with the prior art, the invention has the beneficial effects that:
(1) the concentric drum installation force sensor can interact with computer equipment, and the computer equipment is used for carrying out simulation analysis on the concentric drum training process so as to give guidance to team members, so that the training time is shortened;
(2) the invention establishes an optimal cooperation model, a force application time and force model of the inclination angle of the concentric drum and an adjustment model of the inclination angle of the concentric drum, and obtains the optimal force application time and the optimal component force by comparing with the optimal cooperation model in an ideal state.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application.
FIG. 1 is a schematic structural diagram according to a first embodiment of the present invention;
FIG. 2 is a simulation flowchart according to a first embodiment of the present invention;
FIG. 3 is a diagram illustrating an analysis of the ball drop force in an ideal state according to a first embodiment of the present invention;
FIG. 4 is a diagram illustrating an analysis of the ball lifting process under an ideal condition according to a first embodiment of the present invention;
FIG. 5 is a diagram of the solution result of the optimal collaborative model according to the first embodiment of the present invention;
FIG. 6 is a graph illustrating a force analysis of concentric drums according to a first embodiment of the present invention;
FIG. 7 is a parallelogram resultant diagram according to a first embodiment of the present invention;
FIG. 8 is a diamond-shaped resultant diagram according to a first embodiment of the present invention;
FIG. 9 is a graph of transformed coordinates according to a first embodiment of the present invention;
FIG. 10 is a force direction distribution diagram of a concentric drum according to a first embodiment of the present invention;
FIG. 11 is a diagram of a ball game according to a first embodiment of the present invention;
FIG. 12 is a diagram illustrating the results of a solution of a model for adjusting the inclination angle of a concentric drum according to a first embodiment of the present invention;
FIG. 13 is a force diagram of a team member according to a first embodiment of the invention;
the device comprises a concentric drum 1, a concentric drum 2, a traction rope 3, a tension sensor 4 and computer equipment.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an", and/or "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof;
deflection angle (Yaw)
: the angle of rotation of the drum in the positive z-axis direction;
pitch angle (Pitch)
: the angle of rotation of the drum in the positive y-axis direction;
rolling angle (Roll)
: the angle of rotation of the drum in the positive x-axis direction.
The first embodiment is as follows:
the present invention will be described in detail with reference to fig. 1 to 11, and specifically, the structure is as follows:
the embodiment provides a training system of a concentric drum, which comprises the concentric drum 1, a ball and a computer device 4, wherein the concentric drum 1 is provided with a force sensor for detecting the force of the ball hitting the surface of the concentric drum 1; the concentric drum 1 is uniformly connected with a plurality of traction ropes 2 at intervals in the circumferential direction, and tension sensors 3 are installed on the traction ropes 2. The force sensor and the tension sensor 3 transmit detected data to the computer equipment 4 in a wireless transmission mode; the computer equipment 4 is used for simulating the training process and analyzing an optimal guidance scheme.
The simulation method of the computer device 4 comprises the following steps:
the method comprises the following steps: establishing an optimal cooperation model by taking the constraint conditions that the friction force and the mass of the traction rope 2 are ignored and the traction rope 2 does not have elasticity; and solving the optimal cooperation model to obtain the optimal height of the concentric drum.
Specifically, the optimal cooperation model is established under an ideal condition. In an ideal state, the friction between the drumhead and the ball, the friction between the hand and the rope and other uncontrollable factors are assumed to be ignored; the traction rope 2 has no elasticity, the mass of the traction rope 2 is ignored, and the influence of inertia force on the traction rope 2 is not considered; the surface of the concentric drum 1 is a rigid body with uniform quality and continuous distribution, and the experimental process is in an environment without wind and strong magnetic field.
Ideally, each team member would have precise control over the direction, timing and force of the force, in which case the drumhead would not tilt. But the air resistance and the elastic force between the drumhead and the ball cannot be ignored. The straighter the pull cord is, the less force each player needs to provide to keep the ball up in the air. And taking the vertical direction of the central point of the drumhead as an axis and the central point of the drumhead as a stress point, and carrying out stress analysis to establish a model.
(1) And (3) analyzing the stress of the ball:
the stress analysis is carried out on the falling process of the ball, and the factors such as air resistance and the like cannot be ignored, so that the bounce height of the ball relative to the drumhead can be gradually reduced after the ball collides with the drumhead every time. To balance out the effects of these factors, the concentric drum 1 is given a relative tension so that the balls can keep the rise height always greater than 40cm after the collision. (in the forward direction)
As shown in figure 1, the ball is not only subjected to the self-gravity m in the falling process1g, also receives air resistance fResistance deviceIn which f isResistance deviceKv, the coefficient k of the air resistance of the ball when it freely falls in air is 0.5.
The stress analysis formula is as follows:
wherein m is1Represents the mass of the ball and k represents the coefficient of air resistance when the ball is moving in air.
As shown in figure 2, the ball is also subjected to self-gravity m during the rising process1g and air resistance fResistance deviceThe function of (1): f. ofResistance deviceKv, direction down. The stress analysis formula is as follows:
assuming that the air resistance does the same for the ball during ascent and descent, a model of velocity v with respect to time t and a model of velocity v with respect to displacement x are built only for the descent.
As shown in the above equations (1) and (2), the velocity of the ball changes during the movement due to the influence of the acceleration of gravity during the ascending or descending process of the ball, so equation (3) is simplified to obtain the function of v with respect to x as follows:
wherein C is a constant, and through multiple comparison calculations, it is found that when C is equal to 6.25, the obtained speed function is more consistent with the actual value, and therefore, the above equation can be further simplified as:
the function for v with respect to t is found as follows:
v＝-20(1-e(-t)) (6)
(2) and (3) analyzing the stress of the collision process:
the plane where the drum surface is located at the beginning is taken as a zero potential energy surface, after the zero moment begins, the concentric drum 1 moves upwards under the action of pulling force applied to the traction rope 2, if the concentric drum collides with a ball when the height of h1 rises, the ball is bounced, the collision process is short, the momentum theorem is met, namely the speed of the drum after collision is changed to zero, the speed direction of volleyball is changed, the speed is increased, and the concentric drum moves vertically upwards.
Therefore, the concentric drum 1 is subjected to stress analysis in the process of stress rise, and the following conditions are met:
wherein v is2Representing the speed of the concentric drum 1 before impact with the ball, FCombination of Chinese herbsRepresenting the resultant of the force applied to the concentric drum 1 and the weight of the drum itself.
According to the law of conservation of momentum, the ball and the drumhead satisfy the following conditions during collision:
m1v1-m2v2＝-m1v’1(8)
wherein v is1Denotes the speed, v ', before collision of the ball with the drum surface'1Represents the velocity of the ball after collision with the drumhead, m2Representing the concentric drum mass.
According to the law of conservation of mechanical energy, the condition that the ball and the drumhead satisfy during collision is shown as follows:
therefore, in the collision process of the ball and the drumhead, the energy consumed for overcoming the resistance to do work meets the following conditions:
in an ideal situation, the minimum force min FL that can be met without the ball falling is as follows:
(3) solving the optimal cooperation model:
solving the best fit model using the lingo program resulted in the ideal situation shown in figure 6 when the tension provided to the concentric drum 1 between the players and the force experienced by the ball drop were balanced so that the height at which the ball was pitched each time remained constant was 40.53cm, greater than the specified 40 cm. And the velocity v of the ball before it collides with the drumhead during the fall1Is 2.05 m/s; velocity v 'after collision with drum surface'1The change was 3.38 m/s; speed v of drum in ascending movement2Is 0.41 m/s; the player should begin to apply force 0.30s after the ball falls, resulting in a force FCombination of Chinese herbsEqual to 91.305N.
Step two: establishing a force application time and force model of the inclination angle of the concentric drum 1 by taking the position of the gravity center of the concentric drum 1 not to be changed as a constraint condition; and solving the inclination angle of the concentric drum 1 about the force application time and the force model to obtain the minimum inclination angle.
Specifically, in the actual training process, different force applying opportunities and forces among team members provide conditions for the inclination angle of the drumhead, and the inclination angle is related to the direction and the size of resultant force received by the drumhead at the moment no matter what the inclination direction of the drumhead changes. Therefore, the relationship with respect to the inclination angle is obtained only from the direction and magnitude of the resultant force at a certain time, without considering the force action between each player.
(1) Force analysis on concentric drum 1:
the drum head is horizontally static at the initial moment, and because the distance of the concentric drum 1 in the motion process is small, a right-hand space rectangular coordinate system is established by taking the gravity center of the concentric drum 1 as the origin and the direction of the first player as the x axis on the assumption that the gravity center position of the concentric drum 1 does not change.
When the concentric drum 1 moves, the concentric drum always moves towards the direction of resultant force, and as shown in fig. 6, the stress condition of the concentric drum 1 is analyzed. The forces between team members are different, and assuming that the forces of two team members are different from the others, the magnitude and direction of the resultant force should be related to the forces, and the resultant force is shown in fig. 7. If the forces between the two crews are the same, the parallelogram can be simplified into a diamond shape, as shown in fig. 8.
(2) Analysis of the fixed axis rotation of the concentric drum 1:
the concentric drum 1 is an object with uniform and continuous mass distribution, the concentric drum 1 is assumed to be a thin disc rigid body, and the displacement of the concentric drum 1 is almost not changed in the process from force application to collision of the concentric drum 1 and the concentric drum according to the solving result of the optimal cooperation model, so that the force F applied on the traction rope 2 by a team member is decomposed into the force in the direction vertical to the disc edge of the concentric drum 1 and the force in the horizontal direction, and the included angle between the traction rope 2 and the concentric drum 1 can be obtained because the team member is static and the force in the horizontal direction is not considered.
According to the formula of rigid body rotation, the following formula is obtained:
wherein R represents the radius of the concentric drum 1.
The relational expression for the inclination angle when the drumhead is inclined is obtained from expression (12) as follows:
in the present embodiment, α is obtained as 3.595.
Wherein the content of the first and second substances,
represents the angle of the drumhead normal vector with the vertical, and deltaf represents the difference in force applied about the central symmetry point of the drumhead.
The formula for Δ F is as follows:
ΔF＝(F1-F2)sinθ1(14)
wherein, sin θ1Which represents the sine value of the angle between the traction rope 2 and the horizontal plane at the initial moment.
The initial included angle is 3.438 degrees through radian conversion.
The solving range of the above formula is only suitable for the case that eight persons exert force simultaneously but the force magnitude is not equal, and for the case that the moment of exerting force is different, a method of transforming a coordinate system is adopted, and the coordinate system is shown in fig. 9.
The attitude angle of the concentric drum 1 can be expressed by the angle between the global coordinate system and the local coordinate system, and the rotation sequence thereof is defined by the euler angle description method. Specifically, the angles obtained by sequentially rotating the concentric drum 1 around the axes z, y, and x of the global coordinate system are described.
Definition of
The positive and negative values of (1) should accord with the right-hand spiral rule, that is, the direction pointed by the thumb is consistent with the positive direction of the axis by holding the axis by the right hand, the variation of the attitude angle is positive, otherwise, the variation is negative.
The coordinates of the eight traction rope 1 connection points of the concentric drum 1 are local coordinates, but when the concentric drum 1 is in operation, global coordinates are needed for calculation analysis. It is therefore necessary to derive a transformation of the coordinates in the local coordinate system and the coordinates in the global coordinate system.
Take 8 players as an example, set the position and pose of the concentric drum 1
The connection points of eight players on the concentric drum 1 are in the local coordinate systemHas a coordinate G in the coordinate systemP(xpj,ypj,zpj) (j-1, 2, …,8) and the coordinate in the global coordinate system is GO(Xpj,Ypj,Zpj)(j＝1,2,…,8)。
The sine and cosine of the three attitude angles are noted as follows:
the rotation of the vector is equal to the sum of the two components of the vector, and the conversion matrix T rotating around the direction of the z-axis is obtainedZComprises the following steps:
the same can be obtained:
thus, the concentric drum 1 rotates about the conversion matrix T in three directionsZYXComprises the following steps:
therefore, the transformation formula between the global coordinate system and the local coordinate system can be obtained as follows:
establishing a global coordinate system (X, Y, Z) based on a horizontal plane where the drumhead is located at the initial moment, establishing a local coordinate system (X, Y, Z) based on a plane where the drumhead is located at 0s, analyzing forces applied at different times in two processes, wherein the first process is-0.1 s to 0s, and supposing that the process is applied by a force with a constant magnitude and the rotating angle is theta1And the drum does not continue to rotate in that direction due to inertia after the force is removed. Determining the normal vector of the plane
The vector is in the local coordinate system
Determining the rotation angle and the subtended quantity under the action of the 0s rear force
Rotating to obtain a rotated vector
Then to vector
Coordinate transformation is carried out to obtain
And finally, obtaining the rotation angle relative to the global coordinate.
The connection points of the players on the concentric drum 1 are evenly distributed, and each player holds the end of the rope, so that the stress directions of the concentric drum 1 are distributed as shown in fig. 10.
The model of the inclination angle with respect to the moment and force of exertion is shown as follows:
wherein n is an integer.
When n is 8, there are:
wherein, Fi(i ═ 1..8) the force applied to the pull-cord 2 for each team member is a three-dimensional vector.
In this embodiment, the number of players is 8, the length of the traction rope 1 is 1.7m, the drum surface is horizontally static at the initial moment, the initial position is decreased by 11cm compared with the rope when being horizontal, and the force application time and the drum surface inclination angle under the force application magnitude at each moment are calculated by using MATLAB, as shown in Table 1.
TABLE 2 values of timing (unit: s) and magnitude (unit: N) of exertion
As can be seen from Table 1, when the force exerted by only one or two players is different, the inclination angle of the drumhead is very small; when the actual force exerted by only one or two players is different, the inclination angle of the drum surface is slightly increased; when force applying time and force are different among multiple players, the inclination angle of the drumhead is greatly influenced.
Step three: establishing a concentric drum inclination angle adjustment model by taking the fact that the position of the concentric drum 1 cannot move left and right in the practical training process as a constraint condition; and solving the concentric drum inclination angle adjustment model to obtain the optimal component force applied to each traction rope 2.
Since the ball has already deviated from the vertical direction by the angle β since the previous collision, in order to restore the ball to a vertically bound state and to allow the ball to fall on the drum surface as it is next, it is assumed that the position of the concentric drum 1 does not change from side to side during the course of the game, and therefore, the bound range of the ball cannot exceed the drum surface.
The setting conditions were as follows: the deviation angle of the ball from the vertical direction after the last collision is 1 degree, the lengths of 10 players and the traction ropes 2 are 2m, the rebound height of the ball is 60cm, and the inclination angle of 1 degree is generated relative to the vertical direction.
The players exert forces simultaneously after the ball is thrown ts, describing the course of the ball's motion, calculated to exert forces simultaneously after 0.3899s after the ball is thrown, as shown in fig. 11. Due to the existence of air resistance, the horizontal speed of the ball in the rising processThe degree gradually decreases. Therefore, when the ball falls from the highest point, the force in the horizontal direction is approximately zero, neglecting, and the falling process of the ball is regarded as free falling body movement; h0Indicating the vertical height of the ball rising.
Assuming that the v-X function in the optimal collaborative model is still applicable to the non-free fall process, we obtain:
substituting the parameters to obtain vm＝3.46m/s。
The ascending and descending movement processes of the ball are analyzed, and the air resistance is considered to be a constant force all the time, so that the following results are obtained:
the substitution parameters can be given as:
since the declination angle β that the ball has made from the last collision with the vertical direction is small, it is considered that H is0,H1,H2Approximately equal, i.e.:
H1＝H2＝H3＝H0(26)
it was found that the distance the ball travels at rest in the air after the first rebound to the second rebound was about 3H0。
For the process that the ball changes the inclination angle from rising to falling and collides with the drumhead, the functional relation can be obtained as follows:
according to the above formula, the following is obtained: h5＝0.04m。
The distance from the second-time static position of the ball to the center of the drumhead is as follows:
H4＝H0-H5＝0.56m (28)
calculating the included angle gamma between the second bounce track and the vertical direction1Comprises the following steps:
get gamma by solution1＝1.08°。
In order to make the ball bounce along the vertical direction, the inclination angle of the drumhead is adjusted by MATLAB to obtain an angle gamma of the drumhead before relative adjustment2Comprises the following steps:
γ2＝γ1+1°＝2.08° (30)
the force application patterns of the ten players are shown in fig. 13, and it can be seen that the projection of the trajectory of the ball in the tilting direction in the horizontal direction is between the players 5 and 6 at an angle of 2:1 to the players of 24 ° and 12 °, respectively. On the second revolution, the ball is inclined between players 10 and 1, using the parallelogram rule, to resolve the force on the drum to the force of players 1 and 10. This is achieved by superimposing the resultant force of the rotation of the drum and the force acting on the drum to move the drum upward, and calculating the pulling force applied by each team member in the rope direction by lingo.
Calculating the inclination angle of the drumhead to be 1.07888 by using MATLAB; the force of the drum head lifting the inclined angle is decomposed to each player, the magnitude of the force of ten players on the drum through the rope is obtained by applying a lingo program and is shown in figure 13, and the force applied by each player is shown in table 2.
Table 4: team member force distribution table unit: n is a radical of
| 1 | 2 | 3 | 4 | 5 |
| 100.0000 | 70.0000 | 93.52606 | 100.0000 | 91.43204 |
| 6 | 7 | 8 | 9 | 10 |
| 70.0000 | 100.0000 | 100.0000 | 70.0000 | 100.0000 |
As can be seen from Table 2, the forces applied by players 1, 4, 7, 8, 10 are the same; the force applied by the team members 2, 6 and 9 is the same; player 3 applied force 93.52606N; player 5 applied force 91.43204N.
The above description is only a preferred embodiment of the present application and is not intended to limit the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.
Claims (4)
1. The practical training system of the concentric drum is characterized by comprising the concentric drum and a ball, wherein the concentric drum is provided with a force sensor for detecting the force of the ball impacting the surface of the concentric drum; the concentric drums are uniformly connected with a plurality of traction ropes at intervals in the circumferential direction, and tension sensors are mounted on the traction ropes; the force sensor and the tension sensor send detected data to computer equipment; the computer equipment is used for simulating the training process and analyzing a guidance scheme of a minimum inclination angle, an optimum height and an optimum component force;
the simulation method of the computer equipment comprises the following steps:
(1) establishing an optimal cooperation model by taking the constraint conditions that the friction force and the mass of the traction rope are ignored and the traction rope does not have elasticity; solving the optimal cooperation model to obtain the optimal height of the concentric drum;
taking the vertical direction of the center point of the concentric drum as an axis and the center point of the concentric drum as a stress point to perform stress analysis to establish an optimal cooperation model which prevents a ball from falling;
(2) establishing a force application time and force model of the inclination angle of the concentric drum by taking the position of the gravity center of the concentric drum not to change as a constraint condition; solving the inclination angle of the concentric drum about the force application opportunity and the force model to obtain the minimum inclination angle;
the inclination angle of the concentric drum is as follows with respect to the force application time and force model:
wherein, FiRepresenting the tension of each pull-cord, M representing the rigid body turning moment, theta0Represents the initial inclination angle of the drumhead, R represents the concentric drum radius, theta represents the inclination angle of the concentric drum,
which represents the angle of deflection,
the pitch angle is expressed in terms of,
showing a roll angle, i showing a force application parameter, n being an integer, and t being a force application time;
(3) establishing a concentric drum inclination angle adjustment model by taking the fact that the position of the concentric drum cannot move left and right in the training process as a constraint condition; solving the concentric drum inclination angle adjustment model to obtain the optimal component force applied to each traction rope;
the concentric drum inclination angle adjustment model is as follows:
γ2＝γ1+β；
wherein, the included angle between the rebound track of the ball and the vertical direction, and beta represents the deflection angle between the ball and the vertical direction after the last collision.
2. The practical training system for concentric drums according to claim 1, wherein in the step (2), a global coordinate system and a local coordinate system are established and coordinate transformation is carried out; representing the attitude angle of the concentric drum by the included angle of the global coordinate system and the local coordinate system, wherein the attitude angle comprises a deflection angle
Pitch angle
Roll angle
3. The practical training system for the concentric drum according to claim 1, wherein the inclination angle and the falling direction of the ball during the movement process are obtained according to the movement track of the ball, and then the deflection angle of the concentric drum to be adjusted is obtained.
4. The training system of concentric drums according to claim 1, wherein the pulling force applied to each pulling rope is determined using parallelogram rules.
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