CN111667745A

CN111667745A - Rigid body rotation dynamics experimental device

Info

Publication number: CN111667745A
Application number: CN202010449444.9A
Authority: CN
Inventors: 李淑欣; 苏云帅; 鲁思渊; 余丰; 曹均
Original assignee: Ningbo University
Current assignee: Ningbo University
Priority date: 2020-05-25
Filing date: 2020-05-25
Publication date: 2020-09-15
Anticipated expiration: 2040-05-25
Also published as: CN111667745B

Abstract

The invention provides a rigid body rotation dynamics experimental device, and relates to a mechanics experimental device. The device solves the problem that a simple rigid body rotation dynamics experimental device in the prior art is not available. The experimental device comprises an X axis, a Y axis and a Z axis which are perpendicular to each other, wherein the rotating position of the X axis is fixed, the X axis is connected with an X frame, the X frame is rotatably connected with the Z frame through the Z axis, the Z frame rotates in the X frame, the Z frame is rotatably connected with a Y frame through the Y axis, the Y frame rotates in the Z frame, the Y frame is a circular ring frame, two large mass blocks are symmetrically arranged on the Y frame about the center, and two small mass blocks are symmetrically arranged at the connecting position of the Y axis of the Y frame about the center. The invention provides a simulation model for the research of the rigid body spinning dynamics by utilizing the three-degree-of-freedom rotating device, so that the phenomenon that the rigid body spinning stabilizes the middle shaft can be clearly observed; the mass block is arranged in a position-adjustable mode, so that the function of the experimental device is increased.

Description

Rigid body rotation dynamics experimental device

Technical Field

The invention belongs to the technical field of experimental teaching, relates to a mechanical experimental device, and particularly relates to a rigid body dynamics experimental device.

Background

The rigid body rotation dynamics is a complex and widely applied subject, and is difficult to observe visually in reality, the self-selection of the rigid body rotation dynamics stabilizes relevant theories, gyroscope mechanics theories and the like, the number of relevant equipment is small, most of the existing rigid body rotation dynamics are precise and complex, and the interesting exploration cognition of students is not facilitated.

For example, the tennis racket theorem (also called the middle axis theorem) in the rigid body self-selection stabilization theory is a solution of euler's equation in classical mechanics describing the motion of a free rigid body, which can rotate around three different main axes and three moments of inertia are not equal to each other. This phenomenon is also called the zanibokov effect because it was discovered in space in 1985 by Russian astronauts Frazimiel Zannibeckov (Vladimir Dzhanhanibokov). The theorem can be described as: when the rigid body rotates around the central main shaft, the rotation becomes unstable quickly, and the rotation around the other two shafts is more regular. For example: holding the handle to level the face and then releasing the racquet will not easily catch the racquet because the face will flip over. Correspondingly, if the racket handle is rubbed by hands and then the racket is released, the racket can be easily caught; the swatter surface can be vertical to the ground, and the swatter can be easily caught after being released. This phenomenon occurs as long as the axis of rotation is slightly different from the second spindle, independent of air resistance or gravity.

Disclosure of Invention

The invention aims to solve the problems in the prior art and provides a rigid body rotational dynamics experimental device which can demonstrate the motion phenomenon of rigid body rotational dynamics.

The purpose of the invention can be realized by the following technical scheme: a rigid body rotation dynamics experiment device comprises an X axis, a Y axis and a Z axis which are perpendicular to each other, wherein the rotation position of the X axis is fixed, the X axis is connected with an X frame, the X frame is rotatably connected with the Z frame through the Z axis, the Z frame rotates in the X frame, the Z frame is rotatably connected with the Y frame through the Y axis, the Y frame rotates in the Z frame, the Y frame is a circular ring frame, two large mass blocks are symmetrically arranged on the Y frame relative to the center, two small mass blocks are symmetrically arranged at the position of the Y axis of the Y frame relative to the center, the mass center connecting line of the two large mass blocks is perpendicular to the Y axis, and the mass center connecting line of the two small mass blocks is collinear with the Y axis.

In certain embodiments, the X frame and the Z frame are both circular ring frames.

In some embodiments, one end of the Y-axis has a clutch connection device for matching with the rotating shaft of the driving motor.

In some embodiments, the large mass blocks are four sliding spherical sliding blocks sleeved on the Y frame, wherein the two symmetrical large mass blocks at the centers are connected through a connecting rod, a positioning rod perpendicular to the Y axis is arranged on the Y frame, the center of the positioning rod is located at the center of the Y frame, the center of the connecting rod is rotatably connected with the center of the positioning rod through a rotating shaft, two supporting rods symmetrical about the center are arranged between the two connecting rods, two ends of each supporting rod are temporarily connected with the two connecting rods through separable connecting devices respectively, the middle of each supporting rod is temporarily connected with the positioning rod through the separable connecting devices, and therefore the relative positions of the supporting rods, the connecting rods and the positioning rod can be.

In some embodiments, the end and middle of the support rod are provided with through holes, the connecting rod and the positioning rod are provided with positioning holes along the rod body, and the support rod is temporarily and fixedly connected with the connecting rod and the positioning rod by pins penetrating through the through holes and the positioning holes.

In some embodiments, the two ends of the support rod are rotatably connected with sliding blocks, the sliding blocks are slidably sleeved on the connecting rods, and the middle part of the support rod is temporarily connected with the positioning rod through a separable connecting device.

In some embodiments, the angle between the two corresponding connecting rods of the supporting rod is less than 90 degrees.

In some embodiments, rotation angle detection means for the X-axis and Z-axis are provided.

In some embodiments, the ends of the X and Z axes are different colors.

Compared with the prior art, the rigid body rotation dynamics experimental device has the following advantages:

the invention provides a simulation model for the research of the rigid body spinning dynamics by utilizing the three-degree-of-freedom rotating device, so that the phenomenon that the rigid body spinning stabilizes the middle shaft can be clearly observed; through setting the quality piece to position adjustable mode to realization that can be convenient is to the adjustment of the inertia's that the rotation body inertia axle corresponds size, thereby increases experimental apparatus's function, makes the experiment contrast that can carry out multiple different inertia and distribute, makes the experiment more clear and definite to physical principle and phenomenon reflection, device simple structure, convenient operation, it is with low costs.

Drawings

In the drawings, which are not necessarily drawn to scale, like reference numerals may describe similar components in different views. Like reference numerals having different letter suffixes may represent different examples of similar components. The drawings illustrate generally, by way of example, but not by way of limitation, various embodiments discussed herein.

FIG. 1 is a schematic diagram of a first embodiment;

FIG. 2 is a schematic diagram of the second embodiment;

FIG. 3 is a schematic view showing the apparatus of the second embodiment in which the X frame, the Y frame and the Z frame are all in the same plane;

FIG. 4 is a schematic view of the drive motor cooperating with the Y frame;

FIG. 5 is a schematic AA cross-sectional view of FIG. 4;

FIG. 6 is a schematic view showing the same plane of the X frame, the Y frame and the Z frame in the third embodiment;

FIG. 7 is a schematic view of a Y frame of the third embodiment;

fig. 8 is a schematic BB cross-sectional view of fig. 7.

In the figure, an X axis 1, a Y axis 2, a Z axis 3, an X frame 4, a Y frame 5, a Z frame 6, a Z frame bearing 7, an X frame bearing 8, an external bearing 9, a fixing bracket 10, a large mass block 11, a small mass block 12, a socket 201, a driving motor 13, a plug 131, a connecting rod 14, a shaft hole 141, a positioning rod 15, a through groove 151, a connecting shaft 16, a supporting rod 17, a positioning hole 18, a pin 19 and a slider 20.

Detailed Description

The following are specific examples of the present invention, and the technical solutions of the present invention are further described with reference to the drawings, but the present invention is not limited to these examples, and the following embodiments do not limit the invention according to the claims. Moreover, all combinations of features described in the embodiments are not necessarily essential to the solution of the invention.

It will be understood by those of ordinary skill in the art that all directional references (e.g., above, below, upward, downward, top, bottom, left, right, vertical, horizontal, etc.) are illustratively used in the figures to aid the reader's understanding and do not imply (e.g., position, orientation, or use, etc.) a limitation on the scope of the invention, which is defined by the claims appended hereto. Additionally, the term "substantially" may refer to slight imprecision or deviation in conditions, amounts, values, or dimensions, etc., some of which may be within manufacturing or tolerance limits.

Example one

As shown in FIG. 1, the rigid body rotational dynamics experimental device comprises an X axis 1, a Y axis 2 and a Z axis 3 which are perpendicular to each other, and an X frame 4, a Y frame 5 and a Z frame 6 which are fixedly connected with the rotating shafts.

The X frame is rotatably connected with the Z frame through a Z axis, the Z frame rotates in the X frame, the Z frame is rotatably connected with the Y frame through a Y axis, and the Y frame rotates in the Z frame.

The Z frame is provided with a Z frame bearing 7, the X frame is provided with an X frame bearing 8, the Y shaft is rotatably supported on the Z frame bearing, the Z shaft is rotatably supported on the X frame bearing, the X shaft is rotatably supported on an external bearing 9, and the external bearing is fixed on a fixed support 10, so that each frame can freely rotate around the respective shaft, and the Y frame can freely rotate in three degrees of freedom in three-dimensional space.

X frame, Y frame, Z frame are ring shape frame, and X axle, Y axle, Z axle are two that are located the symmetry setting of X frame, Y frame, Z frame both sides to make: the Z frame is rotatably supported in the X frame, and the Y frame is rotatably supported in the Z frame.

Two large mass blocks 11 are symmetrically arranged on the Y frame about the center, two small mass blocks 12 are symmetrically arranged at the Y shaft connecting part of the Y frame about the center, the mass center connecting line of the two large mass blocks is vertical to the Y shaft, the mass center connecting line of the two small mass blocks is collinear with the Y shaft, the mass blocks can adopt iron blocks or lead blocks, the large mass blocks are preferably far larger than the small mass blocks, the large mass blocks are as large as possible, and the small mass blocks are as small as possible. Therefore, the minimum inertia axis of the Y frame is on the connecting line of the two large masses, the maximum inertia axis is perpendicular to the Y frame and passes through the circle center of the frame, and the moment of inertia taking the Y axis as the inertia axis is slightly smaller than the maximum moment of inertia. Thus, according to the rigid body spin stabilization tennis racket theory, the Y axis is an unstable spin axis, and if the Y frame rotates around the Y axis, the direction of the Y axis (reflected on the motion of the Z frame and the X frame) can be seen to be changed (fluctuation, overturning and the like) continuously.

In order to move more accurate information of the change of the direction of the Y axis, a detection device for detecting the change of the rotation angle of the X axis and the Z axis may be provided, and it is preferable to use a non-contact optical detection device, for example, different colors are used at the ends of the two directions of the X axis or the Z axis, for example, one end is black and the other end is white, so that the change information of the position of the rotation axis can be detected by an optical sensor, and certainly, the motion information of the Z frame and the X frame can also be used for indirectly reflecting the motion information of the Y axis, so that many prior arts for realizing such detection functions are provided, and no further description is provided here, in short, because of the existence of such a specific experimental device, more detailed information of the change process of the spin instability axis can.

The user can make the Y axle begin to rotate through the stirring of hand to the Y axle, also can give an initial velocity for the Y axle through rotary driving device such as motor, for example can set up separation and reunion connecting device (realize the clutch that two axles are linked promptly) at the tip that the Y axle tip exposes from Z frame bearing to after the Y axle reaches certain rotational speed, drive arrangement and Y axle separation, make Y frame rotation. The simplest method can be that a socket 201 is arranged on the end face of the Y shaft, a plug 131 capable of being inserted into the socket is arranged on the front end face of the output shaft of the driving motor 13, certainly, the socket and the plug can not rotate relatively, so that the Y frame can be driven to rotate through the motor shaft, and the motor can be moved away along the axial direction after a certain rotating speed is reached, so that the Y frame can rotate.

In the experiment, in order to quickly see the change of the Y axis, a small disturbing force which is approximately vertical to the Y axis can be given to the Y axis when the Y frame rotates, and the phenomenon can occur more quickly and obviously.

Example two

As shown in fig. 2, 3, 4 and 5, unlike the previous embodiment, the large masses are four, and the large masses are sliding spherical sliders fitted on the Y frame, namely, the spherical sliding block is provided with a hole sleeved on the frame, wherein, every two symmetrical large mass blocks at the center are connected through a connecting rod 14, a positioning rod 15 vertical to the Y axis is arranged on the Y frame, the center of the positioning rod is positioned at the center of the Y frame, the center of the connecting rod is rotationally connected with the center of the positioning rod through a rotating shaft, for example, a connecting shaft 16 which is vertical to the positioning rod is fixed at the center of the positioning rod, the connecting shaft is vertically and crossly connected with the positioning rod, namely, two shaft ends of the connecting shaft are respectively positioned at two sides of the positioning rod, the connecting shafts at two sides of the positioning rod are respectively connected with different connecting rods in a rotating way, the connecting rods may be provided with shaft holes 141 in which the connecting shafts are movably fitted, and two support rods 17 that are symmetrical with respect to the center of the frame are provided between the two connecting rods.

The bracing piece is used for keeping the angle between two connecting rods, and the bracing piece both ends pass through separable connecting device temporary connection with two connecting rods respectively, and the middle part and the locating lever of bracing piece pass through separable connecting device temporary connection for the relative position of bracing piece and connecting rod and locating lever is adjustable, thereby changes the position of quality piece on the frame, thereby changes inertia's distribution.

As a simple embodiment, through holes can be arranged at the end part and the middle part of the supporting rod, positioning holes 18 are arranged on the connecting rod and the positioning rod along the rod body, the supporting rod is temporarily and fixedly connected with the connecting rod and the positioning rod by penetrating pins 19 through the through holes and the positioning holes, and the included angle between the two connecting rods can be adjusted by changing the positions of the connected positioning holes. The positioning rod is provided with a through groove 151 along the rod body, and the supporting rod passes through the through groove. The matching of the pin and the hole can be replaced by a bolt and a bolt hole, so long as the connection mode can be conveniently realized, and the pin and the hole are not listed.

In order to make the moment of inertia around the Y-axis smaller than the maximum moment of inertia, the angle between the two links corresponding to the support bar should be smaller than 90 degrees.

Therefore, the rotational inertia of the Y frame is changed by adjusting the position of the large mass block, so that the experiment can be performed on the conditions under different rotational inertias, and the function of the device is enriched.

EXAMPLE III

As shown in fig. 6, 7 and 8, different from the above embodiments, the two ends of the support rod are rotatably connected with the sliding blocks 20, the sliding blocks are slidably sleeved on the connecting rods, which is equivalent to a connecting rod-sliding block mechanism, and the middle part of the support rod is temporarily connected with the positioning rod through a detachable connecting device, for example, the temporary connection mode of the positioning hole and the positioning pin of the second embodiment can be adopted, and of course, other connection modes, for example, the connection mode of the bolt hole can also be adopted.

Although some terms are used more herein, the possibility of using other terms is not excluded. These terms are used merely to more conveniently describe and explain the nature of the present invention; they are to be construed as being without limitation to any additional limitations that may be imposed by the spirit of the present invention. The order of execution of the operations, steps, and the like in the apparatuses and methods shown in the specification and drawings may be implemented in any order as long as the output of the preceding process is not used in the subsequent process, unless otherwise specified. The descriptions using "first", "next", etc. for convenience of description do not imply that they must be performed in this order.

The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.

Claims

1. A rigid body rotation dynamics experimental device is characterized by comprising an X axis, a Y axis and a Z axis which are perpendicular to each other, wherein the rotation position of the X axis is fixed, the X axis is connected with an X frame, the X frame is rotatably connected with the Z frame through the Z axis, the Z frame rotates in the X frame, the Z frame is rotatably connected with the Y frame through the Y axis, the Y frame rotates in the Z frame, the Y frame is a circular frame, two large mass blocks are symmetrically arranged on the Y frame relative to the center, two small mass blocks are symmetrically arranged at the Y axis connection position of the Y frame relative to the center, the mass center connection line of the two large mass blocks is perpendicular to the Y axis, and the mass center connection line of the two small mass blocks is collinear with the Y axis.

2. The rigid body rotational dynamics experimental apparatus of claim 1, wherein the X-frame and the Z-frame are both circular ring frames.

3. A rigid body rotational dynamics testing apparatus as claimed in claim 1, wherein one end of the Y-axis has a clutch coupling device for engaging with a rotating shaft of a driving motor.

4. The experimental device for rigid body rotation dynamics as claimed in claim 2, wherein the large mass blocks are four sliding spherical sliding blocks sleeved on the Y frame, wherein every two symmetrical large mass blocks at the center are connected through a connecting rod, the Y frame is provided with a positioning rod perpendicular to the Y axis, the center of the positioning rod is located at the center of the Y frame, the center of the connecting rod is rotatably connected with the center of the positioning rod through a rotating shaft, two support rods symmetrical about the center are arranged between the two connecting rods, two ends of the support rods are respectively and temporarily connected with the two connecting rods through separable connecting devices, and the middle parts of the support rods are temporarily connected with the positioning rod through separable connecting devices, so that the relative positions of the support rods, the connecting rods and the positioning.

5. A rigid body rotation dynamics experiment apparatus as claimed in claim 4, wherein the support rod has through holes at the ends and middle thereof, and the connecting rod and the positioning rod have positioning holes along the rod body, and the support rod is temporarily fixed to the connecting rod and the positioning rod by pins passing through the through holes and the positioning holes.

6. The experimental facility for rigid body rotation dynamics as claimed in claim 4, wherein the two ends of the supporting rod are rotatably connected with sliding blocks, the sliding blocks are slidably sleeved on the connecting rod, and the middle part of the supporting rod is temporarily connected with the positioning rod through a detachable connecting device.

7. The experimental apparatus of rigid body rotational dynamics according to claim 4, wherein the included angle between the two links corresponding to the support rod is less than 90 degrees.

8. A rigid body rotational dynamics testing apparatus as claimed in claim 1 or 4, wherein there are provided rotation angle detection means for X-axis and Z-axis.

9. A rigid body rotational dynamics experimental apparatus as claimed in claim 1 or 4, wherein the colors of the two ends of the X-axis and Z-axis are different.