A method for measuring the center of mass of an object based on an IMU chip

Abstract

The present invention discloses a method for measuring the center of mass of an object based on an IMU chip in the technical field of object center of mass measurement, comprising the following steps: performing a heavy liquid experiment on the object to determine the position of the center of mass line and the suspension point of the cycloid of the object; performing a simple pendulum experiment on the object to determine the length of the center of mass of the object from the starting end of the cycloid according to the swing period of the object, and then obtaining the position of the center of mass; an IMU chip is provided on the object to measure the swing period of the object. A method for obtaining the period of the object's simple pendulum motion can be obtained by extracting the regularity of the object's acceleration signal collected by the IMU chip. Whether the object is regular or not, whether it rotates or not, it will not affect the measurement of the simple pendulum motion period, and the center of mass of the measured object is not limited by the shape or volume of the object, and the cost is low and the operation is simple.

Description

Technical Field

[0001] The present invention relates to the technical field of object centroid measurement, and in particular to a method for measuring the centroid of an object based on an IMU chip. Background Art

[0002] The center of mass is an imaginary point at which the entire mass of an object or a system of particles is concentrated. Determining the center of mass of an object is crucial for conducting overall kinematic and dynamic analysis. For objects with uniform mass distribution and regular shapes, the center of mass is the same as the centroid. However, for objects with irregular shapes or uneven mass distribution, the center of mass must be determined. This is particularly challenging for heavy and large three-dimensional objects.

[0003] Currently, the commonly used methods for measuring the center of mass include the heavy liquid pendulum method, the suspension method, the unbalanced moment method, and the multi-point support method.

[0004] The heavy liquid pendulum method is applicable to objects of various sizes and shapes. Specifically, the object is placed in a solution with a density greater than that of the object being measured. The solution is continuously diluted until only a small portion of the object is exposed above the liquid surface. The vertical line passing through this point is the object's center of mass, which also serves as the fixed point for the simple pendulum experiment. The object being measured is suspended from a rigid rope and subjected to simple pendulum motion. By measuring the period of the pendulum motion, the pendulum length is obtained, and thus the location of the object's center of mass.

[0005] Common methods for measuring the period of a simple pendulum include the photogate method and the camera method. The photogate method measures the period of an object's simple pendulum by measuring the number of times the object blocks a photoelectric sensor within a certain period of time, thereby obtaining the object's period. However, since an object inevitably rotates about the cycloid during simple pendulum motion, the photogate method can accurately determine the period of a simple pendulum for spherical objects. However, it cannot accurately determine the period of irregularly shaped objects.

[0006] The video method uses a high-speed camera to measure the period of a simple pendulum. By continuously recording the time and frequency of an object's passage through a characteristic position, the period of the object's swing is determined. However, the high cost of high-speed cameras hinders widespread use. Furthermore, high-speed cameras also have difficulty accurately measuring the period of rotating non-spherical objects.

[0007] In summary, whether it is the photoelectric gate method or the camera method, when an irregular object rotates during its swing, it is difficult to accurately measure the swing period of the object, and then it is difficult to accurately determine the position of the center of mass of the object. Summary of the Invention

[0008] The purpose of the present invention is to provide a method for measuring the center of mass of an object based on an IMU chip, so as to solve the technical problem in the prior art that, whether it is the photoelectric gate method or the camera method, when an irregular object rotates during the swing process, it is difficult to accurately measure the swing period of the object, and then it is difficult to accurately determine the position of the center of mass of the object.

[0009] To solve the above technical problems, the present invention specifically provides a method for measuring the center of mass of an object based on an IMU chip, comprising the following steps:

[0010] Confirm whether the object has an embedded IMU chip. If not, attach an IMU chip to the object to measure its swing period.

[0011] Conduct heavy liquid experiments on objects to determine the location of the object's center of mass line and the suspension point of the cycloid;

[0012] Perform a simple pendulum experiment on the object and determine the distance between the object's center of mass and the starting point of the cycloid based on the object's swing period, thereby obtaining the position of the center of mass.

[0013] As a preferred solution of the present invention, the mass ratio between the IMU chip and the covered object is less than 1:40, so as to ensure that the error of the IMU chip's influence on the center of mass position of the covered object is within 2%.

[0014] As a preferred embodiment of the present invention, the heavy liquid experiment comprises the following steps:

[0015] Placing an object in a solution having a density greater than that of the object so that the object floats on the solution and the solution does not react with the object;

[0016] Gradually add water to the solution to reduce the density of the solution, causing the object to gradually sink into the solution until only the top of the object is exposed above the liquid surface;

[0017] After the object comes to rest, mark the point where the top is above the liquid surface as the hanging point.

[0018] As a preferred embodiment of the present invention, the simple pendulum experiment comprises the following steps:

[0019] Fix one end of the cycloid to the hanging point of the object, and then suspend the object through the cycloid;

[0020] Let the object hang down naturally to do simple pendulum motion;

[0021] After the object has swung for 10-20 cycles, the object can be stopped from swinging;

[0022] Read the data from the IMU chip and analyze the data through the acceleration signal characteristics to obtain the period of the object's simple pendulum motion;

[0023] According to the period formula of the simple pendulum motion, calculate the length L from the center of mass of the object to the starting end of the cycloid, and then subtract the length L of the cycloid. 摆线 , we can get the distance from the center of mass to the hanging point Δx=LL 摆线 ;

[0024] Finally, the exact position of the center of mass is measured by combining the center of mass line.

[0025] As a preferred solution of the present invention, the swing angle of the simple pendulum motion is 3 to 5°.

[0026] As a preferred solution of the present invention, during the simple pendulum experiment, a high-speed camera is used to synchronously observe the simple pendulum motion period to calibrate the data with the IMU chip.

[0027] Taking the measurement of the center of mass of an aluminum sphere with a built-in IMU chip as an example, the method for measuring the center of mass of an object based on an IMU chip described above includes the following steps:

[0028] An aluminum ball with an IMU chip built into it is placed in a 1.8g / cm 3 The aluminum ball 1 is floated in the ZnCl2 solution 4;

[0029] Then gradually add water to the container to reduce the density of the solution so that the aluminum ball gradually sinks into the solution;

[0030] When the aluminum ball can only be exposed in a small area above the liquid surface, stop adding water. After the aluminum ball is still, mark a point just above the part of the ball that is exposed above the liquid surface. This point is the hanging point of the object, and the center of mass of the ball is on the center of mass line where this point is located.

[0031] Take a thin steel wire as the cycloid, the length of the cycloid is greater than 10 times the radius of the aluminum ball, and measure its length as L 摆线 ;

[0032] Fix one end of the cycloid to the suspension point of the aluminum ball using UV-curing glue;

[0033] Fix the starting end of the cycloid with a knife-edge clamp and hang the aluminum ball on the iron stand;

[0034] Allow the aluminum ball to droop naturally and do a simple pendulum motion, and control the pendulum angle between 3 and 5 degrees;

[0035] After the aluminum ball has completed 10-20 simple pendulum cycles, the object can stop swinging;

[0036] Make the aluminum ball repeat the simple pendulum motion multiple times to achieve the purpose of measuring the cycle multiple times;

[0037] Remove the aluminum ball and the IMU chip inside it;

[0038] Read the data from the IMU chip and analyze the acceleration signal characteristics to obtain the period of the simple pendulum motion of the aluminum ball 1 and record it as T;

[0039] From dimensional analysis, it can be concluded that when the deflection angle is less than 5°, the period of the simple harmonic motion of the pendulum is Then we can get the relationship between pendulum length and period:

[0040] Based on the measured period T, the length L from the center of mass of the aluminum ball to the starting end of the cycloid is calculated;

[0041] Determine the distance Δx from the center of mass of the aluminum ball to the hanging point: Δx = LL 摆线 The point inside the aluminum ball that is Δx away from the suspension point along the center of mass line is the center of mass of the aluminum ball.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] The method for measuring the center of mass of an object provided by the present invention combines the heavy liquid method and the simple pendulum method based on an IMU chip. By extracting the regularity of the object's acceleration signal collected by the IMU chip, the period of the object's simple pendulum motion can be obtained. Whether the object is regular or rotating does not affect the measurement of the simple pendulum motion period. The center of mass of the object being measured is not limited by its shape or volume. Furthermore, the method is low-cost and simple to operate. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments or the description of the prior art. Obviously, the drawings described below are merely exemplary, and those skilled in the art can derive other implementation drawings based on the provided drawings without inventive effort.

[0045] Figure 1 is an overall flow chart of the measurement method in an embodiment of the present invention;

[0046] Figure 2 Flow chart of the heavy liquid experiment of aluminum balls in the embodiment of the present invention;

[0047] Figure 3 Flowchart of a simple pendulum experiment of an aluminum ball in an embodiment of the present invention;

[0048] Figure 4 This is a diagram of the apparatus for the heavy liquid experiment of aluminum balls in an embodiment of the present invention;

[0049] Figure 5 A diagram showing an apparatus for a simple pendulum experiment of an aluminum ball in an embodiment of the present invention;

[0050] The numbers in the figure represent the following:

[0051] 1-Aluminum sphere, 2-IMU chip, 3-Suspension point, 4-ZnCl2 solution, 5-Container, 6-Center of mass line, 7-Cycloid, 8-Knife-edge clamp, 9-Iron stand. DETAILED DESCRIPTION

[0052] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0053] The present invention specifically provides a method for measuring the center of mass of an object based on an IMU chip, comprising the following steps:

[0054] Confirm whether the object has an embedded IMU chip. If not, attach an IMU chip to the object to measure its swing period.

[0055] Conduct heavy liquid experiments on objects to determine the location of the object's center of mass line and the suspension point of the cycloid;

[0056] Perform a simple pendulum experiment on the object and determine the distance between the object's center of mass and the starting point of the cycloid based on the object's swing period, thereby obtaining the position of the center of mass.

[0057] This method involves attaching an IMU (Inertial Measurement Unit) based on MEMS (Micro-Electronic Systems) technology to or within an object to measure the period of a simple pendulum, regardless of the object's shape, volume, or mass. The IMU's built-in three-axis gyroscope and three-axis accelerometer enable real-time measurement of X, Y, and Z acceleration and angle.

[0058] When an object performs a simple pendulum motion, its acceleration signal follows the laws of sine and cosine signals. By extracting the laws of the object's acceleration signal collected by the IMU chip, the period of the object's simple pendulum motion can be determined. Whether the object is regular or rotating does not affect the measurement of the pendulum's period.

[0059] Furthermore, with the development of MEMS technology, IMU chips are becoming smaller and lighter, with faster acquisition speeds and lower costs. Currently, civilian-grade IMU chips can be as small as 10mm, weigh only a few grams, and have acquisition rates of up to 1,000 hertz. These chips are typically priced between tens and hundreds of yuan, making them a convenient way to measure the period of a simple pendulum.

[0060] It should also be noted that for some objects that already have an IMU, the period can be measured directly using the data collected by the objects themselves. For objects that do not have an IMU chip but have a mass at least 40 times that of the IMU chip, an IMU chip can be attached or placed on the object to ensure that the error of the IMU chip's influence on the center of mass position of the covered object is within 2%. The impact of adding the chip can be ignored.

[0061] The method provided by the present invention combines the heavy liquid method and the simple pendulum method to measure the center of mass of an object based on an IMU chip. The measured center of mass is not restricted by the object's shape or volume. It is particularly suitable for all materials containing an IMU chip, spherical objects, irregularly shaped objects, and large mass objects. This method can use the acceleration of the IMU chip to obtain the period of the simple pendulum motion. This method can simply and accurately obtain the period of an object's simple pendulum motion, is not affected by the object's shape or rotation, and does not rely on high-speed cameras, photoelectric sensors, etc.

[0062] Furthermore, the heavy liquid experiment comprises the following steps:

[0063] Placing an object in a solution having a density greater than that of the object so that the object floats on the solution and the solution does not react with the object;

[0064] Gradually add water to the solution to reduce the density of the solution, causing the object to gradually sink into the solution until only the top of the object is exposed above the liquid surface;

[0065] After the object comes to rest, mark the point where the top is above the liquid surface as the hanging point.

[0066] Furthermore, the simple pendulum experiment includes the following steps:

[0067] Fix one end of the cycloid to the hanging point of the object, and then suspend the object through the cycloid;

[0068] Let the object hang down naturally to do simple pendulum motion;

[0069] After the object has swung for 10-20 cycles, the object can be stopped from swinging;

[0070] Read the data from the IMU chip and analyze the data through the acceleration signal characteristics to obtain the period of the object's simple pendulum motion;

[0071] According to the period formula of the simple pendulum motion, calculate the length L from the center of mass of the object to the starting end of the cycloid, and then subtract the length L of the cycloid. 摆线 , we can get the distance from the center of mass to the hanging point Δx=LL 摆线 ;

[0072] Finally, the exact position of the center of mass is measured by combining the center of mass line.

[0073] Furthermore, the swing angle of the simple pendulum motion is 3 to 5 degrees.

[0074] Furthermore, during the simple pendulum experiment, a high-speed camera is used to synchronously observe the pendulum motion cycle to calibrate the data with the IMU chip.

[0075] Taking the measurement of the center of mass of an aluminum ball 1 with a built-in IMU chip 2 as an example, the present invention provides a specific embodiment.

[0076] Taking Beijing as the test area, the acceleration of gravity is 9.8015m / s 2 From the dimensional analysis, it can be concluded that when the deflection angle is less than 5°, the period of the simple harmonic motion of the pendulum is

[0077] Aluminum ball 1 is placed in 1.8g / cm 3 The aluminum ball 1 is floated in the ZnCl2 solution 4;

[0078] Then gradually add water to the container 5, thereby reducing the density of the heavy liquid to get closer and closer to the density of the aluminum ball, so that the ball gradually moves from a floating state to a suspended state;

[0079] When only a small area of the aluminum ball 1 is visible above the liquid surface, stop adding water. After the aluminum ball 1 is still, mark a point directly above the part of the ball that is exposed above the liquid surface. This point is the object's hanging point 3. The center of mass of the ball is on the center of mass line 6 where the red dot is located.

[0080] Take a thin steel wire as the cycloid 7, the length of the cycloid 7 is greater than 10 times the radius of the aluminum ball, and measure its length as L 摆线 ;

[0081] One end of the cycloid 7 can be quickly and easily fixed to the suspension point 3 of the aluminum ball 1 using UV curing glue;

[0082] Fix the starting end of the cycloid 7 by the knife-edge clamp 8 and hang the aluminum ball 1 on the iron stand 9;

[0083] Allow the aluminum ball 1 to droop naturally to perform a simple pendulum motion, and control the pendulum angle between 3 and 5 degrees;

[0084] After the aluminum ball 1 has completed about 10-20 simple pendulum cycles, the object can stop swinging.

[0085] Repeat steps 3 and 4 multiple times with the aluminum ball 1 to achieve the purpose of multiple measurement cycles;

[0086] Remove the aluminum ball 1 and the IMU chip 2 inside the aluminum ball 1;

[0087] The data of IMU chip 2 is read, and the period of the simple pendulum motion of aluminum ball 1 is obtained by analyzing the data through the acceleration signal characteristics and recorded as T.

[0088] Through the simple pendulum cycle Get the relationship between pendulum length and period:

[0089] Where L is the length from the center of mass of the aluminum ball 1 to the starting end of the cycloid when it performs a simple pendulum motion, in meters;

[0090] T is the period of the simple pendulum motion of the aluminum ball 1, in seconds;

[0091] g is the acceleration of gravity in the area, in m / s 2 .

[0092] From the measured period T, the length L from the center of mass of the aluminum ball 1 performing a simple pendulum motion to the starting end of the cycloid is obtained.

[0093] Determine the distance Δx from the center of mass of the aluminum ball 1 to the suspension point 3 as: Δx = LL 摆线 The point inside the aluminum ball 1 that is Δx away from the suspension point 3 along the center of mass line 6 is the center of mass of the aluminum ball.

[0094] The above embodiments are merely exemplary embodiments of the present application and are not intended to limit the scope of the present application. The scope of protection of the present application is defined by the claims. Those skilled in the art may make various modifications or equivalent substitutions to the present application within the essence and scope of protection of the present application, and such modifications or equivalent substitutions shall also be deemed to fall within the scope of protection of the present application.

Claims

1. A method for measuring the center of mass of an object based on an IMU chip, characterized in that: The following steps are involved: Confirm whether the object has an embedded IMU chip. If not, attach an IMU chip to the object to measure its swing period. Conduct heavy liquid experiments on objects to determine the location of the object's center of mass line and the suspension point of the cycloid; Perform a simple pendulum experiment on the object and determine the distance between the object's center of mass and the starting point of the cycloid based on the object's swing period, thereby obtaining the position of the center of mass.

2. The method for measuring the center of mass of an object based on an IMU chip according to claim 1, characterized in that: The mass ratio between the IMU chip and the covered object is less than 1:40, so as to ensure that the error of the IMU chip's influence on the center of mass position of the covered object is within 2%.

3. The method for measuring the center of mass of an object based on an IMU chip according to claim 1, characterized in that: The heavy liquid experiment comprises the following steps: Placing an object in a solution having a density greater than that of the object so that the object floats on the solution and the solution does not react with the object; Gradually add water to the solution to reduce the density of the solution, causing the object to gradually sink into the solution until only the top of the object is exposed above the liquid surface; After the object comes to rest, mark the point where the top is above the liquid surface as the hanging point.

4. The method for measuring the center of mass of an object based on an IMU chip according to claim 3, wherein: The simple pendulum experiment comprises the following steps: Fix one end of the cycloid to the hanging point of the object, and then suspend the object through the cycloid; Let the object hang down naturally to do simple pendulum motion; After the object has swung for 10-20 cycles, the object can be stopped from swinging; Read the data from the IMU chip and analyze the data through the acceleration signal characteristics to obtain the period of the object's simple pendulum motion; According to the period formula of the simple pendulum motion, calculate the length L from the center of mass of the object to the starting end of the cycloid, and then subtract the length L of the cycloid. 摆线 , we can get the distance from the center of mass to the hanging point Δx=LL 摆线 ; Finally, the exact position of the center of mass is measured by combining the center of mass line.

5. The method for measuring the center of mass of an object based on an IMU chip according to claim 4, characterized in that: The swing angle of the simple pendulum motion is 3 to 5 degrees.

6. The method for measuring the center of mass of an object based on an IMU chip according to claim 5, characterized in that: The object is an aluminum ball, and measuring the center of mass of the aluminum ball includes the following steps: The aluminum ball (1) with the built-in IMU chip is placed in a 1.8g / cm 3 The aluminum ball (1) is placed in a ZnCl2 solution (4) to float; Then, water is gradually added to the container (5) to reduce the density of the solution (4) so that the aluminum ball (1) gradually sinks into the solution (4); When the aluminum ball (1) can only expose a small area above the liquid surface, stop adding water. After the aluminum ball (1) is still, click a point just above the part of the ball that is exposed above the liquid surface. This point is the hanging point (3) of the object, and the center of mass of the ball is on the center of mass line (6) where this point is located. Take a thin steel wire as the cycloid (7), the length of the cycloid (7) is at least 10 times the radius of the aluminum ball (1), and measure its length as L 摆线 ; Fix one end of the cycloid (7) to the suspension point (3) of the aluminum ball (1) using ultraviolet curing glue; Fix the starting end of the cycloid (7) by the knife-edge clamp (8), and hang the aluminum ball (1) on the iron frame (9); The aluminum ball (1) is allowed to droop naturally to perform a simple pendulum motion, and the pendulum angle is controlled to be between 3° and 5°; After the aluminum ball (1) has completed 10-20 simple pendulum cycles, the object can stop swinging; The aluminum ball (1) is made to repeatedly perform the simple pendulum motion multiple times, so as to achieve the purpose of measuring the period multiple times; Remove the aluminum ball (1) and take out the IMU chip (2) inside the aluminum ball (1); Read the data from the IMU chip (2), and obtain the period of the simple pendulum motion of the aluminum ball (1) by analyzing the data through the acceleration signal characteristics and record it as T; From dimensional analysis, it can be concluded that when the deflection angle is less than 5°, the period of the simple harmonic motion of the pendulum is Then we can get the relationship between pendulum length and period: From the measured period T, the length L from the center of mass of the aluminum ball (1) to the starting end of the cycloid is calculated; Determine the distance Δx from the center of mass of the aluminum ball (1) to the suspension point (3): Δx = LL 摆线 The point inside the aluminum ball (1) that is Δx away from the center of mass line (6) and the suspension point (3) is the center of mass of the aluminum ball.

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