A method for measuring the centroid position and the moment of inertia about the axis passing through the centroid

Abstract

The present invention discloses a method for measuring the centroid position and the moment of inertia about the centroid axis, which includes measuring the swing period T0 of the load disk and the swing period T1 of a regular object with uniform mass distribution placed on the load disk, and determining the torsional constant K; measuring the swing period T2 of the fixture and the regular object with uniform mass distribution placed on the load disk, and further obtaining the moment of inertia I2 of the fixture and the regular object with uniform mass distribution placed on the load disk; selecting a preset number of experimental measurement points according to the preset selection requirements, measuring the swing period Ti of the object to be measured, the fixture and the regular object with uniform mass distribution placed on the load disk passing through the preset number of experimental measurement points in the preset coordinate system, and further obtaining the corresponding moment of inertia Ii; obtaining the coordinates corresponding to the preset number of experimental measurement points on the corresponding projection plane, and obtaining the centroid position of the object to be measured and the moment of inertia about the centroid axis according to the moment of inertia Ii in combination with the expression of the moment of inertia of the object about the new axis.

Description

Technical Field

[0001] The present invention belongs to the technical field of moment of inertia measurement, and particularly relates to a method for measuring the centroid position and the moment of inertia about the centroid axis. Background Art

[0002] For the centroid position of a rigid body with uneven mass distribution, there are many commonly used determination methods in practice, such as the suspension method, the support method, the thimble method, and the plumb line method, etc. These methods are widely used because of their simple operation and easy availability of the required equipment. However, the use of these methods is usually restricted by their assumed conditions and does not have universal applicability, and the determination of their centroid positions is mostly determined through sensory effects, lacking a quantitative evaluation standard, and is not applicable to scientific research that requires accurate determination of the centroid position.

[0003] This method is based on the experimental equipment of the torsion pendulum method to measure the moment of inertia about the centroid axis and the centroid position of a rigid body with uneven mass distribution, and has the characteristics of high measurement accuracy and quantifiable results. Summary of the Invention

[0004] In view of the above technical problems, the present invention provides a method for measuring the centroid position and the moment of inertia about the centroid axis.

[0005] The technical solution adopted by the present invention to solve its technical problems is as follows:

[0006] A method for measuring the centroid position and the moment of inertia about the centroid axis, the method comprising the following steps:

[0007] S100: Record the moment of inertia of the object tray as I 0 , obtain the moment of inertia of a regular object with uniform mass distribution as I 1 , combine the period expression of simple harmonic vibration and the moment of inertia expression to measure the swing period T0 of the object tray and the swing period T of the regular object with uniform mass distribution placed on the object tray 1 , and determine the torsional constant K, and obtain the moment of inertia I according to T0 and the torsional constant K 0 ;

[0008] S200: Measure the swing period T of the fixture and the regular object with uniform mass distribution placed on the object tray 2 , according to the swing period T 2 , the torsional constant K, the moment of inertia I0 and the moment of inertia I 1 obtain the moment of inertia I of the fixture about the rotation axis 2 ;

[0009] S300: Select a preset number of experimental measurement points according to the preset selection requirements, and measure the swing period Ti of the object to be measured, the fixture, and the regular object with uniform mass distribution placed on the load disk at the preset number of experimental measurement points in the preset coordinate system; according to Ti, the moment of inertia I 0 、the moment of inertia I 1 、the moment of inertia I 2 and the torsional constant K, obtain the moment of inertia Ii of the object to be measured, the fixture, and the regular object with uniform mass distribution placed on the load disk at the corresponding coordinate system of the preset number of experimental measurement points;

[0010] S400: Obtain the coordinate points and coordinates corresponding to the preset number of experimental measurement points on the corresponding projection plane, and obtain the centroid position of the object to be measured and the moment of inertia about the axis passing through the centroid according to the moment of inertia Ii in combination with the expression of the moment of inertia of the object about the new axis.

[0011] Preferably, S100 includes:

[0012] S110: Record that the moment of inertia of the load disk is I 0 , and measure the swing period T 0 of the load disk in combination with the period expression of simple harmonic vibration, specifically:

[0013]

[0014] wherein, I 0 is the moment of inertia of the load disk, T 0 is the swing period of the load disk, and K is the torsional constant;

[0015] S120: Obtain that the moment of inertia of the regular object with uniform mass distribution is I 1 , and measure the swing period T 1 of the regular object with uniform mass distribution placed on the load disk in combination with the period expression of simple harmonic vibration and the expression of the moment of inertia, specifically:

[0016]

[0017] wherein, I 1 is the moment of inertia of the regular object with uniform mass distribution, and T 1 is the swing period of the regular object with uniform mass distribution placed on the load disk;

[0018] S130: Obtain the torsional constant K according to the expressions of T 0 and T 1 , specifically:

[0019]

[0020] S140: According to T 0The moment of inertia I0 is obtained from the torsion constant K and the torsion.

[0021] Preferably, S200 is specifically:

[0022]

[0023] Among them, T 2 is the swing period when the fixture and a regular object with uniform mass distribution are placed on the turntable, and I 2 is the moment of inertia of the fixture about the rotation axis.

[0024] Preferably, the preset selection requirements include:

[0025] In the experiment, the selected measurement points should be on the straight line where the rotation axis of the torsion pendulum device is located, and the straight line where the rotation axis of the torsion pendulum device is located should be perpendicular to the projection plane.

[0026] Preferably, in S300, the swing periods Ti of the object to be measured, the fixture, and the regular object with uniform mass distribution placed on the turntable at the preset number of experimental measurement points in the preset coordinate system are measured. Among them, the swing period Ti includes T xi 、T yi and T zi , specifically:

[0027]

[0028]

[0029]

[0030] Among them, T xi 、T yi and T zi are respectively the swing periods of the object to be measured, the fixture, and the regular object with uniform mass distribution placed on the turntable in the x-axis, y-axis, and z-axis directions when passing through the i-th experimental measurement point, and I xi 、I yi and I zi are respectively the moments of inertia of the object to be measured in the x-axis, y-axis, and z-axis directions of the object to be measured, the fixture, and the regular object with uniform mass distribution placed on the turntable when passing through the i-th experimental measurement point.

[0031] Preferably, the moment of inertia Ii includes I xi 、I yi and I zi , in S400, according to the moment of inertia Ii and the expression of the moment of inertia of the object about the new axis, the centroid position of the object to be measured and the moment of inertia about the axis passing through the centroid are obtained, specifically:

[0032] I xi =I xx+m[(y qi -y qo ) 2 +(z qi -z qo ) 2

[0033] I yi =I yy +m[(x qi -x qo ) 2 +(z qi -z qo ) 2

[0034] I zi =I zz +m[(x qi -x qo ) 2 +(y qi -y qo ) 2

[0035] Among them, (I xx , I yy , I zz ) is the moment of inertia of the object to be measured about the axis passing through the center of mass, m is the mass of the object to be measured, (y qi , z qi ) are the coordinate points of the corresponding experimental measurement points projected onto the y q O q z q plane, (x qi , z qi ) are the coordinate points of the corresponding experimental measurement points projected onto the x q O q z q plane, (x qi , y qi ) are the coordinate points of the corresponding experimental measurement points projected onto the x q O q y q plane, (x qo , y qo , z qo ) are the coordinates of the center of mass of the object to be measured.

[0036] Preferably, the coordinates of the center of mass of the object to be measured in the coordinate system are (x qo , y qo , z qo ). Each coordinate will obtain two calculation results, and the average value of the two calculation results is taken as the final coordinate of the center of mass position.

[0037] ​​​Through the above method, high-precision and quantifiable measurements of the moment of inertia about the centroid axis and the centroid position of a rigid body with non-uniform mass distribution are achieved. Description of the Drawings

[0038] Figure 1 This is a flowchart of a method for measuring the centroid position and the moment of inertia about the centroid axis in an embodiment of the present invention;

[0039] Figure 2 This is a schematic structural diagram of a torsion pendulum device in an embodiment of the present invention;

[0040] Figure 3 This is a schematic diagram of the body coordinate system and the particle description coordinate system in an embodiment of the present invention;

[0041] Figure 4 This is a schematic diagram of the parallel movement of the rotating shaft in an embodiment of the present invention;

[0042] Figure 5 This is a schematic diagram of the selection of experimental measurement points in an embodiment of the present invention. Detailed Embodiments

[0043] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0044] In one embodiment, as Figure 1 shown, a method for measuring the centroid position and the moment of inertia about the centroid axis is characterized in that the method includes the following steps:

[0045] S100: Record that the moment of inertia of the object tray is I 0 , obtain the moment of inertia of a regular object with uniform mass distribution as I 1 , combine the period expression of simple harmonic vibration and the moment of inertia expression to measure the swing period T 0 of the object tray and the swing period T 1 when the regular object with uniform mass distribution is placed on the object tray, and determine the torsion constant K. Obtain the moment of inertia I 0 according to T 0 and the torsion constant K;

[0046] S200: Measure the swing period T 2 when the fixture and the regular object with uniform mass distribution are placed on the object tray. According to the swing period T 2 , the torsion constant K, the moment of inertia I 0 and the moment of inertia I 1 , obtain the moment of inertia I 2 of the fixture about the rotation axis;

[0047] S300: Select a preset number of experimental measurement points according to the preset selection requirements, and measure the swing period Ti of the object under test, the fixture, and the regular object with uniform mass distribution placed on the load plate at the preset number of experimental measurement points in the preset coordinate system; according to Ti, the moment of inertia I 0 the moment of inertia I 1 the moment of inertia I 2 and the torsional constant K, obtain the moment of inertia Ii of the object under test, the fixture, and the regular object with uniform mass distribution placed on the load plate at the corresponding coordinate system of the preset number of experimental measurement points;

[0048] S400: Obtain the coordinate points and coordinates corresponding to the preset number of experimental measurement points on the corresponding projection plane, and obtain the centroid position of the object under test and the moment of inertia about the centroid axis according to the moment of inertia Ii in combination with the expression of the moment of inertia of the object about the new axis.

[0049] The above method is implemented based on a torsional pendulum device such as Figure 2 , including the object under test (1), the fixture (2), the regular object with uniform mass distribution (3), the photogate sensor mounting rod (4), the photogate sensor (5), the main body of the torsional pendulum device (6), the mounting base of the torsional pendulum device (7), the electronic scale (8), and the intelligent display (9).

[0050] Before performing the above method, a coordinate system needs to be established first, as shown in Figure 3 , including the body coordinate system (O b -x b y b z b ) and the particle description coordinate system (O q -x q y q z q ), where, for the body coordinate system (O b -x b y b z b ): The origin O b coincides with the centroid of the object, the direction of the x b axis is arbitrary and forms a body coordinate system together with the y b and z b axes, and the directions of the three axes follow the right-hand screw theorem. For the particle description coordinate system (O q -x q y q z q ): The origin O q is selected at a position convenient for marking and measurement, and x q , y q and z q are respectively parallel to x b , y b and zb And the directions are consistent.

[0051] The experimental principle involved in the above method:

[0052] (1) Principle of measuring moment of inertia by the torsion pendulum method

[0053] The core device for measuring moment of inertia by the torsion pendulum method is a thin spiral spring. After the object sleeved on the shaft is rotated by a certain angle θ in the horizontal plane, under the action of the restoring moment of the spring, the object starts to perform reciprocating torsional motion around the vertical axis. According to Hooke's law, the restoring moment M generated by the spring due to torsion is proportional to the rotated angle, that is

[0054] M = -Kθ (1)

[0055] where K is the torsion constant of the spring. From the rotational law:

[0056] M = I·β (2)

[0057] Combining equations (1) and (2), we have:

[0058]

[0059] So Neglecting the frictional moment of the bearing, we have:

[0060]

[0061] That is:

[0062]

[0063] This equation shows that the torsional pendulum motion neglecting the frictional moment of the bearing is a simple harmonic vibration, and the solution of this equation is:

[0064] θ = A·cos(ωt + φ) (6)

[0065] In the formula, A is the angle of the simple harmonic vibration, φ is the initial phase, and ω is the angular frequency. The period of this simple harmonic vibration is:

[0066]

[0067] As can be seen from the above formula, when the period of the torsion pendulum is measured and any one of I and K is a known quantity, the other quantity can be calculated.

[0068] (2) Parallel axis theorem

[0069] If the moment of inertia of an object with mass m about the axis passing through its center of mass is I c , when the axis of rotation is translated parallel by a distance x (as Figure 4 shown), the moment of inertia of the object about the new axis is:

[0070] I′ = I c +mx 2 (8)

[0071] Moment of inertia calculation formula:

[0072] I = ∑Δmr 2 (9)

[0073] As can be seen from the above formula, for two objects on the same axis of rotation, the total moment of inertia of the two objects can be expressed as the sum of the moments of inertia of the two objects respectively.

[0074] In one embodiment, S100 includes:

[0075] S110: Record that the moment of inertia of the object tray is I 0 , and measure the swing period T of the object tray in combination with the period expression of simple harmonic vibration 0 , specifically:

[0076]

[0077] where I 0 is the moment of inertia of the object tray, T 0 is the swing period of the object tray, and K is the torsional constant;

[0078] S120: Obtain that the moment of inertia of a regular object with uniform mass distribution is I 1 , and measure the swing period T of the regular object with uniform mass distribution placed on the object tray in combination with the period expression of simple harmonic vibration and the moment of inertia expression 1 , specifically:

[0079]

[0080] where I 1 is the moment of inertia of the regular object with uniform mass distribution, and T 1 is the swing period of the regular object with uniform mass distribution placed on the object tray;

[0081] S130: Obtain the torsional constant K according to the expressions of T 0 and T 1 , specifically:

[0082]

[0083] S140: Obtain the moment of inertia I according to T 0 and the torsional constant K 0 .

[0084] In one embodiment, S200 is specifically:

[0085]

[0086] Among them, T 2 is the swing period of the fixture and a regular object with uniform mass distribution placed on the load tray, and I 2 is the moment of inertia of the fixture about the rotation axis.

[0087] Through the above formula, the moment of inertia I of the fixture can be measured 2 . When the mass of the fixture is much smaller than the mass of the object to be measured, the influence of the change in the moment of inertia of the fixture caused by the change in the measurement position of the fixture on the measurement of the moment of inertia of the object can be ignored.

[0088] In one embodiment, the preset selection requirements include:

[0089] In the experiment, the selected measurement points should be on the straight line where the rotation axis of the torsion pendulum device is located, and the straight line where the rotation axis of the torsion pendulum device is located should be perpendicular to the projection plane.

[0090] Specifically, in practical applications, the moments of inertia are mainly measured for I xx , I yy and I zz , so this measurement method is mainly for I xx , I yy and I zz . Further, the straight line where the rotation axis of the torsion pendulum device is located should be perpendicular to the projection plane, that is, perpendicular to the y xx O q z q plane when measuring I yy , perpendicular to the x q O q z q plane when measuring I zz , and perpendicular to the x q O q y q plane when measuring I xx .

[0091] The selection of the experimental measurement points should be significantly deviated from the centroid and convenient for marking. When measuring I x , the selected measurement points A x , B x and C x are as shown in , and the projections and coordinates of A x , B x and C q on the y q O q z x plane are denoted as A′ qa (y qa , z x ), B′x (y qb , z_qb) and C′ x (y qc , z qc ). Similarly, the measurement points for measuring I yy and I zz and their corresponding coordinate points A y , B y , C y on the respective projection planes can be selected. A′ y (x qa , z qa ), B′ y (x qb , z qb ), C′ y (x qc , z qc ), and A z , B z , C z , A′ z (x qa , y qa ), B′ z (x qb , y qb ), C′ z (x qc , y qc ).

[0092] In one embodiment, in S300, the swing periods Ti of the object to be measured, the fixture, and the regular object with uniform mass distribution placed on the carrier plate at the preset number of experimental measurement points in the preset coordinate system are measured, where the swing periods Ti include T xi , T yi and T zi , specifically:

[0093]

[0094]

[0095]

[0096] Among them, T xi , T yi and T zi are respectively the swing periods of the object to be measured, the fixture, and the regular object with uniform mass distribution placed on the carrier plate in the x-axis, y-axis, and z-axis directions when passing through the i-th experimental measurement point. I xi , I yi and I ziThe moments of inertia of the object to be measured, the fixture, and the regular object with uniform mass distribution in the x-axis, y-axis, and z-axis directions when they are placed on the load plate and pass through the i-th experimental measurement point are respectively measured.

[0097] Specifically, when measuring I xx , at the selected experimental measurement point, the oscillation periods T xa , T xb , and T xc of the object to be measured, the fixture, and the regular object with uniform mass distribution placed on the load plate are measured. Specifically:

[0098]

[0099]

[0100]

[0101] If the mass of the fixture cannot be ignored and the position of the fixture changes with the measurement position of the object to be measured, the moment of inertia of the fixture at each measurement point can be measured separately, and the measured moment of inertia result is substituted into the formula for calculating the oscillation period to replace the I 2 term.

[0102] The formula for measuring the moment of inertia of the fixture is as follows:

[0103]

[0104] where the subscript j corresponds to the position mark of the fixture when the object to be measured is measured at measurement points such as A x , B x , C x .

[0105] In one embodiment, the moment of inertia Ii includes I xi , I yi , and I zi . In S400, according to the moment of inertia Ii and the expression of the moment of inertia of the object about the new axis, the centroid position of the object to be measured and the moment of inertia about the axis passing through the centroid are obtained. Specifically:

[0106] I xi = I xx + m[(y qi - y qo ) 2 + (z qi - z qo ) 2

[0107] I yi = I yy + m[(x qi - x qo ​) 2 +(z qi -z qo ) 2

[0108] I zi =I zz +m[(x qi -x qo ) 2 +(y qi -y qo ) 2

[0109] Among them, (I xx , I yy , I zz ) is the moment of inertia of the object to be measured about the axis passing through the center of mass, m is the mass of the object to be measured, (y qi , z qi ) is the coordinate point of the corresponding experimental measurement point projected onto the y q O q z q plane, (x qi , z qi ) is the coordinate point of the corresponding experimental measurement point projected onto the x q O q z q plane, (x qi , y qi ) is the coordinate point of the corresponding experimental measurement point projected onto the x q O q y q plane, (x qo , y qo , z qo ) is the coordinate of the center of mass of the object to be measured.

[0110] Taking I xx as an example, there is:

[0111] I xa =I xx +m[(y qa -y qo ) 2 +(z qa -z qo ) 2

[0112] I xb =I xx +m[(y qb -y qo ) 2 +(z qb -z qo ) 2 ​​​​

[0113] I xc = I xx + m[(y qc - y qo ) 2 + (z qc - z qo ) 2

[0114] In the formula, (y qo , z qo ) is the projection coordinates of the centroid of the object to be measured on the plane y q O q z q . m is the mass of the object to be measured. Substitute the measured moment of inertia and the coordinates of the experimental measurement points into the above formula for calculation, and I xx and the projection coordinates of the centroid on the plane y q O q z q can be obtained. (y qo , z qo ). Similarly, measure I yy and I zz respectively, and the moment of inertia of the object about the centroid axis and the projection coordinates of the object centroid in the coordinate system O q -x q y q z q can be obtained. The plane projection coordinates (x qo , z qo ) and (x qo , y qo ).

[0115] Furthermore, the coordinates of the centroid of the object to be measured in the coordinate system are (x qo , y qo , z qo ). Each coordinate will obtain two calculation results, and the average value of the two calculation results is taken as the final centroid position coordinate.

[0116] Specifically, from the finally obtained results, the coordinates (x b , y qo , z qo ) of the centroid O qo in the coordinate system each have two calculation results. Under ideal conditions, the two results should be the same, but due to inevitable measurement and operation errors in the experiment, the final centroid position coordinate can be obtained by taking the average value of the two calculation results.

[0117] ​The above has introduced in detail a method for measuring the centroid position and the moment of inertia about the centroid axis provided by the present invention. Specific examples are used in this article to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the core idea of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A method for measuring the centroid position and the moment of inertia about the centroid axis, characterized in that, the method comprises the following steps: S100: The moment of inertia of the object tray is I 0 , and the moment of inertia of a regular object with uniform mass distribution is obtained as I 1 . Combining the period expression of simple harmonic vibration and the moment of inertia expression to measure the swing period T of the object tray 0 and the swing period T of a regular object with uniform mass distribution placed on the object tray 1 , and determining the torsional constant K. According to the T 0 and the torsional constant K, the moment of inertia I is obtained 0 ; S200: Measure the swing period T of the measuring fixture and the regular object with uniform mass distribution placed on the load tray 2 , according to the swing period T 2 , the torsional constant K, the moment of inertia I 0 and the moment of inertia I 1 Obtain the moment of inertia I of the fixture about the rotation axis 2 ; S300: Select a preset number of experimental measurement points according to the preset selection requirements, and measure the swing period Ti of the object to be measured, the fixture, and the regular object with uniform mass distribution placed on the carrier plate passing through the preset number of experimental measurement points in the preset coordinate system; according to the Ti, the moment of inertia I 0 , the moment of inertia I 1 , the moment of inertia I 2 and the torsional constant K, obtain the moment of inertia Ii of the object to be measured, the fixture, and the regular object with uniform mass distribution placed on the carrier plate in the corresponding coordinate system passing through the preset number of experimental measurement points; S400: Obtain the coordinate points and coordinates corresponding to the preset number of experimental measurement points on the corresponding projection plane, and obtain the centroid position of the object to be measured and the moment of inertia about the centroid axis according to the moment of inertia Ii in combination with the expression of the moment of inertia of the object about the new axis.

2. The method according to claim 1, characterized in that, S100 includes: S110: Denote the moment of inertia of the object tray as I 0 , and measure the oscillation period T of the object tray in combination with the period expression of simple harmonic vibration 0 , specifically: Among them, I 0 is the moment of inertia of the load tray, T 0 is the swing period of the load tray, and K is the torsional constant; S120: Obtain the moment of inertia I of a regular object with uniform mass distribution 1 , and measure the oscillation period T of a regular object with uniform mass distribution placed on the object tray in combination with the period expression of simple harmonic vibration and the moment of inertia expression 1 , specifically: Among them, I 1 is the moment of inertia of a regular object with uniform mass distribution, and T 1 is the oscillation period of a regular object with uniform mass distribution placed on the carrier plate; S130: Obtain the torsional constant K according to the expressions of T 0 and T 1 Specifically, it is as follows: S140: Obtain the moment of inertia I according to the T 0 and the torsional constant K 0 .

3. The method according to claim 2, characterized in that, S200 is specifically: Among them, T 2 is the swing period of the fixture and the regular object with uniform mass distribution placed on the carrier plate, and I 2 is the moment of inertia of the fixture about the rotation axis.

4. The method according to claim 3, characterized in that, the preset selection requirements include: In the experiment, the selected measurement points should be on the straight line where the rotation axis of the torsion pendulum device is located, and the straight line where the rotation axis of the torsion pendulum device is located should be perpendicular to the projection plane.

5. The method according to claim 4, characterized in that, In the S300, measure the swing period Ti of the object to be measured, the fixture, and the regular object with uniform mass distribution placed on the load tray at the preset number of experimental measurement points in the preset coordinate system, where the swing period Ti includes T xi , T yi , and T zi , specifically: Among them, T xi , T yi and T zi are respectively the swing periods in the x-axis, y-axis, and z-axis directions when the object to be measured, the fixture, and the regular object with uniform mass distribution are placed on the load disk passing through the i-th experimental measurement point. I xi , I yi and I zi are respectively the moments of inertia of the object to be measured in the x-axis, y-axis, and z-axis directions when the object to be measured, the fixture, and the regular object with uniform mass distribution are placed on the load disk passing through the i-th experimental measurement point.

6. The method according to claim 5, characterized in that, The moment of inertia Ii includes I xi , I yi and I zi . In S400, according to the moment of inertia Ii and the expression of the moment of inertia of the object about the new axis, the centroid position of the object to be measured and the moment of inertia about the axis passing through the centroid are obtained. Specifically: I xi = I xx + m[(y qi - y qo ) 2 +(z qi - z qo ) 2 ​ I yi = I yy + m[(x qi - x qo ) 2 +(z qi - z qo ) 2 ​ I zi = I zz + m[(x qi - x qo ) 2 +(y qi - y qo ) 2 ​ Among them, (I xx , I yy , I zz ) is the moment of inertia of the object to be measured about the centroid axis, m is the mass of the object to be measured, (y qi , z qi ) are the coordinate points of the corresponding experimental measurement points projected onto the y q O q z q plane, (x qi , z qi ) are the coordinate points of the corresponding experimental measurement points projected onto the x q O q z q plane, (x qi , y qi ) are the coordinate points of the corresponding experimental measurement points projected onto the x q O q y q plane, (x qo , y qo , z qo ) are the coordinates of the centroid of the object to be measured.

7. The method according to claim 6, characterized in that, The coordinates of the centroid of the object to be measured in the coordinate system are (x qo , y qo , z qo ). Two calculation results will be obtained for each coordinate, and the average value of the two calculation results is taken as the final coordinate of the centroid position.

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