Large component gravity center measuring method based on distributed six-dimensional force sensor

Abstract

The invention provides a method for measuring the gravity center of a large component based on a distributed six-dimensional force sensor. The method specifically comprises the steps that firstly, the six-dimensional force sensor is installed below a spherical hinge of a positioner and used for measuring the contact force and friction torque of the spherical hinge; then, according to the conversion principle of force and torque between coordinate systems, the acting force and torque of the positioner on the large component and the gravity and gravitational torque of the large component are converted into the base coordinate system, and therefore a torque balance equation of the large component in the base coordinate system is established; and finally, adjusting the spatial attitude of the large component, and solving the center-of-gravity position by adopting a least square method according to the moment balance equation of the large component under different attitudes. According to the method of the scheme, aiming at the influence of the friction torque of the spherical hinge on the gravity center measurement precision during the gravity center measurement of the large component, the friction torque of the spherical hinge during the posture adjustment of the large component can be calculated, so that the gravity center measurement precision of the large component is improved.

Description

Technical Field

[0001] The present invention relates to the field of centroid measurement of large components, and particularly to a method for measuring the centroid of large components based on a distributed six-dimensional force sensor. Background Technique

[0002] In an automated assembly system for large aerospace components, a three-coordinate numerical control positioner is usually used as a posture adjustment and positioning mechanism to realize the posture adjustment and docking of large components in the assembly space. The accuracy of the centroid position of large components is an important factor affecting the dynamic model of the posture adjustment mechanism and the accuracy of the contact force calculation during the compliant docking process. In order to achieve precise and compliant assembly of large components, it is necessary to accurately measure the centroid position of large structures. Currently, the centroid measurement of large components mainly measures the force exerted by the positioner on the large component under different postures through a three-dimensional force sensor at the end of the positioner, and calculates the centroid position of the large component by using the principle of moment balance and coordinate system transformation method. However, this measurement method does not consider the influence of the ball joint friction moment on the centroid measurement accuracy when the large component's attitude is adjusted. Therefore, the present invention proposes a method for measuring the centroid of large components based on a distributed six-dimensional force sensor, so as to improve the accuracy of the centroid measurement of large components. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for measuring the centroid of large components based on a distributed six-dimensional force sensor to solve the problems raised in the above background technique. The specific implementation methods include: First, install a six-dimensional force sensor below the ball joint of the positioner to measure the contact force and friction moment of the ball joint; then, according to the transformation principle of force and moment between coordinate systems, transform the force and moment exerted by the positioner on the large component, as well as the gravity and gravity moment of the large component, to the base coordinate system, so as to establish a moment balance equation of the large component in the base coordinate system; finally, adjust the spatial attitude of the large component, and solve the centroid position by using the least squares method according to the moment balance equation of the large component under different postures.

[0004] To achieve the above purpose, the present invention provides the following technical solution: A method for measuring the centroid of large components based on a distributed six-dimensional force sensor, the specific steps are as follows:

[0005] Step 1: Install the six-dimensional force sensor below the ball joint used to connect the numerical control positioner and the bracket to measure the contact force and friction moment between the ball joints;

[0006] Step 2: According to the transformation principle of force and moment between coordinate systems, transform the gravity and gravity moment of the large component, as well as the force and friction moment between the ball joints, to the base coordinate system, and establish a moment balance equation;

[0007] Step 3: Adjust the spatial posture of the large component, use the least squares method to solve the center position according to the moment balance equation of the large component in different postures, and calculate the center of gravity position.

[0008] As an improvement, in step one, the large-scale component center of gravity measurement system based on distributed six-dimensional force sensors mainly includes a CNC positioner, a ball joint, a six-dimensional force sensor and a large structure; the CNC positioner is used to support and adjust the posture of the large component, and has three degrees of freedom of X / Y / Z; the ball joint is composed of a ball head and a ball socket, and the CNC positioner is connected to the large structure through the ball joint. When the positioner moves, the position of the center of the ball socket moves but the attitude angle does not change; the six-dimensional force sensor is installed under the ball joint to measure the force exerted by the positioner on the large structure.

[0009] As an improvement, multiple ball joints are provided, preferably 3 or more than 3, wherein one ball joint is correspondingly installed with a six-dimensional force sensor and a CNC positioner.

[0010] As an improvement, in step 1, the coordinates constructed include: base coordinate system O b -xyz, large structure local coordinate system O c -xyz, spherical joint coordinate system O q -xyz and sensor coordinate system O s -xyz. Specifically, the base coordinate system O b -xyz is the reference coordinate system in the entire assembly space, and the z axis is perpendicular to the horizontal plane; the local coordinate system of the large structure O c -xyz is a coordinate system that is fixed to the large structure itself. It moves with the adjustment of the large structure's own position and posture, representing the position and posture of the large structure; the i-th spherical joint coordinate system It is the coordinate system fixed to the i-th ball socket, and its origin is located at the center of the i-th ball socket. After the positioner is installed, the direction of the ball joint coordinate system is consistent with the base coordinate system; the i-th six-dimensional force sensor coordinate system is the coordinate system of the i-th six-dimensional force sensor itself. The force and torque measured by the i-th six-dimensional force sensor are in the sensor coordinate system As shown below, after the sensor is installed, the sensor coordinate system and the ball joint coordinate system are in the same direction.

[0011] As an improvement, in step 1, the calculation process of the force and moment of the positioner on the large component includes:

[0012] The force and moment of the ith positioner on the large component are the contact force and friction moment between the ith ball head and the ith ball socket, respectively expressed as and The force and torque measured by the i-th six-dimensional force sensor are respectively expressed as and It is expressed that the attitude matrix and position vector of the i-th six-dimensional force sensor coordinate system relative to the i-th spherical hinge coordinate system are and According to the transformation principle of force and moment between coordinate systems, and There is the following relationship between them.

[0013]

[0014] Since the directions of the sensor coordinate system and the spherical hinge coordinate system are the same, therefore is the identity matrix, and the following formula can be obtained

[0015]

[0016] where E 3×3 represents the third-order identity matrix. According to the measured force value of the i-th six-dimensional force sensor, the contact force F i q between the i-th ball head and the i-th ball socket can be calculated, as well as the frictional moment

[0017] As an improvement, in step two, the process of establishing the moment balance equation of the large component includes:

[0018] (1) The coordinate representation of the center of the i-th spherical hinge in the local coordinate system of the large component is The coordinate representation of the center of the i-th spherical hinge in the base coordinate system at a certain moment is According to the coordinate transformation principle, the following formula can be obtained

[0019]

[0020] where the coordinate of the spherical hinge center in the base coordinate system can be read out through the servo control system of the locator. According to the coordinates of the centers of three or more spherical hinges in the base coordinate system, the attitude matrix of the local coordinate system of the large component relative to the base coordinate system and the position vector

[0021] (2) When the attitude of the large structure is adjusted, the position of the spherical hinge coordinate system relative to the base coordinate system moves, but the attitude angle does not change. Let the attitude matrix of the i-th spherical hinge coordinate system relative to the base coordinate system be The position vector is Since the origin of the spherical hinge coordinate system is the center of the spherical hinge, therefore According to the transformation principle of force and moment between coordinate systems, the force and moment exerted by the ball socket on the ball head are transformed to the base coordinate system, so there is

[0022]

[0023] Since the directions of the sensor coordinate system and the spherical hinge coordinate system are the same, therefore is the identity matrix. Combining with formula (1), the following formula can be obtained

[0024]

[0025] (3) The coordinate representation of the centroid position of the large component in the local coordinate system of the large component is The coordinate representation of the centroid position in the base coordinate system is According to the coordinate system transformation principle, the following formula holds

[0026]

[0027] The gravity acting on the large structure is mg. Since the direction of gravity is opposite to the Z direction of the base coordinate system, the gravity matrix of the large structure in the base coordinate system is F G = [0 0 -mg]. The moment generated by gravity in the base coordinate system can be obtained as M G = G b × F G . When the large component is in a static state, the resultant force and resultant moment acting on it are 0. Therefore, there is

[0028]

[0029] Substituting equation (5) into equation (7) gives

[0030]

[0031] Formula (8) is the moment balance equation of the large component in a static state.

[0032] As an improvement, in step three, the calculation process of the centroid position includes

[0033] (1) Expand equation (8) and eliminate the equations irrelevant to the centroid position G c to obtain

[0034]

[0035] Substitute into equation (9) to get

[0036]

[0037] where represents taking the new matrix composed of the first two rows of the matrix .

[0038] (2) Equation (12) contains three unknowns All other parameters can be directly obtained or calculated based on the readings of the force sensor and the servo control system. Write Equation (10) in matrix form

[0039]

[0040] where M Q is the moment matrix of the large component

[0041]

[0042] (3) The matrix equation (11) contains two equations. Therefore, the centroid position of the large component is calculated according to a set of moment balance equations of the large component. It can be found from Equation (11) that the moment matrix M Q is only related to the attitude matrix of the large component . In order to obtain different moment balance equations, it is necessary to adjust the spatial attitude of the large component. Suppose that in the jth attitude, the attitude matrix of the large component is and the moment matrix is Obtaining the attitude matrix and moment matrix of the large component in one attitude is called one weighing. After the large component is weighed N (N≥2) times, the following formula can be obtained.

[0043]

[0044] Let and the least squares solution of G c can be calculated as

[0045]

[0046] which is the obtained centroid position.

[0047] Advantageous effects: Compared with the prior art, the present invention has at least the following advantages:

[0048] 1. The present invention uses a six-dimensional sensor to measure the force exerted by the positioner on the large component. The constructed moment balance equation takes into account the influence of the frictional moment of the spherical hinge on the centroid position during large attitude adjustment, thereby improving the accuracy of centroid measurement.

[0049] 2. The centroid measurement of the large component is carried out at the assembly site. There is no need to prepare a special measurement tooling, and only the original three-dimensional force sensor needs to be replaced with a six-dimensional force sensor. Brief description of the drawings

[0050] Figure 1 is a schematic diagram of the composition of the large component centroid measurement system based on the distributed six-dimensional force sensor of the present invention.

[0051] Figure 2Schematic diagram of the ball joint structure of the present invention.

[0052] Figure 3 Schematic flow diagram of the measurement method of the present invention.

[0053] Figure 4 Reading example of the six - dimensional force sensor of the present invention.

[0054] In the figure: the first ball joint 1, the first six - dimensional force sensor 2, the first numerical control positioner 3, the large component 4, the second ball joint 5, the second six - dimensional force sensor 6, the second numerical control positioner 7, the third ball joint 8, the third six - dimensional force sensor 9, the third numerical control positioner 10, the first ball head 11, and the first ball socket 12. Specific implementation mode

[0055] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0056] The large component centroid measurement system based on a distributed six - dimensional force sensor of the present invention includes a numerical control positioner, a ball joint, a six - dimensional force sensor, and a large structure 4; the numerical control positioner is used to support and adjust the pose of the large component 4 and has three degrees of freedom in X / Y / Z; the ball joint is composed of a ball head and a ball socket, and the numerical control positioner is connected to the large structure through the ball joint; the six - dimensional force sensor is installed below the ball joint and is used to measure the force exerted by the positioner on the large structure. One ball joint corresponds to one six - dimensional force sensor and one numerical control positioner. Multiple ball joints can be designed, generally designed to be no less than three. In the present invention, 3 are preferably selected as specific embodiments for illustration.

[0057] See Figure 1 As shown, as a specific implementation mode of the present invention, the large component centroid measurement system includes three ball joints, three six - dimensional sensors, and three numerical control positioners, specifically the first ball joint 1, the first six - dimensional force sensor 2, the first numerical control positioner 3, the large component 4, the second ball joint 5, the second six - dimensional force sensor 6, the second numerical control positioner 7, the third ball joint 8, the third six - dimensional force sensor 9, the third numerical control positioner 10. Each ball joint includes a ball head and a ball socket.

[0058] See Figure 2 As shown, the first ball joint 1 includes the first ball head 11 and the first ball socket 12.

[0059] Please refer to Figure 3 , for the large component centroid measurement method based on a distributed six - dimensional force sensor of the present invention, including:

[0060] Step 1: Install the six-axis force sensor under the ball joint used to connect the CNC positioner and the bracket, and measure the contact force and friction torque between the ball joints.

[0061] (1) A large component center of gravity measurement system based on a distributed six-dimensional force sensor is adaptively installed, wherein in the present invention, when the CNC positioner moves, the position of the ball socket center moves but the attitude angle does not change.

[0062] (2) In the large-scale structure automated assembly system, the coordinate system is constructed, including the base coordinate system O b -xyz, large structure local coordinate system O c -xyz, spherical joint coordinate system O q -xyz and sensor coordinate system O s -xyz.

[0063] Specifically, the base coordinate system O b -xyz is the reference coordinate system in the entire assembly space, and the z axis is perpendicular to the horizontal plane; the local coordinate system of the large structure O c -xyz is a coordinate system that is fixed to the large structure itself. It moves with the adjustment of the large structure's own position and posture, representing the position and posture of the large structure; the i-th spherical joint coordinate system It is the coordinate system fixed to the i-th ball socket, and its origin is located at the center of the i-th ball socket. After the positioner is installed, the direction of the ball joint coordinate system is consistent with the base coordinate system; the i-th six-dimensional force sensor coordinate system is the coordinate system of the i-th six-dimensional force sensor itself. The force and torque measured by the i-th six-dimensional force sensor are in the sensor coordinate system As shown below, after the sensor is installed, the sensor coordinate system and the ball joint coordinate system are in the same direction.

[0064] (3) The force and moment of the i-th positioner on the large component are the contact force and friction moment between the i-th ball head and the i-th socket, respectively expressed as contact force and friction torque The force and torque measured by the i-th six-dimensional force sensor are respectively and torque Represents; the posture matrix of the i-th six-dimensional force sensor coordinate system relative to the i-th spherical joint coordinate system is and the position vector is According to the transformation principle of force and torque between coordinate systems, and The following relationship exists between them.

[0065]

[0066] Since the sensor coordinate system and the ball joint coordinate system are in the same direction, Taking the unit matrix, the following equation can be obtained

[0067]

[0068] where E 3×3 represents the third-order unit matrix. According to the force value measured by the six-axis force sensor the contact force F between the i-th ball head and the i-th ball socket can be calculated i q and the frictional torque when the i-th ball joint rotates

[0069] Step 2: Construct a moment balance equation according to the gravity acting on the large component, as well as the contact force and frictional torque between the ball joints

[0070] (1) The coordinate representation of the center of the i-th ball joint in the local coordinate system of the large component is The coordinate representation of the center of the i-th ball joint in the base coordinate system at a certain moment is According to the coordinate transformation principle, the following equation can be obtained

[0071]

[0072] where the coordinate of the center of the ball joint in the base coordinate system can be read out through the servo control system. According to the coordinates of the centers of three or more ball joints in the base coordinate system, the attitude matrix of the local coordinate system of the large component relative to the base coordinate system can be calculated using the SVD method and the position vector

[0073] (2) When the attitude of the large structure is adjusted, the position of the ball joint coordinate system relative to the base coordinate system moves, but the attitude angle does not change. Let the attitude matrix of the i-th ball joint coordinate system relative to the base coordinate system be The position vector is Since the origin of the ball joint coordinate system is the center of the ball joint, therefore According to the transformation principle of force and moment between coordinate systems, the force and moment exerted by the ball socket on the ball head are transformed to the base coordinate system. Therefore, there is

[0074]

[0075] Since the directions of the sensor coordinate system and the ball joint coordinate system are the same, therefore is the unit matrix. Combining with formula (1), the following equation can be obtained

[0076]

[0077] (3) The coordinate representation of the center of gravity position of the large component in the local coordinate system of the large component is The coordinate representation of the center of gravity position in the base coordinate system is According to the coordinate system transformation principle, the following equation holds

[0078]

[0079] The gravity acting on the large structure is mg. Since the direction of gravity is opposite to the Z direction of the base coordinate system, the gravity matrix of the large structure in the base coordinate system is F G = [0 0 -mg], and the moment generated by gravity in the base coordinate system can be obtained as M G = G b × F G . When the large component is in a static state, the resultant force and resultant moment acting on it are 0. Therefore, we have

[0080]

[0081] Substituting equation (5) into equation (7) gives

[0082]

[0083] Equation (8) is the moment balance equation for the large component in a static state.

[0084] Step 3: Calculate the center of gravity position using the least squares method according to the moment balance equation of the large component in different postures.

[0085] (1) Expand equation (8) and eliminate the equations unrelated to the center of gravity position G c to obtain

[0086]

[0087] Substituting into equation (9) gives

[0088]

[0089] where represents taking the new matrix composed of the first two rows of the matrix .

[0090] (2) Equation (12) contains three unknowns and all other parameters can be directly obtained or calculated from the readings of the force sensors and the servo control system. Write equation (10) in matrix form

[0091]

[0092] where M Q is the moment matrix of the large component

[0093]

[0094] (3) The matrix equation (11) contains two equalities, and the centroid position of the large component is calculated according to a set of moment balance equations of large components. From equation (11), it is found that the moment matrix M Q is only related to the attitude matrix of the large component. To obtain different moment balance equations, it is necessary to adjust the spatial attitude of the large component. Suppose that in the jth attitude, the attitude matrix of the large component is and the moment matrix is Obtaining the coordinates of the spherical hinge center of the large component in the base coordinate system and the readings of the force sensors in one attitude is called one weighing. After the large component is weighed N (N≥2) times, the following formula is obtained.

[0095]

[0096] Let The least-squares solution of G c can be calculated as

[0097]

[0098] The above measurement method will be described and introduced below through specific measurement values.

[0099] Example 1

[0100] It is known that the position vectors of the coordinate system of the six-axis force sensor relative to the corresponding spherical hinge coordinate system are all The coordinates of the spherical hinge center in the local coordinate system of the large component are respectively The large structure is weighed three times. The coordinates of the spherical hinge center in the base coordinate system and the readings of the six-axis force sensor during each weighing are shown in Table 1 below.

[0101] Table 1 Coordinates of the spherical hinge center in the base coordinate system and readings of the six-axis force sensor during each weighing

[0102]

[0103] According to the coordinates of the spherical hinge center in the base coordinate system, the attitude matrix and the position vector of the large structure relative to the base coordinate system during the three weighings can be calculated respectively as

[0104]

[0105] Substituting the above parameters into formulas (10) and (14), the coordinates of the centroid G c can be calculated as (35.61, 73.18, 12.12) mm.

[0106] Since the position of the center of gravity cannot be directly measured, in order to verify the accuracy of the center of gravity position, the spatial pose of the large structure is adjusted. If the center of gravity position of the large structure, as well as the force readings in the X / Y directions and the moment readings about the X / Y / Z directions of the six-axis force sensor are known, the force value in the Z direction of the six-axis force sensor can be calculated according to formula (9). The closer this value is to the reading in the Z direction of the six-axis force sensor, the higher the accuracy of the position. Under the condition of this spatial pose, the coordinates of the ball joint center in the base coordinate system are

[0107]

[0108] The force readings in the X / Y directions and the moment readings about the X / Y / Z directions of the six-axis force sensor are

[0109]

[0110] The weight of the large structure is the average value of the gravity of the large structure measured during the previous three weighings, which is 357.54 N. Substituting the above parameters into formula (9), the force value in the Z direction of the six-axis force sensor can be calculated as (96.372, 112.631, 147.263) N. The readings of the six-axis force sensor are as Figure 4 shown, and the deviation from the calculated value in the Z direction of the six-axis force sensor is less than 0.2 N. Therefore, the center of gravity measurement method proposed by the present invention has high measurement accuracy.

[0111] The above-described embodiments merely represent several implementation manners of the present invention. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the invention patent should be subject to the appended claims.

Claims

1. A method for measuring the center of gravity of a large component based on a distributed six-axis force sensor, characterized in that It includes the following steps: S1: Install the six - dimensional force sensor below the ball joint used to connect the numerical control positioner and the bracket, and measure the contact force and frictional torque between the ball joints; S2: According to the transformation principle of force and torque between coordinate systems, transform the gravity and gravity torque of the large - scale component, as well as the contact force and frictional torque between the ball joints, to the base coordinate system, and establish the torque balance equation of the large - scale component in the base coordinate system; S3: Adjust the spatial attitude of the large - scale component, and use the least - squares method to solve the central position according to the torque balance equation of the large - scale component in different attitudes, and calculate the center - of - gravity position.

2. The method for measuring the center - of - gravity of a large - scale component based on a distributed six - dimensional force sensor according to claim 1, characterized in that: The center - of - gravity measurement method uses a large - scale component center - of - gravity measurement system based on a distributed six - dimensional force sensor. The system includes a numerical control positioner, a ball joint, a six - dimensional force sensor, and a large - scale structure. The numerical control positioner is used to support and adjust the pose of the large - scale component and has three degrees of freedom in X / Y / Z directions; The ball joint includes a ball head and a ball socket; The six - dimensional force sensor is installed below the ball joint and is used to measure the force exerted by the positioner on the large - scale structure. Among them, the numerical control positioner is connected to the large - scale structure through the ball joint. When the positioner moves, the position of the center of the ball socket translates, but the attitude angle does not change.

3. The method for measuring the center - of - gravity of a large - scale component based on a distributed six - dimensional force sensor according to claim 2, characterized in that: Multiple ball joints are provided, and one six - dimensional force sensor and one numerical control positioner are correspondingly installed for each ball joint.

4. The method for measuring the center - of - gravity of a large - scale component based on a distributed six - dimensional force sensor according to claim 1, characterized in that: In S1, when measuring the contact force and frictional torque between the ball joints, the specific steps are: S11 Set the coordinate system in the large - scale structure automatic assembly system Base coordinate system O b -xyz, large structure local coordinate system O c -xyz, spherical joint coordinate system O q -xyz and sensor coordinate system O s -xyz; base coordinate system O b -xyz is the reference coordinate system in the entire assembly space, and the z axis is perpendicular to the horizontal plane; the local coordinate system of the large structure O c -xyz is a coordinate system that is fixed to the large structure itself. It moves with the adjustment of the large structure's own position and posture, representing the position and posture of the large structure; the i-th spherical joint coordinate system It is the coordinate system fixed to the i-th ball socket, and its origin is located at the center of the i-th ball socket. After the positioner is installed, the direction of the ball joint coordinate system is consistent with the base coordinate system; the i-th six-dimensional force sensor coordinate system is the coordinate system of the i-th six-dimensional force sensor itself. The force and torque measured by the i-th six-dimensional force sensor are in the sensor coordinate system As shown below, after the sensor is installed, the directions of the sensor coordinate system and the ball joint coordinate system are consistent; S12 Calculate the contact force and frictional torque between the ball joints The force and moment exerted by the $i$-th locator on the large component are the contact force and frictional moment between the $i$-th ball head and the $i$-th ball socket, which are respectively expressed as and The force and moment measured by the $i$-th six-axis force sensor are respectively denoted by and The attitude matrix and position vector of the coordinate system of the $i$-th six-axis force sensor relative to the corresponding ball hinge coordinate system are and According to the transformation principle of force and moment between coordinate systems, and There is the following relationship between them Since the directions of the sensor coordinate system and the ball joint coordinate system are the same, thus is the identity matrix, and the following equation is obtained Among them, E 3×3 represents the third-order identity matrix. Therefore, according to the force values measured by the six-axis force sensor the contact force F between the i-th ball head and the i-th ball socket is calculated i q and the frictional torque when the i-th ball joint rotates 5. The method for measuring the center - of - gravity of a large - scale component based on a distributed six - dimensional force sensor according to claim 1, characterized in that: The calculation steps of the torque balance equation in S2 are as follows: S21: The coordinate representation of the center of the i-th spherical hinge in the local coordinate system of the large component is The coordinate representation of the center of the i-th spherical hinge in the base coordinate system at a certain moment is According to the coordinate system transformation principle, the following formula is obtained Among them, The coordinates of the ball joint center in the base coordinate system Read out by the servo control system of the locator, and according to the coordinates of more than three ball joint centers in the base coordinate system, the attitude matrix of the local coordinate system of the large component relative to the base coordinate system is calculated by the SVD method and the position vector S22: When the attitude of a large structure is adjusted, the position of the ball joint coordinate system relative to the base coordinate system moves, but the attitude angle does not change; let the attitude matrix of the i-th ball joint coordinate system relative to the base coordinate system be The position vector is Since the origin of the ball joint coordinate system is the center of the ball joint, so According to the transformation principle of force and moment between coordinate systems, the force and moment of the ball socket on the ball head are converted to the base coordinate system, so there is Since the directions of the sensor coordinate system and the spherical hinge coordinate system are the same, therefore is the identity matrix. Combining with Equation (1), the following equation is obtained S23: The coordinate representation of the centroid position of the large component in the local coordinate system of the large component is The coordinate representation of the centroid position in the base coordinate system is According to the coordinate system transformation principle, the following equation holds The gravity acting on the large - scale structure is \(mg\). Since the direction of gravity is opposite to the \(Z\) - direction of the base coordinate system, the gravity matrix of the large - scale structure in the base coordinate system is \(F\) G =\([0\ 0 - mg]\), and the moment generated by gravity in the base coordinate system is \(M\) G =\(G\) b \(\times F\) G ; When the large - scale component is in a static state, the resultant force and resultant moment acting on it are \(0\). Therefore, we have Substitute equation (5) into equation (7) to get Equation (8) is the torque balance equation of the large - scale component in the static state.

6. The method for measuring the center - of - gravity of a large - scale component based on a distributed six - dimensional force sensor according to claim 1, characterized in that: The specific steps in S3 are: S31: Expand the moment balance equation and eliminate the equations irrelevant to the center of gravity position G c to obtain Substitute into Equation (9), we get Among them, Represents taking a matrix A new matrix formed by the first two rows; S32: Write equation (10) in matrix form Among them, M Q is the moment matrix of the large component Equation (12) includes three unknowns All other parameters are directly obtained or calculated based on the readings of the force sensor and the servo control system; S33: The matrix equation (11) contains two equalities. The center of gravity position of the large component is calculated according to a set of moment balance equations of the large components. It is found from equation (11) that the moment matrix M Q is only related to the attitude matrix of the large component . In order to obtain different moment balance equations, it is necessary to adjust the spatial attitude of the large component; Suppose that in the j-th posture, the posture matrix of the large component is and the moment matrix is Obtaining the posture matrix and moment matrix of the large component in one posture is called one weighing. After the large component is weighed N times where N≥2, the following formula is obtained Let calculate the least squares solution of G c to be This is the calculated centroid position.

Images