A ball-joint-based articulated arm coordinate measuring machine and measuring method

Abstract

The present invention discloses an articulated arm coordinate measuring machine and a measuring method based on a ball hinge, comprising three groups of ball hinges, three groups of connecting rods and a probe; the three groups of ball hinges are the core of the entire measuring machine, and each group of ball hinges comprises a motion actuator and an angle measuring device, which can realize three-axis rotation angle measurement while rotating on three axes; the motion actuator of each group of ball hinges comprises a ball socket, a ball head and a ball cover; the angle measuring device comprises a magnetic field sensor array fixed to the ball socket and a permanent magnet array embedded in the ball head and moving synchronously with the ball head; based on a magnetic field angle model, the three-axis rotation angle of each group of ball hinges can be obtained by the output signal of the magnetic field sensor array; a handheld drag-type measurement scheme is adopted, and when the probe touches the workpiece to be measured, a trigger signal is generated, which triggers the three groups of ball hinges to read the three-axis rotation angles respectively and simultaneously, and then based on the measurement model, the spatial position of the probe can be obtained, thereby realizing coordinate measurement.

Description

Technical Field

[0001] The present invention belongs to the technical field of coordinate measurement, and in particular relates to an articulated arm coordinate measuring machine based on a ball hinge and a measuring method. Background Art

[0002] Coordinate measuring machines (CMMs) have been widely and maturely applied for high-precision measurement of the size, shape, and relative position of complex three-dimensional parts. Articulated-arm CMMs are one of the most commonly used CMM models. Articulated-arm CMMs are portable, multi-degree-of-freedom coordinate measuring devices. Compared to orthogonal CMMs, they have a wider measurement range and are easier to carry, making them more suitable for different work scenarios. Currently, mature articulated-arm CMMs all use single-degree-of-freedom rotational joints. An articulated-arm CMM requires at least six rotational joints to ensure measurement flexibility, and each joint requires a set of high-precision angle sensors. This results in a more complex structure and higher cost for the measuring machine. Summary of the Invention

[0003] The object of the present invention is to provide an articulated arm coordinate measuring machine based on a ball joint and a measuring method.

[0004] The purpose of the present invention can be achieved through the following technical solutions:

[0005] A ball-jointed articulated arm coordinate measuring machine includes three sets of ball joints, three sets of connecting rods, and a probe. From the ball joints to the probe, the joints are connected in series in the following order: primary ball joint, primary connecting rod, secondary ball joint, secondary connecting rod, tertiary ball joint, tertiary connecting rod, and probe.

[0006] The first-stage ball hinge, the second-stage ball hinge, and the third-stage ball hinge all have a two-part structure of a motion actuator and an angle measuring device, which can realize three-axis rotation angle measurement while performing three-axis rotation;

[0007] Furthermore, each set of ball hinge motion actuators includes a ball socket, a ball head, and a ball cover. The ball head can perform three-axis rotational motion within the spherical space formed by the ball socket and the ball cover. The angle measurement device includes a magnetic field sensor array fixed to the ball socket and a permanent magnet array embedded in the ball head and moving synchronously with the ball head. The permanent magnet array generates a magnetic field within the ball hinge space. The magnetic field sensor array can sense the magnetic induction intensity at different positions and generate an output signal.

[0008] Furthermore, the ball socket of the first-level ball hinge can be fixed on a horizontal platform during measurement, the ball head of the first-level ball hinge is connected to the front end of the first-level connecting rod; the rear end of the first-level connecting rod is connected to the ball socket of the second-level ball hinge, and the ball head of the second-level ball hinge is connected to the front end of the second-level connecting rod; the rear end of the second-level connecting rod is connected to the ball socket of the third-level ball hinge, the ball head of the third-level ball hinge is connected to the front end of the third-level connecting rod, and the rear end of the third-level connecting rod is connected to the measuring head; the ball heads of the ball hinges at all levels are connected to the front end of the connecting rod by threaded connection, the rear ends of the connecting rods at all levels are connected to the ball sockets of the ball hinge by bolts, and the rear end of the third-level connecting rod is connected to the measuring head by threaded connection;

[0009] Furthermore, the angle measurement devices of the primary ball hinge, the secondary ball hinge, and the tertiary ball hinge, wherein the number of sensors in the magnetic field sensor array is not less than 3, the permanent magnets in the permanent magnet array are all cylindrical neodymium iron boron permanent magnets and the number is not less than 2, and the permanent magnets are all arranged in the lower hemisphere of the ball head;

[0010] Furthermore, the three-axis rotation angle ranges of the first-level ball hinge, the second-level ball hinge, and the third-level ball hinge are all ±50° horizontal X-axis, ±50° horizontal Y-axis, and 360° rotation Z-axis;

[0011] Furthermore, the first-level connecting rod and the second-level connecting rod both include a front-end rod connecting part, a middle-end carbon fiber tube, a middle-end rod connecting part and a rear-end connecting plate. The front-end rod connecting part is used to connect the ball head and the middle-end carbon fiber tube of the previous-level ball hinge, the middle-end rod connecting part is used to connect the middle-end carbon fiber tube and the rear-end connecting plate, and the rear-end connecting plate is used to connect the ball socket of the next-level ball hinge. The middle-end carbon fiber tube of the connecting rod is connected to the front-end rod connecting part and the middle-end rod connecting part by gluing. The middle-end connecting part of the connecting rod is connected to the rear-end connecting plate by threads, and the axes of the two are at an angle of 30°; the third-level connecting rod is an integrally processed cylindrical alloy rod, which is used to connect the ball head and probe of the third-level ball hinge.

[0012] The present invention also proposes a coordinate measurement method for an articulated arm coordinate measuring machine based on a ball hinge, which adopts a handheld drag measurement scheme. The specific steps are as follows: fix the ball socket of the first-level ball hinge of the coordinate measuring machine on a horizontal platform, hold the second-level connecting rod and the third-level connecting rod, and slowly move the probe close to the object to be measured. When the probe touches the object to be measured, the probe generates a trigger signal. At the same time, the angle measurement devices of the three groups of ball hinges respectively read and record the output signals of the magnetic field sensor array at this time, and the three-axis rotation angles of the three groups of ball hinges can be calculated based on the magnetic field angle model. Based on the measurement model, the current spatial position coordinates of the probe can be calculated from the three-axis rotation angles of the three groups of ball hinges, thereby realizing coordinate measurement.

[0013] The measurement model is established as follows:

[0014] To establish the measurement model, it is necessary to first convert the three-axis rotation angles of the three sets of ball hinges and the other structural parameters of the measuring machine into various DH parameters based on the basic principles of the DH method, and then establish the measurement model based on the DH method coordinate transformation matrix;

[0015] Step 1: Calculate the spatial degrees of freedom of the measuring machine. Using the spatial mechanism degrees of freedom formula, the coordinate measuring machine degrees of freedom are calculated as follows:

[0016]

[0017] Among them, n is the number of components, g is the number of kinematic pairs of the mechanism, is the sum of all joint degrees of freedom;

[0018] Step 2: The three-axis rotation angle of the ball hinge is converted into DH parameters. According to the basic principle of the DH method in mechanism, the axis space rectangular coordinate system is established. The coordinate transformation matrix from the i-th level coordinate system to the i+1-level coordinate system is as follows:

[0019]

[0020] Where θ i Z i+1 Axis and Z i Angle between the axes, d i Z i+1 Axis and Z i The distance between the axes, α i For X i+1 Axis and X i The angle between the axes, a i For X i+1 Axis and X i the distance between the axes;

[0021] Step 3: Establish the measurement model of the measuring machine based on the DH method;

[0022] Three sets of ball hinges are connected in series, forming a coordinate measuring machine from the first-level ball hinge to the probe. Based on the measurement model principle of the DH method, the center of the bottom end of the ball socket of the first-level ball hinge is the basic coordinate system, that is, the level 0 coordinate system, and the center of the top end of the probe is the final coordinate system, that is, the level 10 coordinate system. The final measurement model is as follows:

[0023]

[0024] Where (xyz) represents the spatial position coordinates of the probe. The coordinate measuring machine takes the three-axis rotation angles of the three sets of ball hinges as input and obtains the spatial position coordinates of the probe as output through the measurement model, thereby realizing coordinate measurement.

[0025] Beneficial effects of the present invention:

[0026] 1. Compared with traditional articulated arm coordinate measuring machines, the present invention is an articulated arm coordinate measuring machine based on a ball hinge. It uses a ball hinge with three degrees of freedom to replace a single-degree-of-freedom rotational joint. Three ball hinges can replace the three cross joints of a traditional articulated arm coordinate measuring machine, eliminating 12 sets of precision rolling bearings and 6 precision angle measuring circular gratings. It has a more streamlined structure, higher motion measurement flexibility, and higher measurement accuracy.

[0027] 2. The present invention uses an intelligent ball hinge that integrates motion execution and rotation angle measurement. This not only expands the traditional application scope of the ball hinge as a motion actuator only, but also breaks through the technical limitations of the traditional articulated arm coordinate measuring machine that generally adopts the "rotation joint + circular grating angle sensor", promoting new development and new applications of measurement technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0029] Figure 1 It is the overall structure diagram of the measuring machine of the present invention.

[0030] Figure 2 It is a structural diagram of the ball hinge of the present invention.

[0031] Figure 3 It is an exploded view of the ball hinge structure of the present invention.

[0032] Figure 4 It is a cross-sectional view of the ball hinge and the connecting rod of the present invention.

[0033] Figure 5 It is a schematic diagram of the equivalent magnetic charge of a permanent magnet.

[0034] Figure 6 It is a schematic diagram of the three-axis rotation of the ball hinge of the present invention.

[0035] Figure 7 It is a schematic diagram of the sensor position in the ball hinge of the present invention.

[0036] Figure 8 It is the principle diagram of the DH method of the present invention.

[0037] Figure 9 It is a schematic diagram of the three-axis rotation of the ball hinge based on the DH method of the present invention.

[0038] Figure 10 It is a diagram of the measurement principle of the present invention. DETAILED DESCRIPTION

[0039] 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 any creative efforts shall fall within the scope of protection of the present invention.

[0040] An articulated arm coordinate measuring machine based on a ball hinge has a main structure including three sets of ball hinges, three sets of connecting rods and a probe. From the ball hinge to the probe, each joint is connected in series in the following order: primary ball hinge 1, primary connecting rod 2, secondary ball hinge 3, secondary connecting rod 4, tertiary ball hinge 5, tertiary connecting rod 6, and probe 7. Figure 1 As shown;

[0041] The primary ball hinge 1, the secondary ball hinge 3, and the tertiary ball hinge 5 all have a two-part structure of a motion actuator and an angle measuring device, and can realize three-axis rotation angle measurement while performing three-axis rotation.

[0042] Specifically, such as Figure 2 and Figure 3 As shown, each set of ball hinge motion actuators includes a ball socket 8, a ball head 9 and a ball cover 10. The ball head 9 can perform three-axis rotational motion in the spherical space formed by the ball socket 8 and the ball cover 10; the angle measurement device includes a magnetic field sensor array 11 fixed to the ball socket and a permanent magnet array 12 embedded in the ball head and moving synchronously with the ball head. The permanent magnet array 12 forms a magnetic field within the ball hinge space, and the magnetic field sensor array 11 can sense the magnetic induction intensity at different positions and generate an output signal.

[0043] Specifically, the ball socket of the first-level ball hinge 1 can be fixed on a horizontal platform during measurement, and the ball head of the first-level ball hinge 1 is connected to the front end of the first-level connecting rod 2; the rear end of the first-level connecting rod 2 is connected to the ball socket of the second-level ball hinge 3, and the ball head of the second-level ball hinge 3 is connected to the front end of the second-level connecting rod 4; the rear end of the second-level connecting rod 4 is connected to the ball socket of the tertiary ball hinge 5, the ball head of the tertiary ball hinge 5 is connected to the front end of the tertiary connecting rod 6, and the rear end of the tertiary connecting rod 6 is connected to the measuring probe; the ball heads of the ball hinges at all levels are connected to the front end of the connecting rods by threaded connection, the rear ends of the connecting rods at all levels and the ball sockets of the ball hinges are connected by bolts, and the rear end of the tertiary connecting rod 6 is connected to the measuring probe 7 by threaded connection.

[0044] Specifically, the angle measuring devices of the primary ball hinge 1, the secondary ball hinge 3, and the tertiary ball hinge 5, wherein the number of sensors in the magnetic field sensor array 11 is no less than 3, the permanent magnets in the permanent magnet array 12 are all cylindrical neodymium iron boron permanent magnets and the number is no less than 2, and the permanent magnets are all arranged in the lower hemisphere of the ball head 8.

[0045] Specifically, the three-axis rotation angle range of the first-level ball hinge, the second-level ball hinge and the third-level ball hinge are ±50° horizontal X-axis, ±50° horizontal Y-axis and 360° rotation Z-axis.

[0046] Specifically, such as Figure 4 As shown, the first-level connecting rod 2 and the second-level connecting rod 4 both include a front-end rod connecting part 13, a middle-end carbon fiber tube 14, a middle-end rod connecting part 15 and a rear-end connecting plate 16. The front-end rod connecting part 13 is used to connect the ball head 9 and the middle-end carbon fiber tube 14 of the upper-level ball hinge, the middle-end rod connecting part 15 is used to connect the middle-end carbon fiber tube 14 and the rear-end connecting plate 16, and the rear-end connecting plate 16 is used to connect the ball socket 8 of the next-level ball hinge. The middle-end carbon fiber tube 14 of the connecting rod is connected to the front-end rod connecting part 13 and the middle-end rod connecting part 15 by gluing, and the middle-end connecting part 15 of the connecting rod is connected to the rear-end connecting plate 16 by threading, and the axes of the two are at an angle of 30°; the tertiary connecting rod 6 is an integrally processed cylindrical alloy rod, which is used to connect the ball head and the probe 7 of the tertiary ball hinge 5.

[0047] A coordinate measurement method for an articulated arm coordinate measuring machine based on a ball hinge adopts a handheld drag measurement scheme. The specific steps are as follows: the ball socket of the first-level ball hinge 1 of the coordinate measuring machine is fixed on a horizontal platform, the second-level connecting rod 4 and the third-level connecting rod 6 are held, and the probe is slowly approached to the object to be measured. When the probe 7 touches the object to be measured, the probe 7 generates a trigger signal. At the same time, the angle measurement devices of the three groups of ball hinges respectively read and record the output signals of the magnetic field sensor array at this time, and the three-axis rotation angles of the three groups of ball hinges can be calculated based on the magnetic field angle model. Then, based on the measurement model, the current spatial position coordinates of the probe 7 can be calculated from the three-axis rotation angles of the three groups of ball hinges, thereby realizing coordinate measurement.

[0048] Specifically, the ball head 9, ball socket 8, and ball cover 10 in the ball hinge are made of an aluminum alloy with extremely low magnetic susceptibility. Four identical cylindrical blind holes are symmetrically machined in the lower hemisphere of the ball head 9, with the axis of the blind holes passing through the center of the ball head 9. Four identical cylindrical NdFeB permanent magnets are embedded in each of the blind holes to form a permanent magnet array 12. The permanent magnet array 12 forms a stable, strong static magnetic field within and near the entire space where the ball hinge is located. Four identical cylindrical through holes are symmetrically machined in the ball socket 8, with the axis of the through holes also passing through the center of the ball socket 8. Four Hall-type magnetic field sensors are embedded in each of the through holes to form a magnetic field sensor array 11. The sensor array 11 is used to measure the magnetic induction intensity at the location. When the permanent magnet array 12 rotates synchronously with the ball head 8, the static magnetic field also changes, and the output signal of the magnetic field sensor array 11 also changes synchronously. Based on the magnetic field angle model, the three-axis rotation angle of the ball head 9 relative to the ball socket 8, that is, the three-axis rotation angle of the ball hinge, can be calculated from the real-time output signal of the magnetic field sensor array 11.

[0049] To establish a magnetic field angle model, the specific steps are as follows:

[0050] To establish a magnetic field angle model, you first need to create a spatial magnetic field model and a spatial rectangular coordinate system. The spatial rectangular coordinate system defines the spatial positions of the permanent magnet array and the magnetic field sensor array. The spatial magnetic field model calculates and determines the magnetic induction intensity at any spatial position. The established spatial magnetic field model is then linked to the spatial rectangular coordinate system to establish the magnetic field angle model.

[0051] Step 1: Establish a spatial magnetic field model. The theoretical basis for establishing a spatial magnetic field model is the equivalent magnetic charge theory. Analogously, the electrostatic field is generated by static charges, and it is assumed that the static magnetic field is generated by static magnetic charges. For a cylindrical permanent magnet uniformly magnetized along the axial direction, the volume magnetic charge density ρ m is zero, and there is a surface magnetic charge density σ on the boundary of the permanent magnet m ,like Figure 5 As shown, the following relationship exists:

[0052]

[0053] Where B r is the residual magnetic induction intensity of the permanent magnet.

[0054] The magnetic field intensity H generated by a permanent magnet at any point in the space outside the magnet is expressed in the form of a surface integral:

[0055]

[0056] The relationship between magnetic induction intensity B and magnetic field intensity H is:

[0057]

[0058] In formula (3), μ r is the relative magnetic permeability of the magnetized material, μ0 is the vacuum permeability, r + 、r - and r + 、r - are the distance vector and distance scalar from the positive and negative magnetic charges to the field point P, respectively. + 、S - is the surface area of ​​the positive and negative magnetic charges.

[0059] Step 2: Establish a spatial rectangular coordinate system. Figure 6 As shown in the figure, the steps of establishing a spatial rectangular coordinate system are explained in detail by taking the first-level ball hinge as an example. The center of the first-level ball hinge, that is, the center of rotation of the ball head, is the origin of the coordinate system O, and the vertical direction upward from the base is the Z axis and the Z axis is the Z axis. 0 Axis direction, establish the static coordinate system O-XYZ and the dynamic coordinate system OX with the initial position coincident 0 Y0 Z 0 ; The static coordinate system O-XYZ always remains stationary, and the moving coordinate system OX 0 Y 0 Z 0 It is fixed to the ball head and rotates synchronously with the ball head.

[0060] According to Euler angle rotation theory, the rotation of the ball head at any angle in space can be decomposed into the ball head first rotating around the coordinate system OX 0 Y 0 Z 0 X 0 The axis rotates by angle α, and the moving coordinate system OX 0 Y 0 Z 0 The new position forms the moving coordinate system OX 1 Y 1 Z 1 ; The ball head then revolves around the coordinate system OX 1 Y 1 Z 1 Y 1 The axis rotates by angle β, and the moving coordinate system OX 1 Y 1 Z 1 The new position forms the moving coordinate system OX 2 Y 2 Z 2 ; Finally, the ball head revolves around the coordinate system OX 2 Y 2 Z 2 Z 2 The axis rotates by angle γ, and the moving coordinate system OX 2 Y 2 Z 2 The new position forms the moving coordinate system OX 3 Y 3 Z 3 After the ball head rotates three times, the position of the permanent magnet changes from the original M 0 Turn to M 3 point.

[0061] Take a magnetic field sensor S1 as an example. The coordinates of the magnetic field sensor S1 in the static coordinate system O-XYZ are (x1, y1, z1). According to the coordinate rotation formula of Euler angle rotation theory, in the moving coordinate system OX 3 Y 3 Z 3 In the figure, the coordinates of sensor S1 are expressed as:

[0062]

[0063] Step 3: Establish a magnetic field angle model. When the ball joint rotates, that is, when the ball head rotates at any angle, the permanent magnet array embedded in the ball head rotates synchronously, and the static magnetic field generated by the permanent magnet array also changes accordingly, causing the magnetic induction intensity at any point in space to change, and the output signal of the magnetic field sensor array also changes accordingly. Based on the established spatial magnetic field model and spatial rectangular coordinate system, a clear set of mathematical equations is established between the magnetic induction intensity at the sensor array and the three-axis rotation angle of the ball joint, thus establishing the magnetic field angle model.

[0064] The end face radius of the four cylindrical permanent magnets is R0, the height is H, and they are uniformly magnetized along the axial direction. The S pole is close to the center of the ball. The permanent magnet is installed at a distance of R from the center of the ball. m The axes of the four permanent magnets and the four magnetic field sensors all pass through the sphere center O. The projections of the axes on the XOY plane in the static coordinate system start from the positive X axis direction, and the distribution angles are 0°, 90°, 180°, and 270° respectively. Figure 7 As shown in the figure, taking a magnetic field sensor S1 and a permanent magnet M1 as an example, the angle between the axis of the permanent magnet and the negative direction of the Z axis is φ, and the angle between the projection on the XOY plane and the positive direction of the X axis is ω; the angle between the axis of the sensor and the negative direction of the Z axis is Φ, and the angle between the projection on the XOY plane and the positive direction of the X axis is θ. After the permanent magnet M1 rotates with the ball head, according to equations (3) and (4), in the moving coordinate system OX 3 Y 3 Z 3 Under the condition of the magnetic field sensor S1, the three-dimensional magnetic induction intensity component (B ′x1 ,B y ′1,B ′z1 ) are respectively expressed as:

[0065]

[0066]

[0067]

[0068] Where,

[0069] In the moving coordinate OX 3 Y 3 Z 3 The three-dimensional component of the magnetic induction intensity at the lower sensor S1 (B' x1 ,B′ y1 ,B ′z1 ) is transformed into the static coordinate system O-XYZ and expressed as (B x1 ,B y1 ,B z1 ):

[0070]

[0071] Similarly, the magnetic induction intensity (B) of the permanent magnets M2, M3, and M4 at point S1 in the static coordinate system O-XYZ can be obtained. x2 ,B y2 ,B z2 )、(B x3 ,B y3 ,B z3 )、(B x4 ,B y4 ,B z4 ). Under the action of four permanent magnets, the magnetic induction intensity at the magnetic field sensor S1 is the superposition value of the four. After superposition, the magnetic induction intensity B is:

[0072]

[0073] In mathematical theory, at least three magnetic field sensors need to be placed and a set of equations containing at least three equations can be established to solve the three-axis rotation angles α, β and γ of the ball joint. The present invention can choose to use more magnetic field sensors to generate information redundancy to reduce measurement errors. In this example, four magnetic field sensors are used, and the output signals B1, B2, B3, and B4 of the four sensors are related to the three-axis rotation angles α, β and γ of the ball head, which can be simply expressed as B i =f i (α, β, γ), and form a nonlinear equation system:

[0074]

[0075] The least squares method is used to solve the nonlinear equations as follows:

[0076]

[0077] Formula (9) is the magnetic field angle model.

[0078] Based on the magnetic field angle model, the three-axis rotation angles of the three sets of ball hinges can be calculated. Then, based on the measurement model, the current spatial position coordinates of the probe can be calculated from the three-axis rotation angles of the three sets of ball hinges, thereby realizing coordinate measurement.

[0079] Specifically, the measurement model is established as follows:

[0080] To establish a measurement model, it is necessary to first convert the three-axis rotation angles of the three sets of ball hinges and the other structural parameters of the measuring machine into various DH parameters based on the basic principles of the DH method, and then establish a measurement model based on the DH method coordinate transformation matrix.

[0081] Step 1: Calculation of the spatial degrees of freedom of the measuring machine. Using the spatial mechanism degrees of freedom formula, the degrees of freedom of the coordinate measuring machine of the present invention are calculated as follows:

[0082]

[0083] Among them, n is the number of components, g is the number of kinematic pairs of the mechanism, is the sum of all joint degrees of freedom;

[0084] The number of components of this measuring machine is n=4, and the number of kinematic pairs is g=3, so F=6×(4-3-1)+3×3=9, and the measuring machine has 9 degrees of freedom.

[0085] Step 2: Convert the three-axis rotation angle of the ball hinge into DH parameters. Figure 8 As shown, according to the basic principle of DH method in mechanism, the axis space rectangular coordinate system is established, and the coordinate transformation matrix from the i-th level coordinate system to the i+1-level coordinate system is as follows:

[0086]

[0087] Where θ i Z i+1 Axis and Z i Angle between the axes, d i Z i+1 Axis and Z i The distance between the axes, α i For X i+1 Axis and X i The angle between the axes, a i For X i+1 Axis and X i The distance between the axes.

[0088] Taking the first-level ball hinge as an example, the conversion method of the three-axis rotation angle of the ball hinge to the DH parameter is explained. In the present invention, each set of ball hinges has three degrees of freedom and can be described by three coordinate systems with the same coordinate system origin. According to the Euler rotation theorem mentioned above, the three-axis rotation of the ball hinge is decomposed into the ball hinge first rotating around X and then rotating around DH. 0 The axis rotates by an angle of α and then rotates around the Y 1 The axis rotates β angle, and finally around Z 2 The axis rotates by an angle γ, such as Figure 5 As shown; Based on the basic principle of DH method, the three-axis rotation motion of the ball hinge is converted into first rotating around the Z1 axis by an angle α, then rotating around the Z2 axis by an angle β, and finally rotating around the Z3 axis by an angle γ, as shown Figure 9 As shown, the three-axis rotation motion of the primary ball joint can be expressed as follows:

[0089]

[0090] Where α is the angle between the X1 axis and the X2 axis, β is the angle between the X2 axis and the X3 axis, γ is the angle between the X3 axis and the X4 axis, and a3 is the distance between the X3 axis and the X4 axis.

[0091] Step 3: Establish the measurement model of the measuring machine based on the DH method.

[0092] Three sets of ball hinges are connected in series, from the first-level ball hinge to the probe to form a coordinate measuring machine. The measurement model principle based on the DH method is as follows: Figure 10 As shown in the figure, the bottom center of the ball socket of the first-level ball joint is the basic coordinate system, that is, the 0-level coordinate system, and the top center of the probe is the final coordinate system, that is, the 10-level coordinate system. The final measurement model is as follows:

[0093]

[0094] Where (xyz) represents the spatial position coordinates of the probe. The coordinate measuring machine takes the three-axis rotation angles of the three sets of ball hinges as input and obtains the spatial position coordinates of the probe as output through the measurement model, thereby realizing coordinate measurement.

[0095] Throughout this specification, references to terms such as "one embodiment," "example," or "specific example" indicate that the specific features, structures, materials, or characteristics described in conjunction with that embodiment or example are included in at least one embodiment or example of the present invention. In this specification, schematic representations of these terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0096] The above content is merely an example and explanation of the structure of the present invention. Those skilled in the art may make various modifications or additions to the described specific embodiments or replace them in a similar manner. As long as they do not deviate from the structure of the invention or exceed the scope defined by the claims, they should all fall within the scope of protection of the present invention.

Claims

1. An articulated arm coordinate measuring machine based on a ball joint, characterized in that: The invention comprises three sets of ball hinges, three sets of connecting rods and a measuring head, wherein the joints from the ball hinge to the measuring head are connected in series in the following order: a first-level ball hinge (1), a first-level connecting rod (2), a second-level ball hinge (3), a second-level connecting rod (4), a third-level ball hinge (5), a third-level connecting rod (6), and a measuring head (7); The first-stage ball hinge (1), the second-stage ball hinge (3), and the third-stage ball hinge (5) all have a two-part structure consisting of a motion actuator and an angle measuring device; The motion actuators each include a ball socket (8), a ball head (9) and a ball cover (10), wherein the ball head (9) performs a three-axis rotational motion in a spherical space formed by the ball socket (8) and the ball cover (10); The angle measuring device comprises a magnetic field sensor array (11) fixed to the ball socket and a permanent magnet array (12) embedded in the ball head and moving synchronously with the ball head, wherein the permanent magnet array (12) forms a magnetic field within the space of the ball hinge, and the magnetic field sensor array (11) senses the magnetic induction intensity at different positions and generates an output signal; The ball socket of the first-stage ball hinge (1) of the coordinate measuring machine is fixed on a horizontal platform, and the second-stage connecting rod (4) and the third-stage connecting rod (6) are held, and the probe is slowly moved close to the object to be measured. When the probe (7) touches the object to be measured, the probe (7) generates a trigger signal, and at the same time, the angle measuring devices of the three sets of ball hinges respectively read and record the output signals of the magnetic field sensor array (11) at this time, and calculate the three-axis rotation angles of the three sets of ball hinges based on the magnetic field angle model. Then, based on the measurement model, the current spatial position coordinates of the probe (7) are calculated from the three-axis rotation angles of the three sets of ball hinges, thereby realizing coordinate measurement; The measurement model is established as follows: To establish the measurement model, it is necessary to first convert the three-axis rotation angles of the three sets of ball hinges and the other structural parameters of the measuring machine into various DH parameters based on the basic principles of the DH method, and then establish the measurement model based on the DH method coordinate transformation matrix; Step 1: Calculate the spatial degrees of freedom of the measuring machine. Using the spatial mechanism degrees of freedom formula, the coordinate measuring machine degrees of freedom are calculated as follows: Among them, n is the number of components, g is the number of kinematic pairs of the mechanism, is the sum of all joint degrees of freedom; Step 2: The three-axis rotation angle of the ball hinge is converted into DH parameters. According to the basic principle of the DH method in mechanism, the axis space rectangular coordinate system is established. The coordinate transformation matrix from the i-th level coordinate system to the i+1-level coordinate system is as follows: Where θ i Z i+1 Axis and Z i Angle between the axes, d i Z i+1 Axis and Z i The distance between the axes, α i For X i+1 Axis and X i The angle between the axes, a i For X i+1 Axis and X i the distance between the axes; Step 3: Establish the measurement model of the measuring machine based on the DH method; Three sets of ball hinges are connected in series, forming a coordinate measuring machine from the first-level ball hinge to the probe. Based on the measurement model principle of the DH method, the center of the bottom end of the ball socket of the first-level ball hinge is the basic coordinate system, that is, the level 0 coordinate system, and the center of the top end of the probe is the final coordinate system, that is, the level 10 coordinate system. The final measurement model is as follows: Where (xyz) represents the spatial position coordinates of the probe. The coordinate measuring machine takes the three-axis rotation angles of the three sets of ball hinges as input and obtains the spatial position coordinates of the probe as output through the measurement model, thereby realizing coordinate measurement.

2. The articulated arm coordinate measuring machine based on a ball joint according to claim 1, characterized in that: The three-axis rotation angle range of the first-level ball hinge, the second-level ball hinge and the third-level ball hinge are ±50° horizontal X axis, ±50° horizontal Y axis and 360° rotation Z axis; 3. The articulated arm coordinate measuring machine based on a ball joint according to claim 1, characterized in that: The ball socket of the first-level ball hinge (1) is fixed on a horizontal platform, the ball head of the first-level ball hinge (1) is connected to the front end of the first-level connecting rod (2); the rear end of the first-level connecting rod (2) is connected to the ball socket of the second-level ball hinge (3), the ball head of the second-level ball hinge (3) is connected to the front end of the second-level connecting rod (4); the rear end of the second-level connecting rod (4) is connected to the ball socket of the third-level ball hinge (5), the ball head of the third-level ball hinge (5) is connected to the front end of the third-level connecting rod (6), and the rear end of the third-level connecting rod (6) is connected to the measuring head.

4. The ball-jointed articulated arm coordinate measuring machine according to claim 1, characterized in that: The first-stage connecting rod (2) and the second-stage connecting rod (4) both include a front-end rod connecting piece (13), a middle-end carbon fiber tube (14), a middle-end rod connecting piece (15) and a rear-end connecting disc (16). The front-end rod connecting piece (13) is used to connect the ball head (9) and the middle-end carbon fiber tube (14) of the previous stage ball hinge, the middle-end rod connecting piece (15) is used to connect the middle-end carbon fiber tube (14) and the rear-end connecting disc (16), and the rear-end connecting disc (16) is used to connect the ball socket (8) of the next stage ball hinge. The third-stage connecting rod (6) is an integrally processed cylindrical alloy rod, which is used to connect the ball head and the probe (7) of the third-stage ball hinge (5).

5. The articulated arm coordinate measuring machine based on a ball joint according to claim 4, characterized in that: The axes of the middle end connecting piece (15) and the rear end connecting plate (16) form an angle of 30 degrees.

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