Ultrasonic testing system of dual robot arms and method thereof

Abstract

An ultrasonic testing system of dual robot arms and an ultrasonic testing method for use in testing quality of surface and interior of a workpiece. The system includes an extension rod provided between a tail-end of a master robot arm and an emitting probe and/or between a tail-end of a slave robot arm and a receiving probe. One or more connected extension rod rotating shafts is provided between the extension rod and the emitting probe or between the extension rod and the receiving probe. The method uses an X-axis constraint method to convert posture data of the discrete points in a trajectory file of the tested workpiece into Euler angles, and constrain the X-axes of the auxiliary coordinate systems at the same time so that the positive direction of the X-axis of each of the auxiliary coordinate systems is the trajectory tangent direction.

Claims

1. An ultrasonic testing system of dual robot arms, tail-ends of the robot arms being equipped with an oppositely arranged emitting probe and receiving probe, respectively; each of the robot arms being connected with a controller; wherein the tail-end of at least one of the robot arms is provided with an extension rod; the other end of the extension rod is provided with an extension rod rotating shaft; and the probe of the robot arm realizes equipment by mounting on the extension rod rotating shaft.

2. The ultrasonic testing system of dual robot arms as claimed in claim 1, wherein the robot arms are a master robot arm and a slave robot arm, the emitting probe is arranged at the tail-end of the master robot arm, the receiving probe opposing to the emitting probe is arranged at the tail-end of the slave robot arm, the emitting probe and the receiving probe keep perpendicular to a surface of a tested workpiece; a master robot arm controller is electrically connected with the master robot arm; and a slave robot arm controller is electrically connected with the slave robot arm; between the tail-end of the master robot arm and the emitting probe or/and between the tail-end of the slave robot arm and the receiving probe, the extension rod is provided whose length direction is parallel to the axis of the tested workpiece; and between the extension rod and the emitting probe or/and between the extension rod and the receiving probe, the equipment is realized by the extension rod rotating shaft.

3. An ultrasonic testing method by using an ultrasonic testing system of dual robot arms, comprising: a step 1 of calibrating a coordinate system of a tested workpiece for the ultrasonic testing system of dual robot arms, and determining relationships of the coordinate system of the tested workpiece relative to base coordinate systems of the master and slave robot arms; a step 2 of performing a trajectory planning on the tested workpiece to generate a trajectory file of discrete points of the coordinate system of the tested workpiece; the trajectory file including coordinates and posture data; a step 3 of building auxiliary coordinate systems in the coordinate system of the workpiece, using a X-axis constraint method to constrain the X-axes of the auxiliary coordinate systems so that a positive direction of the X-axis of each of the auxiliary coordinate systems is a tangent direction of the trajectory, and using the X-axis constraint method to convert the posture data of the discrete points generated in the step 2 into Euler angles; a step 4 of converting the coordinates of the discrete points generated in the step 3 and the converted Euler angles of the discrete points in the step 3 into coordinates and Euler angles of the base coordinate systems of the master and slave robot arms according to the relationships among the coordinate system of the workpiece and base coordinate systems of the master and slave robot arms, and then downloading the resulting coordinates and the Euler angles to the master and slave robot arm controllers, respectively; a step 5 of inputting transformation relationship of a tool coordinate system of the master robot arm relative to a flange coordinate system of the master robot arm to the master robot arm controller, and inputting transformation relationship of the tool coordinate system of the slave robot arm ii relative to a flange coordinate system of the slave robot arm to the slave robot arm controller; and a step 6 of bringing the testing system of dual robot arms into an operating state, and controlling, by the master and slave robot arm controllers respectively, the master and slave robot arms having the probes to comprehensively test the tested workpiece.

4. The ultrasonic testing method as claimed in claim 3, wherein the step of using the X-axis constraint method to constrain the X-axes of the auxiliary coordinate systems includes: building an imaginary X-axis for each of the auxiliary coordinate systems in the coordinate system of the workpiece so that the imaginary X-axis is in a secant direction of the trajectory, and by taking two points b(x.sub.b,y.sub.b,z.sub.b) and c(x.sub.c,y.sub.c,z.sub.c) on the imaginary X-axis, expressing a vector of the imaginary X-axis as: ox′=(x.sub.c−x.sub.b,y.sub.c−y.sub.b,z.sub.c−z.sub.b), setting a Z-axis of each of the auxiliary coordinate systems as a cutter shaft vector of each of the point b and expressing its vector as: oz=(t.sub.x,t.sub.y,t.sub.z), obtaining a vector of a Y-axis for each of the auxiliary coordinate systems by the following equation: $\begin{array}{c}\mathrm{oy}=\mathrm{oz}\times {\mathrm{ox}}^{\prime }\\ =\left(\begin{array}{c}{t}_y\left(z_c-z_b\right)-t_z\left(y_c-y_b\right),t_z\left(x_c-x_b\right)-\\ (t_x\left(z_c-z_b\right),t_x\left(y_c-y_b\right)-t_y\left(x_c-x_b\right)\end{array}\right)\\ =\left({\mathrm{oy}}_x,{\mathrm{oy}}_y,{\mathrm{oy}}_z\right)\end{array}$ obtaining the vector of the corrected X-axis for each of the auxiliary coordinate systems by a cross product of oy and oz in order to be in a tangent direction of the trajectory, wherein the equation of the cross product is as follows: $\begin{array}{c}\mathrm{ox}=\mathrm{oy}\times \mathrm{oz}\\ =\left(\begin{array}{c}\left(t_z\left(x_c-x_b\right)-t_x\left(z_c-z_b\right)\right)\left(z_c-z_b\right)-\left(t_x\left(y_c-y_b\right)-t_y\left(x_c-x_b\right)\right)\left(y_c-y_b\right),\\ \left(t_x\left(y_c-y_b\right)-t_y\left(x_c-x_b\right)\right)\left(x_c-x_b\right)-\left(t_y\left(z_c-z_b\right)-t_z\left(y_c-y_b\right)\right)\left(z_c-z_b\right),\\ \left(t_y\left(z_c-z_b\right)-t_z\left(y_c-y_b\right)\right)\left(y_c-y_b\right)-\left(t_z\left(x_c-x_b\right)-t_x\left(z_c-z_b\right)\right)\left(x_c-x_b\right)\end{array}\right)\\ =\left(o{x}_x,o{x}_y,o{x}_z\right).\end{array}$

5. The ultrasonic testing method as claimed in claim 4, wherein the converting step of the Euler angles in the step 3 includes obtaining the Euler angles of the coordinate system of the workpiece based on the equal relationship between an Euler angles transformation matrix and a rotation matrix:
α=A tan 2(−p.sub.y,p.sub.z)×180/π
β=A tan 2(p.sub.x,√{square root over (p.sub.y.sup.2+p.sub.z.sup.2)})×180/π
γ=A tan 2(−n.sub.y,n.sub.x)×180/π, wherein $p_x=\frac{t_x}{\sqrt{t_x^2+t_y^2+t_z^2}};p_y=\frac{t_y}{\sqrt{t_x^2+t_y^2+t_z^2}};$ $p_z=\frac{t_z}{\sqrt{t_x^2+t_y^2+t_z^2}};n_y=\frac{o{x}_y}{\sqrt{o{x}_x^2+o{x}_y^2+o{x}_z^2}};$ $n_x=\frac{{\mathrm{ox}}_x}{\sqrt{o{x}_x^2+o{x}_y^2+o{x}_z^2}}.$

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0028] FIG. 1 is an axonometric view showing a collision accident between an extension rod and a workpiece;

[0029] FIG. 2 is a plan view showing the collision accident between the extension rod and the workpiece;

[0030] FIG. 3 is a schematic diagram of a dual robot arms system with an extension rod according to the present disclosure;

[0031] FIG. 4 is a schematic diagram for calibrating a coordinate system of the workpiece;

[0032] FIG. 5 is a schematic diagram showing the principle of motion control of the robot arms;

[0033] FIG. 6 is a schematic diagram of an auxiliary coordinate system;

[0034] and

[0035] FIG. 7 is a schematic diagram showing a building process of the auxiliary coordinate system.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0036] In order to solve the problem that a receiving probe or an emitting probe cannot reach into a workpiece to perform testing, a robot arm may be equipped with an extension rod as a tool to extend into the internal space of the workpiece and perform testing. However, the robot arm with six degrees of freedom may collide with the workpiece due to enter-constraint or improper constraint of postures. As shown in FIG. 1 and FIG. 2, a robot arm 8 is equipped with an extension rod 5 on which an emitting probe 4 is installed, and a robot arm 7 is equipped with a receiving probe 3 at its tail-end, wherein the extension rod 5 collides with the tested workpiece and causes a testing accident. Therefore, it is necessary to propose a new testing method to solve the problem of collision between the probe and the workpiece.

[0037] FIG. 3 shows an ultrasonic testing system of dual robot arms with an extension rod. The ultrasonic testing system includes an ultrasonic acquisition card 1 configured for collecting and storing ultrasonic data, a pulse transceiver 2 connected with the ultrasonic acquisition card 1 and configured for exciting a emitting probe to emit ultrasound waves and a receiving probe to receive ultrasound waves, a master robot arm 7 and a slave robot arm 8 that are provided fixedly, an emitting probe 3 connected with the pulse transceiver 2 and provided at the tail-end of the master robot arm 7, an extension rod 5 fixed with the tail-end of the slave robot arm 8, an extension rod rotating shaft 6 hinged with the tail-end of the extension rod 5, and a receiving probe 4 fixed with the tail-end of the extension rod rotating shaft 6. In this way, the extension rod rotating shaft 6 provided between the extension rod 5 and the receiving probe may make the receiving probe 4 rotatable relative to the extension rod 5, so that the emitting probe 3 and the receiving probe 4 arranged on two opposing sides of the tested workpiece can be both perpendicular to the tested workpiece and their central axes can coincide.

[0038] The system further includes a water tank 9 that provides a coupling medium for ultrasonic transmission (a water pump for sucking the water in the water tank and a water pipe nozzle for jetting on the tested workpiece are not shown), a master robot arm controller 10 connected with the master robot arm 7, a slave robot arm controller 14 connected with the slave robot arm 8, an industrial computer 12 connected with both the master robot arm controller 10 and the slave robot arm controller 14, a position acquisition card 11 connected with the industrial computer 12, the ultrasonic acquisition card 1 and the pulse transceiver 2 and configured for acquiring current testing positions of the robot arms, and a display device 15 connected with the industrial computer 12 and configured for displaying the testing results. As shown in FIG. 3 to FIG. 5, the extension rod rotating shaft 6 can be rotated according to the shape profile of the workpiece when testing the workpiece in order to comprehensively test the tested workpiece.

[0039] Before testing the workpiece, tips 13 of the master robot arm 7 and the slave robot arm 8 are first used to calibrate the position and orientation of the tested workpiece. When the ultrasonic acquisition card 1 starts activation, it is in the automatic mode in which it automatically triggers the pulse transceiver 2 to start operating, and then set the appropriate detection parameters. Once the robot arms are in motion, the ultrasonic acquisition card 1 switches to an external activation mode, in which other devices are required to trigger the ultrasonic acquisition card 1 to operate. The pulse transceiver 2 causes the emitting probe 3 situated at the outer surface of the tested workpiece to emit ultrasonic waves toward the tested workpiece via the aqueous medium and the receiving probe 4 situated at the inner surface of the tested workpiece to receive the ultrasonic waves via the coupling medium, and transmits the received ultrasonic waves to the ultrasonic acquisition card 1. The ultrasonic acquisition card 1 is connected with the industrial computer 12 and the display device 15 on which the received ultrasonic data can be displayed in 256 different colors. The ultrasonic data can be values between 0 and 255, wherein 0 means there is a defect, 255 means there is no defect, and a larger value represents a better surface quality or internal quality of the tested workpiece.

[0040] The industrial computer controls the angle of the rotating shaft 6 of the extension rod and the position and posture of the robot arm through controller 14 according to the shape of the surface of the tested workpiece, so that the receiving probe 4 can be perpendicular to the surface of the tested workpiece so as to receive the ultrasonic waves on the surface of the tested workpiece in a more effective manner. While the position acquisition card 11 starts acquisition, the ultrasonic acquisition card 1 and the pulse transceiver 2 are triggered to operate. The emitting probe 3 and the receiving probe 4 start to emit and receive ultrasonic waves respectively. The position acquisition card 11 collects the three-dimensional coordinates of the surface of the tested workpiece at the tail-end of emitting probe 3 and transmits the collected three-dimensional coordinates of the surface of the tested workpiece to the industrial computer 12 for displaying on the device 15. The user can estimate the surface and internal quality of the tested workpiece based on the three-dimensional coordinates and ultrasonic data.

[0041] The system has multiple degrees of freedom and a high degree of flexibility, and can test various workpieces with complex curved surfaces.

[0042] The ultrasonic testing method of dual robot arms is described in detail below.

[0043] The present disclosure provides an ultrasonic testing method of dual robot arms which utilizes the above-mentioned ultrasonic testing system of dual robot arms to test the quality of surface and interior of the semi-closed workpiece with a narrow internal space. This method can ensure that the emitting probe and the receiving probe keep perpendicular to the surface of the tested workpiece without collision between the robot arms and the workpiece during the testing of the tested workpiece.

[0044] This method first utilizes CAM software to project a trajectory of the tested workpiece so as to generate a trajectory file of the tested workpiece. Then the X-axis constraint method are applied to process the generated trajectory file and constrain the X-axes of the auxiliary coordinate systems so that the positive direction of the X-axis of each of the auxiliary coordinate systems is the tangent direction of the trajectory, which represents that the emitting probe and the receiving probe are perpendicular to the tested workpiece, and the processed trajectory file are then converted into a file readable to the robot arm controllers. Next, the resulting file are download to the robot arm controllers of the ultrasonic testing system of dual robot arms with the extension rod, so that the movement of the robot with the receiving probe mounted on the extension rod is controlled in such a way that the receiving probe keeps perpendicular to the tested workpiece without collision between the robot arms and the tested workpiece.

[0045] Before projecting the trajectory of the tested workpiece, the transformation relationships of the coordinate system of the workpiece relative to the base coordinate systems of the master and slave robot arms are determined in the first place. The following is the detailed derivation.

[0046] Firstly, some relationships among the base coordinate systems of the robot arms and the coordinate system of the workpiece are defined. One of the robot arms is the master robot arm (master robot arm for short, Rm), of which base coordinate system is {M}; the other one of the robot arms is the slave robot arm (slave robot arm for short, Rs), of which base coordinate system is {S}; coordinate system of the workpiece is {W}. Let the origin of the coordinate system of the workpiece be Pori, Px be a point on the X-axis, and Py be a point on the xoy plane located in the positive direction of the Y-axis. Then these three points, as shown in FIG. 5, are expressed as Pmo {x.sub.mo,y.sub.mo,z.sub.mo}, Pmx {x.sub.mx,y.sub.mx,z.sub.mx}, Pmy {x.sub.my,y.sub.my,z.sub.my} and Pso {x.sub.so,y.sub.so,z.sub.so}, Psx {x.sub.sx,y.sub.sx,z.sub.sx}, Psy {x.sub.sy,y.sub.sy,z.sub.sy} in the base coordinate systems of the master and slave robot arms, respectively.

[0047] Based on the right hand rule, it can be obtained:

[00004]$\begin{array}{cc}\{\begin{array}{c}{}^{M}X_W=\frac{\left(x_{\mathrm{mx}}-x_{mo},y_{mx}-y_{yo},z_{\mathrm{mx}}-z_{mo}\right)}{\sqrt{{\left(x_{mx}-x_{mo}\right)}^2+{\left(y_{mx}-y_{yo}\right)}^2+{\left(z_{mx}-z_{mo}\right)}^2}}\\ {}^M\hat{Y}_w=\frac{\left(x_{\mathrm{my}}-x_{mo},y_{my}-y_{mo},z_{\mathrm{my}}-z_{mo}\right)}{\sqrt{{\left(x_{my}-x_{mo}\right)}^2+{\left(y_{my}-y_{mo}\right)}^2+{\left(z_{my}-z_{mo}\right)}^2}}\\ {}^{M}Z_W={}^{M}X_W\times {}^M\hat{Y}_w\\ {}^{M}Y_W={}^{M}X_W\times {}^{M}Z_W\end{array}& \left(1\right)\end{array}$

[0048] In the equation (1):

[0049] .sup.MX.sub.w, .sup.MY.sub.w, .sup.MZ.sub.w represent expressions of unit vectors of the positive directions of the x-axis, y-axis, and z-axis of the coordinate system of the workpiece in the base coordinate system {M} of the master robot arm;

[0050] .sup.MŶ.sub.w represents expressions of arbitrary unit vector of the positive direction of the y-axis of the xoy plane in the base coordinate system {M} of the master robot arm; [0051] further, the transformation matrix of the coordinate system of the workpiece relative to the base coordinate system of the master robot arm is:

[00005]$\begin{array}{cc}{\hspace{0.17em}}_w^{M}T=\left[\begin{array}{cccc}{}^{M}X_W& {}^{M}Y_W& {}^{M}Z_W& \mathrm{Pmo}\\ 0& 0& 0& 1\end{array}\right],& \left(2\right)\end{array}$ [0052] similarly, the transformation matrix of the coordinate system of the workpiece relative to the base coordinate system of the slave robot arm is:

[00006]$\begin{array}{cc}{\hspace{0.17em}}_w^{S}T=\left[\begin{array}{cccc}{}^{S}X_W& {}^{S}Y_W& {}^{S}Z_W& \mathrm{Pso}\\ 0& 0& 0& 1\end{array}\right].& \left(3\right)\end{array}$

[0053] In this way, the transformation relationships of the coordinate system {W} of the workpiece relative to the base coordinate systems of the master and slave robot arms can be determined, respectively. FIG. 4 shows an example defining these coordinate systems.

[0054] Next, the commercial CAM software is used to plan a preliminary trajectory for the tested workpiece and generate a trajectory file including data of coordinates and postures.

[0055] However, the obtained trajectory file cannot be directly downloaded to the robot arm controllers for use, because this type of software was originally developed for the processing and production operations of the five-axis machining tools, not for the non-destructive testing by the robot arms. The format of a discrete point in the trajectory planned by the CAM software is [x, y, z, t.sub.x, t.sub.y, t.sub.z], where the first three numbers represent the position of the discrete point in the coordinate system of the workpiece, and the last three numbers represent the projection of unit normal vectors of the discrete point on the x-axis, y-axis, and z-axis directions. These numbers contain basic information describing the spatial position and posture, but the last three numbers cannot be recognized by the robot arm controllers. Therefore, it is required to convert the last three numbers into XYZ-Euler angles recognized by the robot arm controllers.

[0056] The control principle of movement of the robot arms is to control the coordinate systems {TM} and {TS} of effectors at the ends of the robot arms to coincide with the auxiliary coordinate system {Fi} of an arbitrary discrete point on the workpiece. As shown in FIG. 5, coordinate systems {TM} and {TS} of the effectors at tail-ends of the robot arms are the tool coordinate systems of the master and slave robot arms, which are built based on the base coordinate systems of the master and slave robot arms. According to this principle, auxiliary coordinate systems for discrete points of the workpiece are built in the coordinate system of the workpiece to ensure that the effectors at the tail-ends of the robot arms move in correct postures (perpendicular to the surface of the tested workpiece in real time) and does not collide with the workpiece; then, the postures data of each discrete point of the workpiece in each of the auxiliary coordinate systems is transformed into XYZ-Euler angles. This is the principle of the X-axis constraint method of the present disclosure.

[0057] The following is the detailed derivation of the X-axis constraint method.

[0058] First, variables are defined as follows. P.sub.i is an arbitrary discrete point on the trajectory of the workpiece; {Fi} is the coordinate system of the discrete point in the coordinate system of the workpiece, which is referred to an auxiliary coordinate system of the workpiece herein; and {TM} and {TS} are the tool coordinate systems of the master and slave robot arms, respectively. In addition, when processing the trajectory file, it aims to make the trajectory file recognizable to the robot arm controllers, that is to say, the posture data in the trajectory file of the workpiece is converted into the Euler angles recognizable to the robot arm controllers.

[0059] As shown in FIG. 6, the auxiliary coordinate system is defined in the coordinate system of the workpiece as follows. The X-axis of the auxiliary coordinate system {Fi} is set to be parallel to the trajectory path. Let the direction of the X-axis of the auxiliary coordinate system in an odd-numbered row points from the current point to the next point, and the direction of the X-axis of the auxiliary coordinate system in an even-numbered row points from the current point to the preceding point. That is to say, provision is made that the directions of the X-axes of the auxiliary coordinates system of all points on the trajectory are the same as the X-axis direction of the auxiliary coordinate system of a point in the first row, thereby minimizing the change of the postures of the effectors at the tail-end of the robot arms during the entire testing. Let the Z-axis of the auxiliary coordinate system be the normal vector direction of the discrete point. The Y-axis of the auxiliary coordinate system can be obtained by the cross product of the vectors according to the right-hand rule. However, when the trajectory path is a curve, the X-axis of the auxiliary coordinate system determined according to the above method is not a tangent of the trajectory, which will cause unstable movement. In this case, it is necessary to correct the X-axis. The enlarged view of a trajectory is shown in FIG. 7, in which the X axis of the auxiliary coordinate system defined by the method specified above is the secant direction of the trajectory, called the imaginary X-axis; the corrected X-axis is the tangent direction of trajectory, called the real X-axis.

[0060] The following is the theoretical derivation of the X-axis constraint method of the present disclosure.

[0061] (1) Correcting the X-Axis and Calculating the Rotation Matrix

[0062] Firstly, an imaginary X-axis of an auxiliary coordinate system is built. Suppose there are two points b(x.sub.b,y.sub.b,z.sub.b) on the and c(x.sub.c,y.sub.c,z.sub.c) on the imaginary X-axis, and ox′ is represented as:

ox′=(x.sub.c−x.sub.b,y.sub.c−y.sub.b,z.sub.c−z.sub.b),  (4)

[0063] and the Z-axis of the auxiliary coordinate system is set as cutter shaft vector of the point b, that is:

oz=(t.sub.x,t.sub.y,t.sub.z),  (5)

[0064] the Y-axis of the auxiliary coordinate system can be obtained by the cross product of the equations (5) and (4):

[00007]$\begin{array}{cc}\begin{array}{c}\mathrm{oy}=\mathrm{oz}\times {\mathrm{ox}}^{\prime }\\ =\left(\begin{array}{c}{t}_y\left(z_c-z_b\right)-t_z\left(y_c-y_b\right),t_z\left(x_c-x_b\right)-\\ (t_x\left(z_c-z_b\right),t_x\left(y_c-y_b\right)-t_y\left(x_c-x_b\right)\end{array}\right)\\ =\left({\mathrm{oy}}_x,{\mathrm{oy}}_y,{\mathrm{oy}}_z\right)\end{array}& \left(6\right)\end{array}$

[0065] further, the X-axis of the auxiliary coordinate system is corrected by the cross product of oy and oz:

[00008]$\begin{array}{cc}\begin{array}{c}\mathrm{ox}=\mathrm{oy}\times \mathrm{oz}\\ =\left(\begin{array}{c}\left(t_z\left(x_c-x_b\right)-t_x\left(z_c-z_b\right)\right)\left(z_c-z_b\right)-\left(t_x\left(y_c-y_b\right)-t_y\left(x_c-x_b\right)\right)\left(y_c-y_b\right),\\ \left(t_x\left(y_c-y_b\right)-t_y\left(x_c-x_b\right)\right)\left(x_c-x_b\right)-\left(t_y\left(z_c-z_b\right)-t_z\left(y_c-y_b\right)\right)\left(z_c-z_b\right),\\ \left(t_y\left(z_c-z_b\right)-t_z\left(y_c-y_b\right)\right)\left(y_c-y_b\right)-\left(t_z\left(x_c-x_b\right)-t_x\left(z_c-z_b\right)\right)\left(x_c-x_b\right)\end{array}\right)\\ =\left(o{x}_x,o{x}_y,o{x}_z\right)\end{array}& \left(7\right)\end{array}$

[0066] In this way, the corrected X-axis is in the tangent direction of the trajectory, which ensures the perpendicular postures of the two probes in relative to the tested workpiece and a more stable movement.

[0067] Then, a projection matrix R of the auxiliary coordinate system in relative to the coordinate system of the workpiece, i.e., the rotation matrix of the auxiliary coordinate system in relative to the coordinate system of the workpiece, is obtained by normalizing ox, oy, and oz:

[00009]$\begin{array}{cc}R=\left[\begin{array}{ccc}\frac{{\mathrm{ox}}_x}{\sqrt{o{x}_x^2+o{x}_y^2+o{x}_z^2}}& \frac{{\mathrm{oy}}_x}{\sqrt{o{y}_x^2+o{y}_y^2+o{y}_z^2}}& \frac{t_x}{\sqrt{t_x^2+t_y^2+t_z^2}}\\ \frac{{\mathrm{ox}}_y}{\sqrt{o{x}_x^2+o{x}_y^2+o{x}_z^2}}& \frac{{\mathrm{oy}}_y}{\sqrt{o{y}_x^2+o{y}_y^2+o{y}_z^2}}& \frac{t_y}{\sqrt{t_x^2+t_y^2+t_z^2}}\\ \frac{{\mathrm{ox}}_Z}{\sqrt{o{x}_x^2+o{x}_y^2+o{x}_z^2}}& \frac{{\mathrm{oy}}_z}{\sqrt{o{y}_x^2+o{y}_y^2+o{y}_z^2}}& \frac{t_Z}{\sqrt{t_x^2+t_y^2+t_z^2}}\end{array}\right]=\hspace{1em}\left[\begin{array}{ccc}{n}_x& o_x& p_x\\ n_y& o_y& p_y\\ n_z& o_z& p_z\end{array}\right]& \left(8\right)\end{array}$

[0068] In the above equation, the first column represents the projection of the X-axis of the auxiliary coordinate system on the coordinate system of the workpiece, denoted by n; the second column represents the projection of the Y-axis of the auxiliary coordinate system on the coordinate system of the workpiece, denoted by o; and the third column represents the projection of the Z-axis of the auxiliary coordinate system on the coordinate system of the workpiece, denoted by p.

[0069] (2) Obtaining Euler angles based on an XYZ-Euler angles transformation matrix and a rotation matrix.

[0070] Based on the robotics and equal relation between the XYZ-Euler angles transformation matrix R.sub.XYZ and the rotation matrix of the coordinate system, it can be obtained:

[00010]$\begin{array}{cc}{R}_{XYZ}=R_{X\left(\alpha \right)}{R}_{Y\left(\beta \right)}{R}_{Z\left(\gamma \right)}=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \alpha & -\sin \alpha \\ 0& \sin \alpha & \cos \alpha \end{array}\right]\left[\begin{array}{ccc}\cos \beta & 0& \sin \beta \\ 0& 1& 0\\ -\sin \beta & 0& \cos \beta \end{array}\right]\left[\begin{array}{ccc}\cos \gamma & -\sin \gamma & 0\\ \sin \gamma & \cos \gamma & 0\\ 0& 0& 1\end{array}\right]=\hspace{1em}\left[\begin{array}{ccc}\cos \beta \cos \gamma & -\cos \beta \sin \gamma & \sin \beta \\ \sin \mathrm{\alpha sin\beta cos\gamma }+\cos \mathrm{\alpha sin\gamma \gamma }& -\sin \mathrm{\alpha sin\beta sin\gamma }+\cos \mathrm{\alpha cos\gamma }& -\sin \alpha \cos \beta \\ -\cos \alpha \sin \beta \cos \gamma +\sin \alpha \sin \gamma & \cos \alpha \sin \beta \sin \gamma +\sin \alpha \cos \gamma & \cos \mathrm{\alpha cos\beta }\end{array}\right]=\hspace{1em}\left[\begin{array}{ccc}{r}_{11}& r_{12}& r_{13}\\ r_{21}& r_{22}& r_{23}\\ r_{31}& r_{32}& r_{33}\end{array}\right]=R=\left[\begin{array}{ccc}{n}_x& o_x& p_x\\ n_y& o_y& p_y\\ n_z& o_z& p_z\end{array}\right]& \left(9\right)\end{array}$

[0071] From the equation (9), it can be obtained:

cos β=±√{square root over (r.sub.23.sup.2+r.sub.33.sup.2)}=±√{square root over (p.sub.y.sup.2+p.sub.z.sup.2)},  (10)

[0072] during calculation, let cos β positive, that is, assuming −90°≤β≤90°, it can be obtained:

cos β=√{square root over (r.sub.23.sup.2+r.sub.23.sup.2)}=√{square root over (p.sub.y.sup.2+p.sub.z.sup.2)},  (11)

[0073] when calculating α, β and γ, bivariate arctangent function A tan 2(y, x) (four-quadrant arctangent function) can be used to determine the quadrants of α, β and γ.

[0074] If cos β≠0, then

α=A tan 2(−r.sub.23,r.sub.33)×180/π=A tan 2(−p.sub.y,p.sub.z)×180/π

β=A tan 2(r.sub.13,√{square root over (r.sub.23.sup.2+r.sub.33.sup.2)})×180/π=A tan 2(p.sub.x,√{square root over (p.sub.y.sup.2+p.sub.z.sup.2)})×180/π

γ=A tan 2(−r.sub.23,r.sub.11)×180/π=A tan 2(−n.sub.y,n.sub.x)×180/π.  (12)

[0075] If cos β=0, then the rotation matrix R.sub.xyz degenerates to:

[00011]$\begin{array}{cc}{R}_{XYZ}=\left[\begin{array}{ccc}0& 0& \sin \beta \\ \sin \left(\alpha +\gamma \right)& \cos \left(\alpha +\gamma \right)& 0\\ -\cos \left(\alpha +\gamma \right)& \sin \left(\alpha +\gamma \right)& 0\end{array}\right].& \left(13\right)\end{array}$

[0076] At this time, assuming α=0, then

α=0

β=A tan 2(r.sub.13,0)×180/π=A tan 2(p.sub.x,0)×180/π

γ=A tan 2(r.sub.21,r.sub.22)×180/π=A tan 2(n.sub.y,o.sub.y)×180/π,  (14)

and further,

└x,y,z,t.sub.x,t.sub.y,t.sub.z┘=[x,y,z,α,β,γ].  (15)

[0077] In this way, the discrete points obtained by trajectory planning can be converted into a trajectory file recognizable to the robot controllers, and the X-axis of the auxiliary coordinate system is constrained.

[0078] The X-axis constraint method provided is simple in terms of calculation, and is thus in particular suitable to a full-coverage testing of the semi-closed workpiece with a narrow internal space by the testing system of dual robot arms. The method also helps to avoid a collision accident among the effectors of the robot arms and the tested workpiece during testing.

[0079] The implementation steps of the method of the present disclosure are described as follows.

[0080] At a step 1, a coordinate system of a workpiece for the ultrasonic testing system of dual robot arms is defined.

[0081] Particularly, the two robot arms are controlled simultaneously to reach three points on a reference coordinate system of the workpiece via a teach box (first one is the origin of the coordinate system of the workpiece, second one is a point on the positive side of the X-axis of the coordinate system of the workpiece, and third one is a point on the xoy plane located in the positive direction of the Y-axis of the coordinate system of the workpiece), and the teach box is used to record these points, thereby determining relationships of the coordinate system of the workpiece relative to the base coordinate systems of the two robot arms.

[0082] At a step 2, a trajectory file of the tested workpiece is generated.

[0083] Particularly, the commercial CAM software is used to perform a preliminary trajectory planning on the tested workpiece and generate a trajectory file including coordinates and posture data. This trajectory file is generally a text file with a .txt suffix.

[0084] At a step 3, auxiliary coordinate systems are built in the coordinate system of the workpiece, the X-axis constraint method is used to constrain the X-axes of the auxiliary coordinate systems so that the positive direction of the X-axis of each of the auxiliary coordinate systems is the tangent direction of the trajectory, and the X-axis constraint method is used to convert the posture data generated in the Step 2 into Euler angles recognizable to the master and slave robot arm controllers.

[0085] At a step 4, the coordinates of the discrete points generated in the step 2 and the converted Euler angles of the discrete points in the step 3 are converted into the coordinates and the Euler angles of the base coordinate systems of the master and slave robot arms according to the relationships among the workpiece coordinate system and the base coordinate systems of the master and slave robot arms, and the resulting coordinates and Euler angles are downloaded to the master and slave robot arm controllers, respectively.

[0086] At a step 5, transformation relationships of tool coordinate systems of the master and slave robot arms in relative to flange coordinate systems of the master and slave robot arms is input to the master and slave robot arm controllers.

[0087] Particularly, the transformation relationship of the tool coordinate system {TM} of the master robot arm in relative to the flange coordinate system of the master robot arm is input to the master robot arm controller, and the transformation relationship of the tool coordinate system {TS} of the slave robot arm in relative to the flange coordinate system of the slave robot arm is input to the slave robot arm controller.

[0088] At a step 6, the tested workpiece is tested by the testing system of dual robot arms.

[0089] Particularly, the testing system of dual robot arms is brought into an operating state, the industrial computer is turned on, and the master and slave robot arm controllers control the master and slave robot arms having the probes respectively to comprehensively test the tested workpiece.

[0090] The above is only the preferred embodiments of the present disclosure and is not intended to limit the present disclosure. Any modifications, equivalent replacements, improvements and likes made within the spirit and principles of the present disclosure should be included in the scope of protection of the present disclosure.

[0091] The extension rod and the extension rod rotating shaft may also be mounted at the tail-end of the master robot arm. As a result, the extension rod and the extension rod rotating shaft mounted at the tail-ends of the master robot arm allow the master robot arm to extend into the interior of the tested workpiece, and the extension rod and the extension rod rotating shaft mounted at the tail-ends of the slave robot arm allow the slave robot arm to extend into the interior of the tested workpiece, for quality testing. The extension rod rotating shaft may be provided between the emitting probe and the robot arm, and may be provided between the receiving probe and the robot arm, so that the receiving probe and the emitting probe can be adjusted to be perpendicular to the surface of the workpiece, thereby receiving ultrasonic signals in a more effective way.

[0092] In addition, the robot arm can be provided with multiple extension rod rotating shafts connected in turn, if necessary, where the first ends of the extension rod rotating shafts connect with the extension rod and the last ends of the extension rod rotating shafts connect with the emitting probe or the receiving probe.

[0093] The master robot arm and the slave robot arm are two cooperating robot arms. The master robot arm can be mounted with one of the emitting probe and the receiving probe, while the slave robot arm can be mounted with the other one of the emitting probe and the receiving probe.