阅读说明：本技术 一种利用机器人定位辙叉的测量方法 (Measuring method for positioning frog by using robot ) 是由 崔洪亮 王瑞成 李超 宋志伟 李天伟 夏武强 于 2020-12-29 设计创作，主要内容包括：本发明提供一种利用机器人定位辙叉的测量方法,所述机器人的输出端上设有测距传感器,其特征在于,包括如下步骤：基于所述测距传感器的工具坐标系生成标准向量；对所述辙叉进行第一次定位,检测所述辙叉在世界坐标系中的X轴方向的偏移量和Y轴方向的偏移量；计算所述交点在世界坐标系中的坐标位置；根据所述交点在世界坐标系中的坐标位置计算出所述辙叉的标准工件坐标系W-(obj),通过机器人可以准确测量辙叉上料后的空间位置,从而可以根据该空间位置对机器人程序进行补偿,保证能够准确对辙叉进行打磨。本发明的技术方案降低铁路辙叉的测量时间,提高工作效率,减少工作强度。(The invention provides a measuring method for positioning a frog by using a robot, wherein a distance measuring sensor is arranged on an output end of the robot, and the measuring method is characterized by comprising the following steps of: generating a standard vector based on a tool coordinate system of the ranging sensor; positioning the frog for the first time, and detecting the offset of the frog in the X-axis direction and the offset of the frog in the Y-axis direction in a world coordinate system; calculating the coordinate position of the intersection point in a world coordinate system; calculating a standard workpiece coordinate system W of the frog according to the coordinate positions of the intersection points in the world coordinate system obj The spatial position of the frog after being fed can be accurately measured through the robot, so that the robot program can be compensated according to the spatial position, and the frog can be accurately polished. The technical scheme of the invention reduces the measuring time of the railway frog, improves the working efficiency and reduces the working strength.)

1. A measuring method for positioning a frog by using a robot is characterized in that a distance measuring sensor is arranged on an output end of the robot, and the measuring method comprises the following steps:

s1: generating a standard vector based on a tool coordinate system of the ranging sensor;

s2: positioning the frog for the first time, and detecting the offset of the frog in the X-axis direction and the offset of the frog in the Y-axis direction in a world coordinate system;

s3: carrying out second positioning on the frog, selecting one end point of the frog and three measuring surfaces adjacent to the end point, measuring intersection points between the three measuring surfaces and the three measuring surfaces through the distance measuring sensor, and calculating the coordinate position of the intersection points in a world coordinate system;

s4: calculating a standard workpiece coordinate system W of the frog according to the coordinate positions of the intersection points in the world coordinate system_obj。

2. A method of measuring using a robot to locate a frog according to claim 1, further comprising the steps of:

s5: repeating step S3 after the frog is machined, and calculating a compensation workpiece coordinate system of the frog according to the coordinate positions of the intersection points in the world coordinate system, calculating a difference value between the compensation workpiece coordinate system and the standard workpiece coordinate system Wobj, and supplementing the difference value into the standard workpiece coordinate system Wobj.

3. The method as claimed in claim 1, wherein the step S3 of measuring the intersection points between the three measuring surfaces and the three measuring surfaces by the distance measuring sensor comprises:

s31: measuring at least 5 measuring points on each measuring surface by the distance measuring sensor;

s32: calculating the coordinates of the measuring surface in the world coordinate system through at least 5 measured points on each measuring surface;

s33: and calculating the coordinates of the intersection point in the world coordinate system based on the position of the measuring surface in the world coordinate system.

4. The method as claimed in claim 3, wherein in step S3, the measuring surfaces include a first measuring surface, a second measuring surface and a third measuring surface, and the measuring points on the first measuring surface include: first measurement point P₃₁A second measurement point P₃₂And a third measurement point P₃₃And a fourth measurement point P₃₄And a fifth measurement point P₃₅Said first measurement point P₃₁The second measurement point P₃₂And the third measurement point P₃₃And the fourth measurement point P₃₄And the fifth measurement point P₃₅Average value of (2)

The first measurement point P₃₁And the average value P_averageDifference value P between₁₀₁＝<P₃₁[1]-P_average[1]|P₃₁[2]-P_average[2]|P₃₁[3]-P_average[3]>Formula (2)

The second measurement point P₃₂And the average value P_averageDifference value P between₁₀₂＝<P₃₂[1]-P_average[1]|P₃₂[2]-P_average[2]|P₃₂[3]-P_average1[3]>Formula (3)

The third measurement point P₃₃And the average value P_averageBetweenDifference value P of₁₀₃＝<P₃₃[1]-P_average[1]|P₃₃[2]-P_average[2]|P₃₃[3]-P_average[3]>Formula (4)

The fourth measurement point P₃₄And the average value P_averageDifference value P between₁₀₄＝<P₃₄[1]-P_average[1]|P₃₄[2]-P_average[2]|P₃₄[3]-P_average[3]>Formula (5)

The fifth measurement point P₃₅And the average value P_averageDifference value P between₁₀₅＝<P₃₅[1]-P_average[1]|P₃₅[2]-P_average[2]|P₃₅[3]-P_average[3]>Formula (6)

Matrix F is A C formula (7)

Matrix C ═<<P₁₀₁[1]|P₁₀₁[1]|-1>，<P₁₀₂[1]|P₁₀₂[1]|-1>，<P₁₀₃[1]|P₁₀₃[1]|-1><P₁₀₄[1]|P₁₀₄[1]|-1>，<P₁₀₅[1]|P₁₀₅[1]|-1>>Formula (8)

Matrix E ═<-P₁₀₁[2]，-P₁₀₂[2]，-P₁₀₃[2]，-P₁₀₄[2]，-P₁₀₅[2]>Formula (9)

Matrix a ═ C^TFormula (10)

Matrix B is A.E (11)

B＝<<(P₁₀₁[1]·P₁₀₁[1]+P₁₀₂[1]·P₁₀₂[1]+P₁₀₃[1]·P₁₀₃[1]+P₁₀₄[1]·P₁₀₄[1]+P₁₀₅[1]·P₁₀₅[1])|(P₁₀₁[1]·P₁₀₁[3]+P₁₀₂[1]·P₁₀₂[3]+P₁₀₃[1]·P₁₀₃[3]+P₁₀₄[1]·P₁₀₄[3]+P₁₀₅[1]·P₁₀₅[3])|P₁₀₁[1]+P₁₀₂[1]+P₁₀₃[1]+P₁₀₄[1]+P₁₀₅[1]>，<(P₁₀₁[3]·P₁₀₁[1]+P₁₀₂[3]·P₁₀₂[1]+P₁₀₃[3]·P₁₀₃[1]+P₁₀₄[3]·P₁₀₄[1]+PP₁₀₅[3]·P₁₀₅[1])|(P₁₀₁[3]·P₁₀₁[3]+P₁₀₂[3]·P₁₀₂[3]+P₁₀₃[3]·P₁₀₃[3]+P₁₀₄[3]·P₁₀₄[3]+P₁₀₅[3]·P₁₀₅[3])|-(P₁₀₁[3]+P₁₀₂[3]+P₁₀₃[3]+P₁₀₄[4]+P₁₀₅[5])>，<-(P₁₀₁[3]+P₁₀₂[3]+P₁₀₃[3]+P₁₀₄[4]+P₁₀₅[5])|-(P₁₀₁[3]+P₁₀₂[3]+P₁₀₃[3]+P₁₀₄[3]+P₁₀₅[3])|(1+1+1+1+1)>>Formula (12)

F, X ═ B formula (13)

The solver function L of X in the formula (14) is F [1] [1] (F [2] [2 ]. F [3] [3] + F [2] [3 ]. F [3] [2]) + F [1] [1] (F [2] [3 ]. F [3] [1] -F [2] [1 ]. F [3] [3]) + F [1] [3] (F [2] [1 ]. F [3] [2] -F [2 ]. F [3] [1]) formula (14)

Let B [1 ]. F [2] [2 ]. F [3] [3] + F [2] [3 ]. F [3] [2]) + F [1] [2 ]. F [2] [3 ]. B [3] -B [2 ]. F [3] [3]) + F [1] [3 ]. B [2 ]. F [3] [2] -F [2 ]. F [2] [2 ]. B [3]) h [1] formula (15)

Let F [1] [1] (B [2 ]. F [3] [3] + F [2] [3 ]. B [3]) + B [1] (F [2] [3 ]. F [3] [1] -F [2] [1 ]. F [3]) + F [1] [3] (F [2] [1 ]. B [3] -B [2 ]. F [3]) h [2] formula (16)

Let F [1] [1] (B [2 ]. F [3] [3] + F [2] [3 ]. B [3]) + F [1] [1] (B [2 ]. F [3] [1] -F [2] [1 ]. B [3]) + B [1] (F [2] [1 ]. F [3] [2] -F [2 ]. F [3] [1]) h [3] (17)

The expression of the first measuring surface is as follows: a. the₁x+B₁y+C₁z＝d_yFormula (18)

Constant d_y＝W_y[1]·(P_average[1])+(P_average[2])+W_y[2]·(P_average[3])-W_y[3]Formula (22)

The measurement point on the second measurement plane includes: sixth measurement point P₁₁And a seventh measurement point P₁₂And an eighth measurement point P₁₃And a ninth measurement point P₁₄The tenth measurement point P₁₅Said sixth measurement point P₁₁And the seventh measurement point P₁₂And the eighth measurement point P₁₃And the ninth measurement point P₁₄And the tenth measurement point P₁₅Average value of (2)

The sixth measurement point P₁₁And the average value P_average2Difference value P between₁＝<P₁₁[1]-P_average2[1]|P₁₁[2]-P_average2[2]|P₁₁[3]-P_average2[3]>Formula (24)

The seventh measurement point P₁₂And the average value P_average2Difference value P between₂＝<P₁₂[1]-P_average2[1]|P₁₂[2]-P_average2[2]|P₁₂[3]-P_average2[3]> Equation (25)

The eighth measurement point P₁₃And the average value P_average2Difference value P between₃＝<P₁₃[1]-P_average2[1]|P₁₃[2]-P_average2[2]|P₁₃[3]-P_average2[3]>Formula (26)

The ninth measurement point P₁₄And the average value P_average2Difference value P between₄＝<P₁₄[1]-P_average2[1]|P₁₄[2]-P_average2[2]|P₁₄[3]-P_average2[3]>Formula (27)

The tenth measurement point P₁₅And the average value P_average2Difference value P between₅＝<P₁₅[1]-P_average2[1]|P₁₅[2]-P_average2[2]|P₁₅[3]-P_average2[3]>Formula (28)

Matrix C_x＝<<P₁[1]|P₁[1]|-1>，<P₂[1]|P₂[1]|-1>，<P₃[1]|P₃[1]|-1><P₄[1]|P₄[1]|-1>，<P₅[1]|P₅[1]|-1>>Formula (29)

Matrix E_x＝<-P₁[2]，-P₂[2]，-P₃[2]，-P₄[2]，-P₅[2]>Formula (30)

Matrix A_x＝C_x ^TFormula (31)

Matrix B_x＝A_x·E_xFormula (32)

Matrix B_x＝<<-(P₁[1]·P₁[2]+P₂[1]·P₂[2]+P₃[1]·P₃[12]+P₄[1]·P₄[2]+P₅[1]·P₅[2])>，<-(P₁[2]·P₁[3]+P₂[2]·P₂[3]+P₃[2]·P₃[3]+P₄[2]·P₄[3]+P₅[2]·P₅[3])>，<P₁[2]+P₂[2]+P₃[2]+P₄[2]+P₅[2]>>Formula (33)

Matrix F_x＝A_x·C_xFormula (34)

F_x＝<<(P₁[1]·P₁[1]+P₂[1]·P₂[1]+P₃[1]·P₃[1]+P₄[1]·P₄[1]+P₅[1]·P₅[1])|(P₁[1]·P₁[3]+P₂[1]·P₂[3]+P₃[1]·P₃[3]+P₄[1]·P₄[3]+P₅[1]·P₅[3])|P₁[1]+P₂[1]+P₃[1]+P₄[1]+P₅[1]>，<(P₁[3]·P₁[1]+P₁[3]·P₂[1]+P₃[3]·P₃[1]+P₄[3]·P₄[1]+P₅[3]·P₅[1])|(P₁[3]·P₁[3]+P₂[3]·P₂[3]+P₃[3]·P₃[3]+P₄[3]·P₄[3]+P₅[3]·P₅[3])|-(P₁[3]+P₂[3]+P₃[3]+P₄[4]+P₅[5])>，<-(P₁[3]+P₂[3]+P₃[3]+P₄[4]+P₅[5])|-(P₁[3]+P₂[3]+P₃[3]+P₄[3]+P₅[3])|(1+1+1+1+1)>>Formula (35)

F_x·X＝B_xFormula (36)

Solving function L of X in the formula (36)_x＝F_x[1][1]·(F_x[2][2]·F_x[3][3]+F_x[2][3]·F_x[3][2])+F_x[1][2]·(F_x[2][3]·F_x[3][1]-F_x[2][1]·F_x[3][3])+F_x[1][3]·(F_x[2][1]·F_x[3][2]-F_x[2][2]·F_x[3][1]) Formula (37)

Let B_x[1]·(F_x[2][2]·F_x[3][3]+F_x[2][3]·F_x[3][2])+F_x[1][2]·(F_x[2][3]·B[3]-B_x[2]·F_x[3][3])+F_x[1][3]·(B_x[2]·F_x[3][2]-F_x[2][2]·F_x[2][2]·B_x[3])＝h_x[1]Formula (38)

Let F_x[1][1]·(B_x[2]·F_x[3][3]+F_x[2][3]·B_x[3])+B_x[1]·(F_x[2][3]·F_x[3][1]-F_x[2][1]·F[3][3])+F_x[1][3]·(F_x[2][1]·B_x[3]-B[2]·F_x[3][1])＝h_x[2]Formula (39)

Let F_x[1][1]·(B_x[2]·F_x[3][3]+F_x[2][3]·B_x[3])+F_x[1][1]·(B_x[2]·F_x[3][1]-F_x[2][1]·B_x[3])+B_x[1]·(F_x[2][1]·F_x[3][2]-F_x[2][2]·F_x[3][1])＝h_x[3]Formula (40)

The expression of the second measurement surface is as follows: a. the₂x+B₂y+C₃z＝d_xFormula (41)

Constant d_x＝W_x[1]·(P_average2[2])+(P_average2[1])+W_x[2]·(P_average2[3])-W_x[3]Formula (45)

The measurement point on the third measurement plane includes: eleventh measurement point P₂₁And a twelfth measurement point P₂₂Thirteenth measurement Point P₂₃Fourteenth measurement point P₂₄And a fifteenth measurement point P₂₅Said eleventh measurement point P₂₁And the twelfth measurement point P₂₂And the thirteenth measurement point P₂₃The fourteenth measurement point P₂₄And the fifteenth measurement point P₂₅Average value of (2)

The eleventh measurement point P₂₁And the average value P_average3Difference value P between₆＝<P₂₁[1]-P_average3[1]|P₂₁[2]-P_average3[2]|P₂₁[3]-P_average3[3]>Formula (47)

The twelfth measurement point P₂₂And the average value P_average3Difference value P between₇＝<P₂₂[1]-P_average3[1]|P₂₂[2]-P_average3[2]|P₂₂[3]-P_average3[3]>Formula (48)

The thirteenth measurement point P₂₃And the average value P_average3Difference value P between₈＝<P₂₃[1]-P_average3[1]|P₂₃[2]-P_average3[2]|P₂₃[3]-P_average3[3]>Formula (49)

The fourteenth measurement point P₂₄And the average value P_average3Difference value P between₉＝<P₂₄[1]-P_average3[1]|P₂₄[2]-P_average3[2]|P₂₄[3]-P_average3[3]>Formula (50)

The fifteenth measurement point P₂₅And the average value P_average3Difference value P between₁₀＝<P₂₅[1]-P_average3[1]|P₂₅[2]-P_average3[2]|P₂₅[3]-P_average3[3]>Formula (51)

Matrix C_z＝<<P₆[1]|P₆[1]|-1>，<P₇[1]|P₇[1]|-1>，<P₈[1]|P₈[1]|-1><P₉[1]|P₉[1]|-1>，<P₁₀[1]|P₁₀[1]|-1>>Formula (52)

Matrix E_z＝<-P₆[2]，-P₇[2]，-P₈[2]，-P₉[2]，-P₁₀[2]> (53)

Matrix A_z＝C_z ^TFormula (54)

Matrix B_z＝A_z·E_zFormula (55)

Matrix B_z＝<<-(P₆[1]·P₆[2]+P₇[1]·P₇[2]+P₈[1]·P₈[12]+P₉[1]·P₉[2]+P₁₀[1]·P₁₀[2])>，<-(P₆[2]·P₆[3]+P₇[2]·P₇[3]+P₈[2]·P₈[3]+P9[2]·P₉[3]+P₁₀[2]·P₁₀[3])>，<P₆[2]+P₇[2]+P₈[2]+P₉[2]+P₁₀[2]>>Formula (56)

Matrix F_z＝A_z·C_zFormula (57)

Matrix F_z＝<<(P₆[1]·P₆[1]+P₇[1]·P₇[1]+P₈[1]·P₈[1]+P₉[1]·P₉[1]+P₁₀[1]·P₁₀[1])|(P₆[1]·P₆[3]+P₇[1]·P₇[3]+P₈[1]·P₈[3]+P₉[1]·P₉[3]+P₁₀[1]·P₁₀[3])|P₆[1]+P₇[1]+P₈[1]+P₉[1]+P₁₀[1]>，<(P₆[3]·P₆[1]+P₇[3]·P₇[1]+P₈[3]·P₈[1]+P₉[3]·P₉[1]+P₁₀[3]·P₁₀[1])|(P₆[3]·P₆[3]+P₇[3]·P₇[3]+P₈[3]·P₈[3]+P₉[3]·P₉[3]+P₁₀[3]·P₁₀[3])|-(P₆[3]+P₇[3]+P₈[3]+P₉[4]+P₁₀[5])>，<-(P₆[3]+P₇[3]+P₈[3]+P₉[4]+P₁₀[5])|-(P₆[3]+P₇[3]+P₈[3]+P₉[3]+P₁₀[3])|(1+1+1+1+1)>>Formula (58)

F_z·X＝B_zFormula (59)

Solving function L of X in the formula (59)_z＝F_z[1][1]·(F_z[2][2]·F_z[3][3]+F_z[2][3]·F_z[3][2])+F_z[1][2]·(F_z[2][3]·F_z[3][1]-F_z[2][1]·F_z[3][3])+F_z[1][3]·(F_z[2][1]·F_z[3][2]-F_z[2][2]·F_z[3][1]) Formula (60)

Let B_z[1]·(F_z[2][2]·F_z[3][3]+F_z[2][3]·F_z[3][2])+F_z[1][2]·(F_z[2][3]·B_z[3]-B_z[2]·F_z[3][3])+F_z[1][3]·(B_z[2]·F_z[3][2]-F_z[2][2]·F_z[2][2]·B_z[3])＝h_z[1]Formula (61)

Let F_z[1][1]·(B_z[2]·F_z[3][3]+F_z[2][3]·B_z[3])+B_z[1]·(F_z[2][3]·F_z[3][1]-F_z[2][1]·F_z[3][3])+F_z[1][3]·(F_z[2][1]·B_z[3]-B_z[2]·F_z[3][1])＝h_z[2]Formula (62)

Let F_z[1][1]·(B_z[2]·F_z[3][3]+F_z[2][3]·B_z[3])+F_z[1][1]·(B_z[2]·F_z[3][1]-F_z[2][1]·B_z[3])+B_z[1]·(F_z[2][1]·F_z[3][2]-F_z[2][2]·F_z[3][1])＝h_z[3]Formula (63)

The expression of the third measurement surface is as follows: a. the₃x+B₃y+C₃z＝d_zFormula (64)

Constant d_z＝W_z[1]·(P_average3[1])+W_z[2]·(P_average3[2])+(P_average3[3])-W_z[3]Formula (68)

An intersection point of the first measuring surface, the second measuring surface and the third measuring surface

H：＝<<d_x>，<d_v>，<d_z>>Equation (69).

5. The measuring method of claim 4, wherein step S4 includes:

the standard workpiece coordinate system W_objZ-axis direction vector Z_wobjIs the normal vector A of the second measuring surface₁And a normal vector A of the third measuring surface₂The direction of the vector product of (a), the normal vector of the third measuring plane (A)₂In the direction of the standard workpiece coordinate system W_objOf the X-axis, the standard workpiece coordinate system W_objDirection vector of Y axis of

Y_wobj＝Z_wobj×A₂Formula (70)

The intersection point H is the standard workpiece coordinate system W_objOf the origin.

6. The method of claim 1, wherein the distance measuring sensor is a laser sensor and the distance between the distance measuring sensor and the frog is no greater than 100 mm.

7. A method of measurement using a robot to locate frog according to claim 6 wherein the direction of the standard vector is the same as the direction of the calibrated laser centre point of the ranging sensor.

8. The method of claim 1, wherein the detecting the offset of the frog in the world coordinate system in the X-axis direction and the Y-axis direction comprises:

s21: fixing the frog through a tooling clamp;

s21: selecting two adjacent planes of the frog, wherein the two planes are adjacent to the bottom surface of the frog;

s22: and measuring the offset of the two planes in the X-axis direction and the offset of the two planes in the Y-axis direction in the world coordinate system.

Technical Field

The invention relates to the technical field of industrial measurement, in particular to a measuring method for positioning a frog by using a robot.

Background

Railway frog is a rail plane crossing component that allows a railway wheel to switch from one track to another, which is a consumable part that needs to be replaced when worn to a certain extent, and therefore has a large production demand. The two ends of the railway frog are required to be accurately assembled with the steel rails, the assembling surfaces matched with the steel rails have higher dimensional precision requirements, and the traditional mode is that the dimensional requirements are realized through a manual polishing mode. The mode has higher requirement on the technical level of workers, the production efficiency is low, dust generated by polishing also has great harm to human bodies, so that the robot polishing technology is developed, but the frog is a casting part, the overall dimension is up to 4 meters at most, the weight is nearly 1 ton, the size deviation of the frog is great, and the spatial position of the frog is difficult to ensure in a robot polishing system through a clamping mode.

Disclosure of Invention

The invention aims to provide a measuring method for positioning a frog by using a robot, which is used for measuring the spatial position of the frog after manual feeding relative to an industrial robot so as to ensure that the robot can accurately polish the frog.

In order to achieve the above purpose, the invention provides the following technical scheme: a measuring method for positioning a frog by using a robot is characterized in that a distance measuring sensor is arranged on an output end of the robot, and the measuring method comprises the following steps:

s1: generating a standard vector based on a tool coordinate system of the ranging sensor;

s2: positioning the frog for the first time, and detecting the offset of the frog in the X-axis direction and the offset of the frog in the Y-axis direction in a world coordinate system;

s3: carrying out second positioning on the frog, selecting one end point of the frog and three measuring surfaces adjacent to the end point, measuring intersection points between the three measuring surfaces and the three measuring surfaces through the distance measuring sensor, and calculating the coordinate position of the intersection points in a world coordinate system;

s4: calculating a standard workpiece coordinate system W of the frog according to the coordinate positions of the intersection points in the world coordinate system_obj。

Further, the method also includes step S5: repeating the step S3 after the frog is machined, calculating a compensation workpiece coordinate system of the frog according to the coordinate position of the intersection point in the world coordinate system, and calculating the compensation workpiece coordinate system and the standard workpiece coordinate system W_obj and supplementing said differences to said standard object coordinate system W_obj.

Further, in the step S3, the measuring, by the distance measuring sensor, intersection points between the three measuring surfaces and the three measuring surfaces includes:

s31: measuring at least 5 measuring points on each measuring surface by the distance measuring sensor;

s32: calculating the coordinates of the measuring surface in the world coordinate system through at least 5 measured points on each measuring surface;

s33: and calculating the coordinates of the intersection point in the world coordinate system based on the position of the measuring surface in the world coordinate system.

Further, in step S3, the measurement surfaces include a first measurement surface, a second measurement surface, and a third measurement surface, and the measurement point on the first measurement surface includes: first measurement point P₃₁A second measurement point P₃₂And a third measurement point P₃₃And a fourth measurement point P₃₄And a fifth measurement point P₃₅Said first measurement point P₃₁The second measurement point P₃₂And the third measurement point P₃₃And the fourth measurement point P₃₄And the fifth measurement pointP₃₅Average value of (2)

The first measurement point P₃₁And the average value P_averageDifference value P between₁₀₁＝<P₃₁[1]-P_average[1]|P₃₁[2]-P_average[2]|P₃₁[3]-P_average[3]>Formula (2)

The second measurement point P₃₂And the average value P_averageDifference value P between₁₀₂＝<P₃₂[1]-P_average[1]|P₃₂[2]-P_average[2]|P₃₂[3]-P_average1[3]>Formula (3)

The third measurement point P₃₃And the average value P_averageDifference value P between₁₀₃＝<P₃₃[1]-P_average[1]|P₃₃[2]-P_average[2]|P₃₃[3]-P_average[3]>Formula (4)

The fourth measurement point P₃₄And the average value P_averageDifference value P between₁₀₄＝<P₃₄[1]-P_average[1]|P₃₄[2]-P_average[2]|P₃₄[3]-P_average[3]>Formula (5)

The fifth measurement point P₃₅And the average value P_averageDifference value P between₁₀₅＝<P₃₅[1]-P_average[1]|P₃₅[2]-P_average[2]|P₃₅[3]-P_average[3]>Formula (6)

Matrix F is A C formula (7)

Matrix C ═<<P₁₀₁[1]|P₁₀₁[1]|-1>，<P₁₀₂[1]|P₁₀₂[1]|-1>，<P₁₀₃[1]|P₁₀₃[1]|-1><P₁₀₄[1]|P₁₀₄[1]|-1>，<P₁₀₅[1]|P₁₀₅[1]|-1>>Formula (8)

Matrix E ═<-P₁₀₁[2]，-P₁₀₂[2]，-P₁₀₃[2]，-P₁₀₄[2]，-P₁₀₅[2]>Formula (9)

Matrix a ═ C^TFormula (10)

Matrix B is A.E (11)

B＝<<(P₁₀₁[1]·P₁₀₁[1]+P₁₀₂[1]·P₁₀₂[1]+P₁₀₃[1]·P₁₀₃[1]+P₁₀₄[1]·P₁₀₄[1]+P₁₀₅[1]·P₁₀₅[1])|(P₁₀₁[1]·P₁₀₁[3]+P₁₀₂[1]·P₁₀₂[3]+P₁₀₃[1]·P₁₀₃[3]+P₁₀₄[1]·P₁₀₄[3]+P₁₀₅[1]·P₁₀₅[3])|P₁₀₁[1]+P₁₀₂[1]+P₁₀₃[1]+P₁₀₄[1]+P₁₀₅[1]>，<(P₁₀₁[3]·P₁₀₁[1]+P₁₀₂[3]·P₁₀₂[1]+P₁₀₃[3]·P₁₀₃[1]+P₁₀₄[3]·P₁₀₄[1]+P₁₀₅[3]·P₁₀₅[1])|(P₁₀₁[3]·P₁₀₁[3]+P₁₀₂[3]·P₁₀₂[3]+P₁₀₃[3]·P₁₀₃[3]+P₁₀₄[3]·P₁₀₄[3]+P₁₀₅[3]·P₁₀₅[3])|-(P₁₀₁[3]+P₁₀₂[3]+P₁₀₃[3]+P₁₀₄[4]+P₁₀₅[5])>，<-(P₁₀₁[3]+P₁₀₂[3]+P₁₀₃[3]+P₁₀₄[4]+P₁₀₅[5])|-(P₁₀₁[3]+P₁₀₂[3]+P₁₀₃[3]+P₁₀₄[3]+P₁₀₅[3])|(1+1+1+1+1)>>Formula (12)

F, X ═ B formula (13)

The solver function L of X in the formula (14) is F [1] [1] (F [2] [2 ]. F [3] [3] + F [2] [3 ]. F [3] [2]) + F [1] [1] (F [2] [3 ]. F [3] [1] -F [2] [1 ]. F [3] [3]) + F [1] [3] (F [2] [1 ]. F [3] [2] -F [2 ]. F [3] [1]) formula (14)

Let B [1 ]. F [2] [2 ]. F [3] [3] + F [2] [3 ]. F [3] [2]) + F [1] [2 ]. F [2] [3 ]. B [3] -B [2 ]. F [3] [3]) + F [1] [3 ]. B [2 ]. F [3] [2] -F [2 ]. F [2] [2 ]. B [3]) h [1] formula (15)

Let F [1] [1] (B [2 ]. F [3] [3] + F [2] [3 ]. B [3]) + B [1] (F [2] [3 ]. F [3] [1] -F [2] [1 ]. F [3]) + F [1] [3] (F [2] [1 ]. B [3] -B [2 ]. F [3]) h [2] formula (16)

Let F [1] [1] (B [2 ]. F [3] [3] + F [2] [3 ]. B [3]) + F [1] [1] (B [2 ]. F [3] [1] -F [2] [1 ]. B [3]) + B [1] (F [2] [1 ]. F [3] [2] -F [2 ]. F [3] [1]) h [3] (17)

The expression of the first measuring surface is as follows: a. the₁x+B₁y+C₁z＝d_yFormula (18)

Coefficient of performance

Coefficient of performance

Coefficient of performance

Constant d_y＝W_y[1]·(P_average[1])+(P_average[2])+W_y[2]·(P_average[3])-W_y[3]Formula (22)

The measurement point on the second measurement plane includes: sixth measurement point P₁₁And a seventh measurement point P₁₂And an eighth measurement point P₁₃And a ninth measurement point P₁₄The tenth measurement point P₁₅Said sixth measurement point P₁₁And the seventh measurement point P₁₂And the eighth measurement point P₁₃And the ninth measurement point P₁₄And the tenth measurement point P₁₅Average value of (2)

The sixth measurement point P₁₁And the average value P_average2Difference value P between₁＝<P₁₁[1]-P_average2[1]|P₁₁[2]-P_average2[2]|P₁₁[3]-P_average2[3]>Formula (24)

The seventh measurement point P₁₂And the average value P_average2Difference value P between₂＝<P₁₂[1]-P_average2[1]|P₁₂[2]-P_average2[2]|P₁₂[3]-P_average2[3]>Equation (25)

The eighth measurement point P₁₃And the average value P_average2Difference value P between₃＝<P₁₃[1]-P_average2[1]|P₁₃[2]-P_average2[2]|P₁₃[3]-P_average2[3]>Formula (26)

The ninth measurement point P₁₄And the average value P_average2Difference between P4 ═<P₁₄[1]-P_average2[1]|P₁₄[2]-P_average2[2]|P₁₄[3]-P_average2[3]>Formula (27)

The tenth measurement point P₁₅And the average value P_average2Difference value P between₅＝<P₁₅[1]-P_average2[1]|P₁₅[2]-P_average2[2]|P₁₅[3]-P_average2[3]>Formula (28)

Matrix C_x＝<<P₁[1]|P₁[1]|-1>，<P₂[1]|P₂[1]|-1>，<P₃[1]|P₃[1]|-1><P₄[1]|P₄[1]|-1>，<P₅[1]|P₅[1]|-1>>Formula (29)

Matrix E_x＝<-P₁[2]，-P₂[2]，-P₃[2]，-P₄[2]，-P₅[2]>Formula (30)

Matrix A_x＝C_x ^TFormula (31)

Matrix B_x＝A_x·E_xFormula (32)

Matrix B_x＝<<-(P₁[1]·P₁[2]+P₂[1]·P₂[2]+P₃[1]·P₃[12]+P₄[1]·P₄[2]+P₅[1]·P₅[2])>，<-(P₁[2]·P₁[3]+P₂[2]·P₂[3]+P₃[2]·P₃[3]+P₄[2]·P₄[3]+P₅[2]·P₅[3])>，<P₁[2]+P₂[2]+P₃[2]+P₄[2]+P₅[2]>>Formula (33)

Matrix F_x＝A_x·C_xFormula (34)

F_x＝<<(P₁[1]·P₁[1]+P₂[1]·P₂[1]+P₃[1]·P₃[1]+P₄[1]·P₄[1]+P₅[1]·P₅[1])|(P₁[1]·P₁[3]+P₂[1]·P₂[3]+P₃[1]·P₃[3]+P₄[1]·P₄[3]+P₅[1]·P₅[3])|P₁[1]+P₂[1]+P₃[1]+P₄[1]+P₅[1]>，<(P₁[3]·P₁[1]+P₂[3]·P₂[1]+P₃[3]·P₃[1]+P₄[3]·P₄[1]+P₅[3]·P₅[1])|(P₁[3]·P₁[3]+P₂[3]·P₂[3]+P₃[3]·P₃[3]+P₄[3]·P₄[3]+P₅[3]·P₅[3])|-(P₁[3]+P₂[3]+P₃[3]+P₄[4]+P₅[5])>，<-(P₁[3]+P₂[3]+P₃[3]+P₄[4]+P₅[5])|-(P₁[3]+P₂[3]+P₃[3]+P₄[3]+P₅[3])|(1+1+1+1+1)>>Formula (35)

F_x·X＝B_xFormula (36)

Solving function L of X in the formula (36)_x＝F_x[1][1]·(F_x[2][2]·F_x[3][3]+F_x[2][3]·F_x[3][2])+F_x[1][2]·(F_x[2][3]·F_x[3][1]-F_x[2][1]·F_x[3][3])+F_x[1][3]·(F_x[2][1]·F_x[3][2]-F_x[2][2]·F_x[3][1]) Formula (37)

Let B_x[1]·(F_x[2][2]·F_x[3][3]+F_x[2][3]·F_x[3][2])+F_x[1][2]·(F_x[2][3]·B[3]-B_x[2]·F_x[3][3])+F_x[1][3]·(B_x[2]·F_x[3][2]-F_x[2][2]·F_x[2][2]·B_x[3])＝h_x[1]Formula (38)

Let F_x[1][1]·(B_x[2]·F_x[3][3]+F_x[2][3]·B_x[3])+B_x[1]·(F_x[2][3]·F_x[3][1]-F_x[2][1]·F[3][3])+F_x[1][3]·(F_x[2][1]·B_x[3]-B[2]·F_x[3][1])＝h_x[2]Formula (39)

Let F_x[1][1]·(B_x[2]·F_x[3][3]+F_x[2][3]·B_x[3])+F_x[1][1]·(B_x[2]·F_x[3][1]-F_x[2][1]·B_x[3])+B_x[1]·(F_x[2][1]·F_x[3][2]-F_x[2][2]·F_x[3][1])＝h_x[3]Formula (40)

The expression of the second measurement surface is as follows: a. the₂x+B₂y+C₃z＝d_xFormula (41)

Coefficient of performance

Coefficient of performance

Coefficient of performanceConstant d_x＝W_x[1]·(P_average2[2])+(P_average2[1])+W_x[2]·(P_average2[3])-W_x[3]Formula (45)

The measurement point on the third measurement plane includes: eleventh measurement point P₂₁And a twelfth measurement point P₂₂Thirteenth testFixed point P₂₃Fourteenth measurement point P₂₄And a fifteenth measurement point P₂₅Said eleventh measurement point P₂₁And the twelfth measurement point P₂₂And the thirteenth measurement point P₂₃The fourteenth measurement point P₂₄And the fifteenth measurement point P₂₅Average value of (2)

The eleventh measurement point P₂₁And the average value P_average3Difference value P between₆＝<P₂₁[1]-P_average3[1]|P₂₁[2]-P_average3[2]|P₂₁[3]-P_average3[3]>Formula (47)

The twelfth measurement point P₂₂And the average value P_average3Difference value P between₇＝<P₂₂[1]-P_average3[1]|P₁₂[2]-P_average3[2]|P₂₂[3]-P_average3[3]>Formula (48)

The thirteenth measurement point P₂₃And the average value P_average3Difference value P between₈＝<P₂₃[1]-P_average3[1]|P₂₃[2]-P_average3[2]|P₂₃[3]-P_average3[3]>Formula (49)

The fourteenth measurement point P₂₄And the average value P_average3Difference value P between₉＝<P₂₄[1]-P_average3[1]|P₂₄[2]-P_average3[2]|P₂₄[3]-P_average3[3]>Formula (50)

The fifteenth measurement point P₂₅And the average value P_average3Difference value P between₁₀＝<P₂₅[1]-P_average3[1]|P₂₅[2]-P_average3[2]|P₂₅[3]-P_average3[3]>Formula (51)

Matrix C_z＝<<P₆[1]|P₆[1]|-1>，<P₇[1]|P₇[1]|-1>，<P₈[1]|P₈[1]|-1><P₉[1]|P₉[1]|-1>，<P₁₀[1]|P₁₀[1]|-1>>Formula (52)

Matrix E_z＝<-P₆[2]，-P₇[2]，-P₈[2]，-P₉[2]，-P₁₀[2]>(53)

Matrix A_z＝C_z ^TFormula (54)

Matrix B_z＝A_z·E_zFormula (55)

Matrix B_z＝<<-(P₆[1]·P₅[2]+P₇[1]·P₇[2]+P₈[1]·P₈[12]+P₉[1]·P₉[2]+P₁₀[1]·P_10[2])>，<-(P₆[2]·P₆[3]+P₇[2]·P₇[3]+P₈[2]·P₈[3]+P₉[2]·P₉[3]+P₁₀[2]·P₁₀[3])>，<P₆[2]+P₇[2]+P₈[2]+P₉[2]+P₁₀[2]>>Formula (56)

Matrix F_z＝A_z·C_zFormula (57)

Matrix F_z＝<<(P₆[1]·P₆[1]+P₇[1]·P₇[1]+P₈[1]·P₈[1]+P₉[1]·P₉[1]+P₁₀[1]·P₁₀[1])|(P₆[1]·P₆[3]+P₇[1]·P₇[3]+P₈[1]·P₈[3]+P₉[1]·P₉[3]+P₁₀[1]·P₁₀[3])|P₆[1]+P₇[1]+P₈[1]+P₉[1]+P₁₀[1]>，<(P₆[3]·P₆[1]+P₇[3]·P₇[1]+P₈[3]·P₈[1]+P₉[3]·P₉[1]+P₁₀[3]·P₁₀[1])|(P₆[3]·P₆[3]+P₇[3]·P₇[3]+P₈[3]·P₈[3]+P₉[3]·P₉[3]+P₁₀[3]·P₁₀[3])|-(P₆[3]+P₇[3]+P₈[3]+P₉[4]+P₁₀[5])>，<-(P₆[3]+P₇[3]+P₈[3]+P₉[4]+P₁₀[5])|-(P₆[3]+P₇[3]+P₈[3]+P₉[3]+P₁₀[3])|(1+1+1+1+1)>>Formula (58)

F_z·X＝B_zFormula (59)

Solving function L of X in the formula (59)_z＝F_z[1][1]·(F_z[2][2]·F_z[3][3]+F_z[2][3]·F_z[3][2])+F_z[1][2]·(F_z[2][3]·F_z[3][1]-F_z[2][1]·F_z[3][3])+F_z[1][3]·(F_z[2][1]·F_z[3][2]-F_z[2][2]·F_z[3][1]) Formula (60)

Let B_z[1]·(F_z[2][2]·F_z[3][3]+F_z[2][3]·F_z[3][2])+F_z[1][2]·(F_z[2][3]·B_z[3]-B_z[2]·F_z[3][3])+F_z[1][3]·(B_z[2]·F_z[3][2]-F_z[2][2]·F_z[2][2]·B_z[3])＝h_z[1]Formula (61)

Let F_z[1][1]·(B_z[2]·F_z[3][3]+F_z[2][3]·B_z[3])+B_z[1]·(F_z[2][3]·F_z[3][1]-F_z[2][1]·F_z[3][3])+F_z[1][3]·(F_z[2][1]·B_z[3]-B_z[2]·F_z[3][1])h_z[2]Formula (62)

Let h_z[3]＝F_z[1][1]·(B_z[2]·F_z[3][3]+F_z[2][3]·B_z[3])+F_z[1][1]·(B_z[2]·F_z[3][1]-F_z[2][1]·B_z[3])+B_z[1]·(F_z[2][1]·F_z[3][2]-F_z[2][2]·F_z[3][1]) Formula (63)

The expression of the third measurement surface is as follows: a. the₃x+B₃y+C₃z＝d_zFormula (64)

Coefficient of performance

Coefficient of performance

Coefficient of performance

Constant d_z＝W_z[1]·(P_average3[1])+W_z[2]·(P_average3[2])+(P_average3[3])-W_z[3]Formula (68)

An intersection point of the first measuring surface, the second measuring surface and the third measuring surface

H：＝<<d_x>，<d_y>，<d_z>>Equation (69).

Further, step S4 includes: the standard workpiece coordinate system W_objZ-axis direction vector Z_wobjIs the normal vector A of the second measuring surface₁And a normal vector A of the third measuring surface₂The direction of the vector product of (a), the normal vector of the third measuring plane (A)₂In the direction of the standard workpiece coordinate system W_objOf the X-axis, the standard workpiece coordinate system W_objDirection vector of Y axis of

Y_wobj＝Z_wobj×A₂Formula (70)

The intersection point H is the standard workpiece coordinate system W_objOf the origin.

Further, the distance measuring sensor is a laser sensor, and the distance between the distance measuring sensor and the frog is not more than 100 mm.

Further, the direction of the standard vector is the same as the direction of the calibration laser center point of the ranging sensor.

Further, the detecting the offset of the frog in the world coordinate system in the X-axis direction and the offset in the Y-axis direction includes:

s21: fixing the frog through a tooling clamp;

s21: selecting two adjacent planes of the frog, wherein the two planes are adjacent to the bottom surface of the frog;

s22: and measuring the offset of the two planes in the X-axis direction and the offset of the two planes in the Y-axis direction in the world coordinate system.

The robot can accurately measure the spatial position of the frog after the frog is fed, so that the robot program can be compensated according to the spatial position, and the frog can be accurately polished. The technical scheme of the invention reduces the measuring time of the railway frog, improves the working efficiency and reduces the working strength.

Drawings

The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. Wherein:

fig. 1 is a schematic view of a second positioning of a measuring method for positioning a frog by a robot according to an embodiment of the present invention.

Fig. 2 is a schematic view of a first positioning of a measuring method for positioning a frog by a robot according to an embodiment of the present invention.

Fig. 3 is a schematic position diagram of a standard workpiece coordinate system for a measurement method using a robot to locate a frog according to an embodiment of the present invention.

FIG. 4 is a flow chart of a measurement method for locating a frog using a robot in accordance with one embodiment of the present invention

Description of reference numerals: 1-frog; 2-a second measuring surface; 3-a first measuring surface; 4-third measuring surface; 5-plane.

Detailed Description

The present invention will be described in detail below with reference to the embodiments with reference to the attached drawings. The various examples are provided by way of explanation of the invention, and not limitation of the invention. In fact, it will be apparent to those skilled in the art that modifications and variations can be made in the present invention without departing from the scope or spirit thereof. For instance, features illustrated or described as part of one embodiment, can be used with another embodiment to yield a still further embodiment. It is therefore intended that the present invention encompass such modifications and variations as fall within the scope of the appended claims and equivalents thereof.

In the description of the present invention, the terms "longitudinal", "lateral", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, which are for convenience of description of the present invention only and do not require that the present invention must be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present invention. The terms "connected," "connected," and "disposed" as used herein are intended to be broadly construed, and may include, for example, fixed and removable connections; can be directly connected or indirectly connected through intermediate components; the connection may be a wired electrical connection, a wireless electrical connection, or a wireless communication signal connection, and a person skilled in the art can understand the specific meaning of the above terms according to specific situations.

One or more examples of the invention are illustrated in the accompanying drawings. The detailed description uses numerical and letter designations to refer to features in the drawings. Like or similar designations in the drawings and description have been used to refer to like or similar parts of the invention. As used herein, the terms "first," "second," "third," and "fourth" may be used interchangeably to distinguish one component from another and are not intended to denote the position or importance of the individual components.

As shown in fig. 1 to 4, according to an embodiment of the present invention, there is provided a measuring method for positioning a frog by using a robot, wherein a distance measuring sensor is disposed on an output end of the robot, and the frog 1 is fixed by a tooling fixture, including:

s1: generating a standard vector based on a tool coordinate system of the distance measuring sensor, wherein the direction of the standard vector is the same as the direction of a calibration laser central point of the distance measuring sensor;

s2: the method comprises the following steps of carrying out first positioning on a frog 1, wherein the first positioning is rough positioning, and the bottom of the railway frog 1 is subjected to finish machining, so that the offset of the railway frog 1 in the X direction and the Y direction in a world coordinate system can be detected only by detecting the offset of the railway frog 1 in the X axis direction and the offset of the railway frog 1 in the Y axis direction in the world coordinate system, a distance measuring sensor is a laser sensor, and the distance between the distance measuring sensor and the frog 1 is not more than 100 mm;

detecting the offset amount of the frog 1 in the X-axis direction and the offset amount in the Y-axis direction in the world coordinate system includes:

s21: fixing the frog 1 through a tooling clamp;

s21: selecting two adjacent planes 5 of the frog 1, wherein the two planes 5 are adjacent to the bottom surface of the frog 1;

s22: the amount of offset in the X-axis direction and the amount of offset in the Y-axis direction in the world coordinate system of the two planes 5 are measured.

S3: carrying out second positioning on the frog 1, wherein the second positioning is fine positioning, transmitting the positioned data to a controller of an industrial robot, selecting one end point of the frog 1 and three measuring surfaces adjacent to the end point, measuring intersection points between the three measuring surfaces through a distance measuring sensor, and calculating the coordinate position of the intersection point in a world coordinate system;

measuring the three measuring surfaces and the intersection points between the three measuring surfaces by the distance measuring sensor comprises:

s31: measuring at least 5 measuring points on each measuring surface by a distance measuring sensor;

s32: calculating the coordinates of the measuring surface in a world coordinate system through at least 5 measured points on each measuring surface;

s33: and calculating the coordinates of the intersection point in the world coordinate system based on the position of the measuring plane in the world coordinate system.

S4: calculating the standard workpiece coordinate system W of the frog 1 according to the coordinate positions of the intersection points in the world coordinate system_obj。

Standard workpiece coordinate system W_objZ-axis direction vector Z_wobjIs the normal vector A of the second measuring surface 2₁And the normal vector A of the third measuring surface 4₂Direction of the vector product of (1), normal vector a of the third measuring surface 4₂In the direction of a standard workpiece coordinate system W_objDirection vector of the X-axis, standard workpiece coordinate system W_objDirection vector of Y axis of

Y_wobj＝Z_wobj×A₂Formula (70)

The intersection point H is a standard workpiece coordinate system W_objOf the origin.

S5: repeating S3 after the frog 1 has been machined, calculating a compensation workpiece coordinate system of the frog 1 from the coordinate positions of the intersection points in the world coordinate system, calculating the difference between the compensation workpiece coordinate system and the standard workpiece coordinate system Wobj, and supplementing the difference to the standard workpiece coordinate system Wobj

Preferably, the measuring surface comprises a first measuring surface 3, a second measuring surface 2 and a third measuring surface 4, and the measuring points on the first measuring surface 3 comprise: first measurement point P₃₁A second measurement point P₃₂And a third measurement point P₃₃And a fourth measurement point P₃₄And a fifth measurement pointP₃₅First measurement point P₃₁A second measurement point P₃₂And a third measurement point P₃₃And a fourth measurement point P₃₄And a fifth measurement point P₃₅Average value of (2)

The first measurement point P₃₁And the average value P_averageDifference value P between₁₀₁＝<P₃₁[1]-P_average[1]|P₃₁[2]-P_average[2]|P₃₁[3]-P_average[3]>Formula (2)

The second measurement point P₃₂And the average value P_averageDifference value P between₁₀₂＝<P₃₂[1]-P_average[1]|P₃₂[2]-P_average[2]|P₃₂[3]-P_average1[3]>Formula (3)

The third measurement point P₃₃And the average value P_averageDifference value P between₁₀₃＝<P₃₃[1]-P_average[1]|P₃₃[2]-P_average[2]|P₃₃[3]-P_average[3]>Formula (4)

The fourth measurement point P₃₄And the average value P_averageDifference value P between₁₀₄＝<P₃₄[1]-P_average[1]|P₃₄[2]-P_average[2]|P₃4[3]-P_average[3]>Formula (5)

The fifth measurement point P₃₅And the average value P_averageDifference value P between₁₀₅＝<P₃₅[1]-P_average[1]|P₃₅[2]-P_average[2]|P₃₅[3]-P_average[3]>Formula (6)

Matrix F is A C formula (7)

Matrix C ═<<P₁₀₁[1]|P₁₀₁[1]|-1>，<P₁₀₂[1]|P₁₀₂[1]|-1>，

<P₁₀₃[1]|P₁₀₃[1]|-1><P₁₀₄[1]|P₁₀₄[1]|-1>，<P₁₀₅[1]|P₁₀₅[1]|-1>>Formula (8)

Matrix E ═<-P₁₀₁[2]，-P₁₀₂[2]，-P₁₀₃[2]，-P₁₀₄[2]，-P₁₀₅[2]>Formula (9)

Matrix a ═ C^TFormula (10)

Matrix B is A.E (11)

B＝<<(P₁₀₁[1]·P₁₀₁[1]+P₁₀₂[1]·P₁₀₂[1]+P₁₀₃[1]·P₁₀₃[1]+P₁₀₄[1]·P₁₀₄[1]+P₁₀₅[1]·P₁₀₅[1])|(P₁₀₁[1]·P₁₀₁[3]+P₁₀₂[1]·P₁₀₂[3]+P₁₀₃[1]·P₁₀₃[3]+P₁₀₄[1]·P₁₀₄[3]+P₁₀₅[1]·P₁₀₅[3])|P₁₀₁[1]+P₁₀₂[1]+P₁₀₃[1]+P₁₀₄[1]+P₁₀₅[1]>，<(P₁₀₁[3]·P₁₀₁[1]+P₁₀₂[3]·P₁₀₂[1]+P₁₀₃[3]·P₁₀₃[1]+P₁₀₄[3]·P₁₀₄[1]+P₁₀₅[3]·P₁₀₅[1])|(P₁₀₁[3]·P₁₀₁[3]+P₁₀₂[3]·P₁₀₂[3]+P₁₀₃[3]·P₁₀₃[3]+P₁₀₄[3]·P₁₀₄[3]+P₁₀₅[3]·P₁₀₅[3])|-(P₁₀₁[3]+P₁₀₂[3]+P₁₀₃[3]+P₁₀₄[4]+P₁₀₅[5])>，<-(P₁₀₁[3]+P₁₀₂[3]+P₁₀₃[3]+P₁₀₄[4]+P₁₀₅[5])|-(P₁₀₁[3]+P₁₀₂[3]+P₁₀₃[3]+P₁₀₄[3]+P₁₀₅[3])|(1+1+1+1+1)>>Formula (12)

F, X ═ B formula (13)

The solver function L of X in the formula (14) is F [1] [1] (F [2] [2 ]. F [3] [3] + F [2] [3 ]. F [3] [2]) + F [1] [1] (F [2] [3 ]. F [3] [1] -F [2] [1 ]. F [3] [3]) + F [1] [3] (F [2] [1 ]. F [3] [2] -F [2 ]. F [3] [1]) formula (14)

Let B [1 ]. F [2] [2 ]. F [3] [3] + F [2] [3 ]. F [3] [2]) + F [1] [2 ]. F [2] [3 ]. B [3] -B [2 ]. F [3] [3]) + F [1] [3 ]. B [2 ]. F [3] [2] -F [2 ]. F [2] [2 ]. B [3]) h [1] formula (15)

Let F [1] [1] (B [2 ]. F [3] [3] + F [2] [3 ]. B [3]) + B [1] (F [2] [3 ]. F [3] [1] -F [2] [1 ]. F [3]) + F [1] [3] (F [2] [1 ]. B [3] -B [2 ]. F [3]) h [2] formula (16)

Let F [1] [1] (B [2 ]. F [3] [3] + F [2] [3 ]. B [3]) + F [1] [1] (B [2 ]. F [3] [1] -F [2] [1 ]. B [3]) + B [1] (F [2] [1 ]. F [3] [2] -F [2 ]. F [3] [1]) h [3] (17)

The expression of the first measuring surface is as follows: a. the₁x+B₁y+C₁z＝d_yFormula (18)

Coefficient of performance

Coefficient of performance

Coefficient of performance

Constant d_y＝W_y[1]·(P_average[1])+(P_average[2])+W_y[2]·(P_average[3])-W_y[3]Formula (22)

The measurement point on the second measurement plane includes: sixth measurement point P₁₁And a seventh measurement point P₁₂And an eighth measurement point P₁₃And a ninth measurement point P₁₄The tenth measurement point P₁₅Said sixth measurement point P₁₁And the seventh measurement point P₁₂And the eighth measurement point P₁₃And the ninth measurement point P₁₄And the tenth measurement point P₁₅Average value of (2)

The sixth measurement point P₁₁And the average value P_average2Difference value P between₁＝<P₁₁[1]-P_average2[1]|P₁₁[2]-P_average2[2]|P₁₁[3]-P_average2[3]>Formula (24)

The seventh measurement point P₁₂And the average value P_average2Difference value P between₂＝<P₁₂[1]-P_average2[1]|P₁₂[2]-P_average2[2]|P₁₂[3]-P_average2[3]>Equation (25)

The eighth measurement point P₁₃And the average value P_average2Difference value P between₃＝<P₁₃[1]-P_average2[1]|P₁₃[2]-P_average2[2]|P₁₃[3]-P_average2[3]>Formula (26)

The ninth measurement point P₁₄And the average value P_average2Difference value P between₄＝<P₁₄[1]-P_average2[1]|P₁₄[2]-P_average2[2]|P₁₄[3]-P_average2[3]>Formula (27)

The tenth measurement point P₁₅And the average value P_average2Difference value P between₅＝<P₁₅[1]-P_average2[1]|P₁₅[2]-P_average2[2]|P₁₅[3]-P_average2[3]>Formula (28)

Matrix C_x＝<<P₁[1]|P₁[1]|-1>，<P₂[1]|P₂[1]|-1>，<P₃[1]|P₃[1]|-1><P₄[1]|P₄[1]|-1>，<P₅[1]|P₅[1]|-1>>Formula (29)

Matrix E_x＝<-P₁[2]，-P₂[2]，-P₃[2]，-P₄[2]，-P₅[2]>Formula (30)

Matrix A_x＝C_x ^TFormula (31)

Matrix B_x＝A_x·E_xFormula (32)

Matrix B_x＝<<-(P₁[1]·P₁[2]+P₂[1]·P₂[2]+P₃[1]·P₃[12]+P₄[1]·P₄[2]+P₅[1]·P₅[2])>，<-(P₁[2]·P₁[3]+P₂[2]·P₂[3]+P₃[2]·P₃[3]+P₄[2]·P₄[3]+P₅[2]·P₅[3])>，<P₁[2]+P₂[2]+P₃[2]+P₄[2]+P₅[2]>>Formula (33)

Matrix F_x＝A_x·C_xFormula (34)

F_x＝<<(P₁[1]·P₁[1]+P₂[1]·P₂[1]+P₃[1]·P₃[1]+P₄[1]·P₄[1]+P₅[1]·P₅[1])|(P₁[1]·P₁[3]+P₂[1]·P₂[3]+P₃[1]·P₃[3]+P₄[1]·P₄[3]+P₅[1]·P₅[3])|P₁[1]+P₂[1]+P₃[1]+P₄[1]+P₅[1]>，<(P₁[3]·P₁[1]+P₂[3]·P₂[1]+P₃[3]·P₃[1]+P₄[3]·P₄[1]+P₅[3]·P₅[1])|(P₁[3]·P₁[3]+P₂[3]·P₂[3]+P₃[3]·P₃[3]+P₄[3]·P₄[3]+P₅[3]·P₅[3])|-(P₁[3]+P₂[3]+P₃[3]+P₄[4]+P₅[5])>，<-(P₁[3]+P₂[3]+P₃[3]+P₄[4]+P₅[5])|-(P₁[3]+P₂[3]+P₃[3]+P₄[3]+P₅[3])|(1+1+1+1+1)>>Formula (35)

F_x·X＝B_xFormula (36)

Solving function L of X in the formula (36)_x＝F_x[1][1]·(F_x[2][2]·F_x[3][3]+F_x[2][3]·F_x[3][2])+F_x[1][2]·(F_x[2][3]·F_x[3][1]-F_x[2][1]·F_x[3][3])+F_x[1][3]·(F_x[2][1]·F_x[3][2]-F_x[2][2]·F_x[3][1]) Formula (37)

Let B_x[1]·(F_x[2][2]·F_x[3][3]+F_x[2][3]·F_x[3][2])+F_x[1][2]·(F_x[2][3]·B[3]-B_x[2]·F_x[3][3])+F_x[1][3]·(B_x[2]·F_x[3][2]-F_x[2][2]·F_x[2][2]·B_x[3])＝h_x[1]Formula (38)

Let F_x[1][1]·(B_x[2]·F_x[3][3]+F_x[2][3]·B_x[3])+B_x[1]·(F_x[2][3]·F_x[3][1]-F_x[2][1]·F[3][3])+F_x[1][3]·(F_x[2][1]·B_x[3]-B[2]·F_x[3][1])＝h_x[2]Formula (39)

Let F_x[1][1]·(B_x[2]·F_x[3][3]+F_x[2][3]·B_x[3])+F_x[1][1]·(B_x[2]·F_x[3][1]-F_x[2][1]·B_x[3])+B_x[1]·(F_x[2][1]·F_x[3][2]-F_x[2][2]·F_x[3][1])＝h_x[3]Formula (40)

The expression of the second measurement surface is as follows: a. the₂x+B₂y+C₃z＝d_xFormula (41)

Coefficient of performance

Coefficient of performance

Coefficient of performance

Constant d_x＝W_x[1]·(P_average2[2])+(P_average2[1])+W_x[2]·(P_average2[3])-W_x[3]Formula (45)

The measurement point on the third measurement plane includes: eleventh measurement point P₂₁[1]And a twelfth measurement point P₂₂[1]Thirteenth measurement Point P₂₃[1]Fourteenth measurement point P₂₄[1]And a fifteenth measurement point P₂₅[1]Said eleventh measurement point P₂₁[1]And the twelfth measurement point P₂₂[1]And the thirteenth measurement point P₂₃[1]The fourteenth measurement point P₂₄[1]And the fifteenth measurement point P₂₅[1]Average value of (2)

The eleventh measurement point P₂₁[1]And the average value P_average3Difference value P between₆＝<P₂₁[1]-P_average3[1]|P₂₁[2]-P_average3[2]|P₂₁[3]-P_average3[3]>Formula (47)

The twelfth measurement point P₂₂[1]And the average value P_average3Difference value P between₇＝<P₂₂[1]-P_average3[1]|P₂₂[2]-P_average3[2]|P₂₂[3]-P_average3[3]>Formula (48)

The thirteenth measurement point P₂₃[1]And the average value P_average3Difference value P between₈＝<P₂₃[1]-P_average3[1]|P₂₃[2]-P_average3[2]|P₂₃[3]-P_average3[3]>Formula (49)

The fourteenth measurement point P₂₄[1]And the average value P_average3Difference value P between₉＝<P₂₄[1]-P_average3[1]|P₂₄[2]-P_average3[2]|P₂₄[3]-P_average3[3]>Formula (50)

The fifteenth measurement point P₂₅[1]And the average value P_average3Difference value P between₁₀＝<P₂₅[1]-P_average3[1]|P₂₅[2]-P_average3[2]|P₂₅[3]-P_average3[3]>Formula (51)

Matrix C_z＝<<P₆[1]|P₆[1]|-1>，<P₇[1]|P₇[1]|-1>，<P₈[1]|P₈[1]|-1><P₉[1]|P₉[1]|-1>，<P₁₀[1]|P₁₀[1]|-1>>Formula (52)

Matrix E_z＝<-P₆[2]，-P₇[2]，-P₈[2]，-P₉[2]，-P₁₀[2]> (53)

Matrix A_z＝C_z ^TFormula (54)

Matrix B_z＝A_z·E_zFormula (55)

Matrix B_z＝<<-(P₆[1]·P₆[2]+P₇[1]·P₇[2]+P₈[1]·P₈[12]+P₉[1]·P₉[2]+P₁₀[1]·P₁₀[2])>，<-(P₆[2]·P₆[3]+P₇[2]·P₇[3]+P₈[2]·P₈[3]+P₉[2]·P₉[3]+P₁₀[2]·P₁₀[3])>，<P₆[2]+P₇[2]+P₈[2]+P₉[2]+P₁₀[2]>>Formula (56)

Matrix F_z＝A_z·C_zFormula (57)

Matrix F_z＝<<(P₆[1]·P₆[1]+P₇[1]·P₇[1]+P₈[1]·P₈[1]+P₉[1]·P₉[1]+P₁₀[1]·P₁₀[1])|(P₆[1]·P₆[3]+P₇[1]·P₇[3]+P₈[1]·P₈[3]+P₉[1]·P₉[3]+P₁₀[1]·P₁₀[3])|P₆[1]+P₇[1]+P₈[1]+P₉[1]+P₁₀[1]>，<(P₆[3]·P₆[1]+P₇[3]·P₇[1]+P₈[3]·P₈[1]+P₉[3]·P₉[1]+P₁₀[3]·P₁₀[1])|(P₆[3]·P₆[3]+P₇[3]·P₇[3]+P₈[3]·P₈[3]+P₉[3]·P₉[3]+P₁₀[3]·P₁₀[3])|-(P₆[3]+P₇[3]+P₈[3]+P₉[4]+P₁₀[5])>，<-(P₆[3]+P₇[3]+P₈[3]+P₉[4]+P₁₀[5])|-(P₆[3]+P₇[3]+P₈[3]+P₉[3]+P₁₀[3])|(1+1+1+1+1)>>Formula (58)

F_z·X＝B_zFormula (59)

Solving function L of X in the formula (59)_z＝F_z[1][1]·(F_z[2][2]·F_z[3][3]+F_z[2][3]·F_z[3][2])+F_z[1][2]·(F_z[2][3]·F_z[3][1]-F_z[2][1]·F_z[3][3])+F_z[1][3]·(F_z[2][1]·F_z[3][2]-F_z[2][2]·F_z[3][1]) Formula (60)

Let B_z[1]·(F_z[2][2]·F_z[3][3]+F_z[2][3]·F_z[3][2])+F_z[1][2]·(F_z[2][3]·B_z[3]-B_z[2]·F_z[3][3])+F_z[1][3]·(B_z[2]·F_z[3][2]-F_z[2][2]·F_z[2][2]·B_z[3])＝h_z[1]Formula (61)

Let F_z[1][1]·(B_z[2]·F_z[3][3]+F_z[2][3]·B_z[3])+B_z[1]·(F_z[2][3]·F_z[3][1]-F_z[2][1]·F_z[3][3])+F_z[1][3]·(F_z[2][1]·B_z[3]-B_z[2]·F_z[3][1])＝h_z[2]Formula (62)

Let F_z[1][1]·(B_z[2]·F_z[3][3]+F_z[2][3]·B_z[3])+F_z[1][1]·(B_z[2]·F_z[3][1]-F_z[2][1]·B_z[3])+B_z[1]·(F_z[2][1]·F_z[3][2]-F_z[2][2]·F_z[3][1])＝h_z[3]Formula (63)

The expression of the third measurement surface is as follows: a. the₃x+B₃y+C₃z＝d_zFormula (64)

Coefficient of performance

Coefficient of performance

Tying ticket

Constant d_z＝W_z[1]·(P_average3[1])+W_z[2]·(P_average3[2])+(P_average3[3])-W_z[3]Formula (68)

An intersection point of the first measuring surface, the second measuring surface and the third measuring surface

H：＝<<d_x>，<d_y>，<d_z>>Equation (69).

The actual verification is as follows, the difference of the first measuring surface 3 is first verified, and the results are as follows:

W_y[1]·x+y+W_y[2]·z-d_y＝0

W_y[1]·P₃₁[1]+P₃₁[2]+W_y[2]·P₃₁[3]-d_y＝0.0577568133091404

W_y[1]·P₃₂[1]+P₃₂[2]+W_y[2]·P₃₂[3]-d_y＝-0.0687316767096604

W_y[1]·P₃₃[1]+P₃₃[2]+W_y[2]·P₃₃[3]-d_y＝0.225713130039082

W_y[1]·P₃₄[1]+P₃₄[2]+W_y[2]·P₃₄[3]-d_y＝-0.0690957233220786

W_y[1]·P₃₅[1]+P₃₅[2]+W_y[2]·P₃₅[3]-d_y＝0.057498705137255

next, the difference of the second measuring surface 2 is verified, with the following results:

x+W_x[1]·y+W_x[2]·z-d_x＝0

P₁₁[1]+W_x[1]·P₁₁[2]+W_x[2]·P₁₁[3]-d_x＝0.116537297318473

P₁₂[1]+W_x[1]·P₁₂[2]+W_x[2]·P₁₂[3]-d_x＝0.155312333241000

P₁₃[1]+W_x[1]·P₁₃[2]+W_x[2]·P₁₃[3]-d_x＝-0.462872419254609

P₁₄[1]+W₁[1]·P₁₄[2]+W_x[2]·P₁₄[3]-d_x＝0.147472809564761

P₁₅[1]+W_x[1]·P₁₅[2]+W_x[2]·P₁₅[3]-d_x＝0.0435518592230437

finally, the difference of the third measuring plane 4 is verified, with the following results:

W_z[1]·x+W_z[2]·y+z-d_z＝0

W_z[1]·P₂₁[1]+P₂₁[2]·W_z[2]+P₂₁[3]-d_z＝-0.252114583240200

W_z[1]·P₂₂[1]+P₂₂[2]·W_z[2]+P₂₂[3]-d_z＝-0.0267218586602667

W_z[1]·P₂₃[1]+P₂₃[2]·W_z[2]+P₂₃[3]-d_z＝0.0567166752875892

W_z[1]·P₂₄[1]+P₂₄[2]·W_z[2]+P₂₄[3]-d_z＝-0.0297226693094217

W_z[1]·P₂₅[1]+P₂₅[2]·W_z[2]+P₂₅[3]-d_z＝0.251842419044124

from the above description, it can be seen that the above-described embodiments of the present invention achieve the following technical effects: the industrial robot is used for carrying out multi-surface detection by adopting a distance detection sensor, the position relation of different surfaces of the frog in a robot world coordinate system is detected, and a special algorithm is adopted for calculation so as to finally determine the spatial position of the frog. The robot can accurately measure the spatial position of the frog after feeding, so that the robot program can be compensated according to the spatial position, and the frog can be accurately polished. Compared with the prior art, the frog measuring device has the advantages that the frog measuring speed is higher, the frog measuring operation is simpler, the working efficiency is improved, and the working strength is reduced.

The above is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made to the present invention by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.