CN113137903B - Angle Ruler and Angle Calculation Method - Google Patents

Abstract

The invention discloses an angle ruler and an angle calculation method. The angle ruler includes a first measuring arm and a second measuring arm, the first measuring arm is pivotally connected to the second measuring arm, and also includes: connection, set at the pivot joint between the first measuring arm and the second measuring arm, the speed increasing device can speed up the rotation of the first measuring arm and output; the first angle detection unit can detect the rotation of the first measuring arm relative to the second measuring arm and output the first signal; the second angle detection unit can detect the angle at which the output end of the speed increasing device rotates relative to the first measuring arm and output the second signal; the data processing unit is configured to compare the first signal and the second The signal is processed, and the final result of measuring the angle with the angle ruler is output. The angle ruler of the present invention is provided with a speed increasing device on the first measuring arm, and the final angle value is determined by measuring the rotation angle value of the speed increasing device and the rotation angle value of the first measuring arm, so that accurate angle measurement can be realized.

Description

Angle Ruler and Angle Calculation Method

technical field

The invention relates to the technical field of angle measurement, in particular to an angle ruler and an angle calculation method.

Background technique

The angle ruler is a tool for measuring angles. There are two measuring arms on the angle ruler, which are a fixed arm and a rotating arm. Fit the fixed arm to one side of the angle to be measured, and then rotate the rotating arm so that the rotating arm It is attached to the other side of the angle to be measured, and the sensor on the angle ruler detects the rotation angle of the rotating arm, and the angle value of the angle to be measured can be measured. The existing angle ruler only uses a group of sensors to detect the rotation angle of the rotating arm and measure the angle value, but the measurement result is not accurate enough and the measurement accuracy is not high.

Therefore, it is necessary to propose an angle ruler with accurate measurement results and high measurement precision.

Contents of the invention

The object of the present invention is to provide an angle ruler and an angle calculation method to solve the problems of inaccurate side measurement results and low measurement accuracy of the angle ruler in the prior art.

For reaching this purpose, the present invention adopts following technical scheme:

An angle ruler, comprising a first measuring arm and a second measuring arm, the first measuring arm is pivotally connected to the second measuring arm, and also includes:

The speed-up device is connected with the first measuring arm, and is arranged at the pivot joint between the first measuring arm and the second measuring arm, and the speed-up device can speed up the rotation of the first measuring arm to output;

The first angle detection unit is capable of detecting the rotation angle of the first measuring arm relative to the second measuring arm and outputting a first signal;

The second angle detection unit can detect the angle at which the output end of the speed increasing device rotates relative to the first measuring arm and output a second signal;

The data processing unit is electrically connected to the first angle detection unit and the second angle detection unit, and can process the first signal and the second signal, output and display the final result of the angle measured by the angle ruler.

In an optional embodiment of the present invention, the speed-up device is a gear speed-up device.

In an optional embodiment of the present invention, the speed-up device is a planetary gear speed-up device.

In an optional embodiment of the present invention, the speed increasing device includes:

The turntable is connected with the first measuring arm and can rotate with the first measuring arm, and the turntable is provided with an inner ring gear;

The planetary gear, which meshes with the ring gear, is connected to the turntable through a pin shaft;

The sun gear meshes with the planetary gear, and the sun gear is the output end of the speed increasing device.

In an optional embodiment of the present invention, the angle ruler further includes an upper shell and a lower shell pivotally connected with the upper shell;

The first measuring arm is arranged on the lower case, and the second measuring arm is arranged on the upper case, so that the first measuring arm and the second measuring arm are pivotally connected.

In an optional embodiment of the present invention, the lower case is provided with a first installation rib, and the first installation rib extends from the lower case to the upper case;

The first angle detection unit includes:

The first magnetic block is arranged on the top of the upper case;

The first angle sensing chip is arranged on the first mounting rib and opposite to the first magnetic block.

In an optional implementation manner of the present invention, the second angle detection unit includes:

The second magnetic block is arranged at the bottom of the lower case;

The second angle sensing chip is arranged at the bottom end of the sun gear and opposite to the second magnetic block.

In an optional embodiment of the present invention, the lower case is provided with a second installation rib, and the second installation rib extends from the lower case to the bottom of the turntable, and the turntable is connected to the second installation rib.

In an optional embodiment of the present invention, a third installation rib is provided on the upper case, and the third installation rib extends from the upper case to the top of the sun gear, and the top of the sun gear is pivotally connected to the third installation rib.

An angle calculation method for an angle ruler, the angle ruler comprising: a first measuring arm and a second measuring arm, the first measuring arm is pivotally connected to the second measuring arm;

The speed-up device is connected with the first measuring arm and is arranged at the pivot joint between the first measuring arm and the second measuring arm, and the speed-up device can speed up the rotation of the first measuring arm to output ;

a first angle detection unit capable of detecting the rotation angle of the first measuring arm relative to the second measuring arm;

The second angle detection unit can detect the angle at which the output end of the speed increasing device rotates relative to the first measuring arm;

The speed-up device includes:

A turntable, connected to the first measuring arm, capable of following the rotation of the first measuring arm, the turntable is provided with an inner ring gear;

a planetary gear meshing with the ring gear and connected to the turntable through a pin shaft;

a sun gear meshing with the planetary gear, and the sun gear is the output end of the speed increasing device;

The transmission ratio of the turntable and the sun gear is N1:N2;

The angle detected by the first angle detection unit is A1; the angle detected by the second angle detection unit is A2;

The angle calculation method includes:

R＝＝360°*(N1/N2), measuring ruler R is the minimum range of dividing 360° into (N2/N1);

M=[A1/R]*R, M is the intermediate value calculated by A1, and M is the integer multiple of R;

A0=M+A2*(N1/N2)+A', A0 is the middle angle value, A' is the correction value, and the angle ruler 100 is calibrated before the measurement, so that A'=0;

δ=A1-[A1/R]*R,

When δ is less than or equal to R/2 and A2 is greater than or equal to 180°, the precise angle measurement value A=A0-R;

When δ is greater than R/2 and A2 is less than 180°, the precise angle measurement value A=A0+R;

When (δ-R/2)*(A2-180°) is greater than 0, the precise angle measurement value A=A0.

Compared with prior art, the beneficial effect of the present invention is:

In the present invention, a speed-up device is arranged on the first measuring arm, and the speed-up device outputs the speed-up of the rotation of the first measuring arm, and measures the rotation angle after the speed-up, so as to realize the precise measurement of the angle, combined with the direct measurement of the first measuring arm The rotation of the angle is used for rough measurement of the angle. Finally, according to the measurement results of the rough measurement and the fine measurement, the final angle value of the angle measured by the angle ruler is calculated through an algorithm, so that the angle measurement result is more accurate.

Description of drawings

Fig. 1 is a schematic structural view of the angle ruler of the present invention in a closed state;

Fig. 2 is the structural representation that angle ruler of the present invention is in open state;

Fig. 3 is a schematic diagram of an exploded structure of an upper shell, a lower shell, and a speed-increasing device in the present invention;

Fig. 4 is the structural representation of speed-up device among the present invention;

Fig. 5 is a schematic cross-sectional structure diagram of the speed increasing device in the present invention.

In the picture:

100-angle ruler; 10-first measuring arm; 20-second measuring arm; 30-upper shell; 40-lower shell; 50-increasing device; 60-first angle detection unit; 70-second angle detection unit ;80-display screen;

31-the third installation rib; 41-the first installation rib; 42-the second installation rib; 51-turntable; 52-planetary gear; 53-sun gear; An angle sensing chip; 71—the second magnetic block; 72—the second angle sensing chip; 511—columnar connection.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, but not to limit the present invention. In addition, it should be noted that, for the convenience of description, only some structures related to the present invention are shown in the drawings but not all structures.

The present invention provides a kind of angle ruler, as shown in Figure 1 and Figure 2, angle ruler 100 comprises first measuring arm 10 and second measuring arm 20, and first measuring arm 10 is pivotally connected with second measuring arm 20, so that The first measuring arm 10 can be rotated so that the angle ruler 100 is opened for angle measurement. The first measuring arm 10 and the second measuring arm 20 may be the rotating arm and the fixed arm of the angle ruler 100 respectively. The first measuring arm 10 and the second measuring arm 20 may be pivotally connected directly, or may be pivotally connected through other pivoting members, which is not limited here. In some embodiments, the angle ruler 100 further includes an upper shell 30 and a lower shell 40 , and the first measuring arm 10 and the second measuring arm 20 are pivotally connected through the upper shell 30 and the lower shell 40 . Specifically, the lower case 40 is pivotally connected with the upper case 30 to form a pivot joint, the first measuring arm 10 is arranged on the lower case 40, and the second measuring arm 20 is arranged on the upper case 30, so that the first measuring arm 10 and the upper case The second measuring arm 20 is pivotally connected. When measuring, put the second measuring arm 20 close to one side of the angle to be measured, and move the first measuring arm 10 to the other side of the angle to be measured, and the first measuring arm 10 will drive the lower shell 40 to rotate around the pivot point to Complete the angle measurement.

As shown in FIG. 3 and FIG. 4 , the angle ruler 100 further includes a speed increasing device 50 , a first angle detection unit 60 , a second angle detection unit 70 and a data processing unit. The speed-up device 50 is arranged at the pivot joint between the first measuring arm 10 and the second measuring arm 20, so that the speed-up device 50 can be driven when the first measuring arm 10 rotates, and the speed-up device 50 can convert the first measuring arm 10 Accurate measurement of the angle is achieved by measuring the rotation angle output by the speed-up device 50 and the angle value detected by the first angle detection unit 60 for the rotation speed-up output. In some embodiments, the speed increasing device 50 is arranged on the lower case 40 so that the speed increasing device 50 is indirectly connected with the first measuring arm 10, so that when the first measuring arm 10 rotates, it drives the lower case 40 to rotate, thereby making the lower case 40 drives speed increasing device 50 to rotate.

Specifically, the first angle detection unit 60 can detect the angle at which the first measuring arm 10 rotates relative to the second measuring arm 20 and output the first signal, and the second angle detecting unit 70 can detect that the output end of the speed increasing device 50 is measured relative to the first measuring angle. the rotation angle of the arm 10, and output a second signal. The first angle detection unit 60 and the second angle detection unit 70 send the detection results to the data processing unit, the data processing unit is electrically connected with the first angle detection unit 60 and the second angle detection unit 70, and the data processing unit is configured to The first signal output by the first angle detection unit 60 and the second signal output by the second angle detection unit 70 are processed, and the final measurement result of the angle measured by the angle ruler is calculated by an algorithm, and displayed, so that the user can intuitively see the measured value angle value. In some embodiments, the first signal can reflect the rotation angle of the first measuring arm 10 relative to the second measuring arm 20 , and the second signal can reflect the rotation angle of the output end of the speed increasing device 50 relative to the first measuring arm 10 .

It can be understood that the data processing unit includes a processor (such as a single-chip microcomputer) and a display screen 80. In one embodiment, the data processing unit is arranged on the second measuring arm 20, as shown in FIG. 2, the display of the data processing unit The screen 80 is arranged on the upper surface of the second measuring arm 20, which is convenient for users to view the test results. In some other implementations, the data processing unit can also be arranged on the first measuring arm 10 , which is not limited here. The display screen 80 is preferably an LED display screen.

The present invention is provided with two sets of angle detection units, one set is used for the rotation angle of the first measuring arm 10 to realize the rough measurement of the angle, and the other set is used for detecting the rotation of the output end of the speed increasing device 50 relative to the first measuring arm 10 Angle, to realize the precise measurement of the angle, and finally through the algorithm, the detection results of the two sets of angle detection units are integrated, and the final detection result is output to make the angle measurement more accurate.

In one embodiment, the speed-up device 50 is a gear speed-up device. Specifically, the speed-up device 50 is a planetary gear speed-up device. Of course, the speed-up device 50 can also be other speed-up devices, which is not limited here.

As shown in FIG. 4 and FIG. 5 , the speed increasing device 50 includes a turntable 51 , a planetary gear 52 and a sun gear 53 . The turntable 51 is connected with the first measuring arm 10 and can rotate following the first measuring arm 10 . During specific implementation, the turntable 51 is connected to the lower case 40 and indirectly connected to the first measuring arm 10 , the rotation of the first measuring arm 10 drives the lower case 40 to rotate, and then the lower case 40 drives the turntable 51 to rotate. As shown in Figure 5, the ring gear 51 is provided with a ring gear, and there are several planetary gears 52, which are meshed with the ring gear rings on the dial 51. Follow the turntable 51 to rotate. The sun gear 53 meshes with the planetary gear 52, and the sun gear 53 is meshed in the middle of several planetary gears 52, and the sun gear 53 is driven to rotate by the planetary gear 52. It can be understood that the diameter of the sun gear 53 is small, and the torque is transmitted to the sun gear After 53, the rotational speed increases to realize speed-up, that is to say, the sun gear 53 is the output end of the speed-up device 50 .

In some embodiments, a first installation rib 41 is disposed on the lower case 40 , and the first installation rib 41 extends from the lower case 40 to the upper case 30 . The first angle detection unit 60 includes a first magnetic block 61 and a first angle sensing chip 62, the first magnetic block 61 is disposed on the top of the upper case 30, the first angle sensing chip 62 is disposed on the first mounting rib 41, and The first angle sensing chip 62 is disposed opposite to the first magnetic block 61 , so that the first angle sensing chip 62 detects the relative rotation angle between itself and the first magnetic block 61 . When the lower case 40 rotates under the driving of the first measuring arm 10, the first mounting rib 41 on the lower case 40 will drive the first angle sensing chip 62 to rotate, and the first magnetic block 61 is installed on the upper case 30, fixed Still, the second measuring arm 20 is also arranged on the upper shell 30 , so that the first angle sensing chip 62 can detect the rotation angle of the first measuring arm 10 relative to the second measuring arm 20 .

Specifically, the second angle detection unit 70 includes a second magnetic block 71 and a second angle sensing chip 72, the second magnetic block 71 is arranged at the bottom of the lower case 40, and the second angle sensing chip 72 is arranged at the bottom of the sun gear 53 , and the second angle sensing chip 72 is arranged opposite to the second magnetic block 71, so that the second angle sensing chip 72 detects the relative rotation angle between it and the second magnetic block 71, that is, detects the rotation of the sun gear 53 angle. The second magnetic block 71 is arranged at the bottom of the lower case 40, and the lower case 40 is connected with the first measuring arm 10, and will follow the first measuring arm 10 to rotate, then the second magnetic block 71 will also follow the first measuring arm 10 to rotate, and the second The second angle sensing chip 72 is arranged at the bottom of the sun gear 53 and will follow the rotation of the sun gear 53 , so the second angle sensing chip 72 can detect the rotation angle of the sun gear 53 relative to the first measuring arm 10 .

During specific detection, after the torque of the first measuring arm 10 is transmitted through the turntable 51 and the planetary gear 52, when it is transmitted to the sun gear 53, the rotation direction is reversed, that is to say, the rotation direction of the sun gear 53 is the same as that of the first measuring arm 10. The direction of rotation is opposite.

In some embodiments, the lower case 40 is provided with a second installation rib 42, the second installation rib 42 extends from the lower case 40 to the bottom of the turntable 51, the turntable 51 is connected with the second installation rib 42, and the second installation rib 42 Set on the lower case 40 again, like this, the turntable 51 is connected on the lower case 40 through the second mounting rib 42, the first measuring arm 10 is arranged on the lower case 40, when the first measuring arm 10 rotates, the torque passes through the lower case 40 and the second mounting rib 42 are transmitted to the turntable 51, which drives the turntable 51 to rotate, and then further drives the planetary gear 52 and the sun gear 53 to realize speed-up.

Specifically as shown in Figure 5, the bottom of the turntable 51 is provided with a columnar connecting portion 511 for connecting with the second mounting rib 42, and a through hole for the sun gear 53 to pass through is provided in the middle of the columnar connecting portion 511, so that the sun gear 53 passes through the turntable 51 from the through hole, and penetrates below the turntable 51, so that the second angle sensing chip 72 at the bottom of the sun gear 53 can be opposite to the second magnet block 71 to detect the rotation angle of the sun gear 53.

In one embodiment, in order to support the sun gear 53, the upper case 30 is provided with a third installation rib 31, and the third installation rib 31 extends from the upper case 30 to the top of the sun gear 53, and the top of the sun gear 53 is in contact with the top of the sun gear 53. The third mounting rib 31 is pivotally connected so that the sun gear 53 rotates on the third mounting rib 31 , and the third mounting rib 31 supports the sun gear 53 to improve the stability of the speed increasing device 50 .

In one embodiment, the first angle sensing chip 62 and the second angle sensing chip 72 are Hall sensors. As shown in FIG. 4 and FIG. 5 , both the first angle sensing chip 62 and the second angle sensing chip 72 are installed on the PCB circuit board.

The present invention also discloses an angle calculation method for an angle ruler. The angle ruler 100 includes: a first measuring arm 10 and a second measuring arm 20, and the first measuring arm 10 and the second measuring arm 20 are pivotally connected;

Also includes speed-up device 50, speed-up device 50 is connected with first measuring arm 10, is located at the pivot joint of first measuring arm 10 and second measuring arm 20, speed-up device 50 can increase the rotation of first measuring arm 10 speed output;

Also includes a first angle detection unit 60, the first angle detection unit 60 can detect the rotation angle of the first measuring arm 10 relative to the second measuring arm 20;

Also includes a second angle detection unit 70, the second angle detection unit 70 can detect the angle at which the output end of the speed increasing device 50 rotates relative to the first measuring arm 10;

Speed-up device 50 comprises:

A turntable 51, the turntable 51 is connected to the first measuring arm 10, and can follow the rotation of the first measuring arm 10, and the turntable 51 is provided with an inner gear ring;

The planetary gear 52, the planetary gear 52 meshes with the ring gear, and is connected to the turntable 51 through a pin shaft 54;

The sun gear 53, the sun gear 53 meshes with the planetary gear 52, the sun gear 53 is the output end of the speed increasing device 50, that is to say, what the second angle detection unit 70 detects is that the sun gear 53 rotates relative to the first measuring arm 10 angle.

The planetary deceleration structure composed of the ring gear, the planetary gear 52 and the sun gear 53 is already in the prior art, and will not be repeated here.

When the angle ruler 100 detects the angle, the detection algorithm is as follows:

Suppose the transmission ratio between the turntable 51 and the sun gear 53 is N1:N2, where N1 is the rotation speed of the turntable 51 and N2 is the rotation speed of the slave sun gear 53 . N1 to N2 can also be multi-stage transmission, and only the final transmission ratio is considered in the calculation;

Let the measurement data of the main measuring ruler (that is, the data measured by the first angle detection unit 60) be A1;

Let the measurement data of the auxiliary measuring ruler (that is, the data measured by the second angle detection unit 70) be A2;

Let the measuring ruler be R; the measuring ruler R is the minimum range that divides 360° into (N2/N1) on average, then R=360°*(N1/N2);

Let the intermediate value calculated by A1 be M, and M is an integer multiple of R, that is, M=[A1/R]*R, "[]" represents rounding, for example, [X] is the operation of taking the integer value of X, Example 1: [3.6]=3, another example 2: [2.1]=2;

Let the measurement result be A0, A0=M+A2*(N1/N2)+A',

A' is the correction value, and the angle ruler 100 is calibrated before the measurement, so that A'=0;

Due to the existence of measurement errors, a correction algorithm must be added, specifically:

δ=A1-[A1/R]*R,

1) When δ is less than or equal to R/2 and A2 is greater than or equal to 180°, the final result is A=A0-R,

2) When δ is greater than R/2 and A2 is less than 180°, the final result is A=A0+R,

3) When (δ-R/2)*(A2-180°) is greater than 0, the final result is A=A0;

A is the final displayed measurement result of the angle measured by the angle ruler 100 , which is a more accurate angle measurement value.

During specific implementation, other transmission ratios and other transmission methods can be used to transmit rotation. Gears are preferred for transmission, and other stable transmission methods can also be selected.

Concrete application examples of the algorithm described above:

Example 1:

A1=35°, A2=358°;

N2/N1=10, R=360°*(N1/N2)=36°, M=[35°/36°]*36°=0;

A0＝0+358*(1/10)＝35.8°, δ＝35°-(35°/36°)*36°＝35°;

Since (δ-R/2)*(A2-180) is greater than 0, A=A0=35.8°.

Example two:

A1=35°, A2=358°;

N2/N1=20, R=360°*(N1/N2)=18°, M=[35°/18°]*18°=18;

A0=18+358*(1/20)=35.9°, δ=35°-[35°/18°]*18°=17°;

Since (δ-R/2)*(A2-180) is greater than 0, A=A0=35.9°.

In this way, through the cooperation of the first angle detection unit 60 and the second angle detection unit 70, combined with the angle ruler measurement algorithm, the precise measurement of the angle can be realized.

Apparently, the above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, rather than limiting the implementation of the present invention. Various obvious changes, readjustments, and substitutions will occur to those skilled in the art without departing from the scope of the present invention. It is not necessary and impossible to exhaustively list all the implementation manners here. All modifications, equivalent replacements and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the claims of the present invention.

Claims (7)

1. An angle ruler, comprising a first measuring arm and a second measuring arm, the first measuring arm is pivotally connected with the second measuring arm, it is characterized in that it also includes: The speed-up device is connected with the first measuring arm and is arranged at the pivot joint between the first measuring arm and the second measuring arm, and the speed-up device can speed up the rotation of the first measuring arm to output ; a first angle detection unit, capable of detecting the rotation angle of the first measuring arm relative to the second measuring arm and outputting a first signal; The second angle detection unit is capable of detecting the rotation angle of the output end of the speed increasing device relative to the first measuring arm and outputting a second signal; A data processing unit, electrically connected to the first angle detection unit and the second angle detection unit, the data processing unit is configured to process the first signal and the second signal, and output the angle The final result of measuring the angle with the ruler and displaying it; The speed-up device is a planetary gear speed-up device; The speed-up device includes: A turntable, connected to the first measuring arm, capable of following the rotation of the first measuring arm, the turntable is provided with an inner ring gear; a planetary gear meshing with the ring gear and connected to the turntable through a pin shaft; The sun gear meshes with the planetary gear, and the sun gear is the output end of the speed increasing device. 2. The angle ruler according to claim 1, wherein the angle ruler further comprises an upper shell and a lower shell pivotally connected with the upper shell; The first measuring arm is arranged on the lower case, and the second measuring arm is arranged on the upper case, so that the first measuring arm is pivotally connected to the second measuring arm. 3. The angle ruler according to claim 2, characterized in that, the lower case is provided with a first installation rib, and the first installation rib extends from the lower case to the upper case; The first angle detection unit includes: The first magnetic block is arranged on the top of the upper case; The first angle sensing chip is arranged on the first mounting rib and opposite to the first magnetic block. 4. angle ruler according to claim 3, is characterized in that, described second angle detection unit comprises: The second magnetic block is arranged at the bottom of the lower case; The second angle sensing chip is arranged at the bottom end of the sun gear and opposite to the second magnetic block. 5. The angle ruler according to claim 2, characterized in that, the lower case is provided with a second installation rib, and the second installation rib extends from the lower case to the bottom of the turntable, and the turntable It is connected with the second installation rib. 6. The angle ruler according to claim 5, wherein a third installation rib is arranged on the upper case, and the third installation rib extends from the upper case to the top end of the sun gear, the The top of the sun gear is pivotally connected to the third installation rib. 7. An angle calculation method for an angle ruler, the angle ruler comprising: a first measuring arm and a second measuring arm, the first measuring arm is pivotally connected to the second measuring arm; The speed-up device is connected with the first measuring arm and is arranged at the pivot joint between the first measuring arm and the second measuring arm, and the speed-up device can speed up the rotation of the first measuring arm to output ; a first angle detection unit capable of detecting the rotation angle of the first measuring arm relative to the second measuring arm; The second angle detection unit can detect the angle at which the output end of the speed increasing device rotates relative to the first measuring arm; The speed-up device includes: A turntable, connected to the first measuring arm, capable of following the rotation of the first measuring arm, the turntable is provided with an inner ring gear; a planetary gear meshing with the ring gear and connected to the turntable through a pin shaft; a sun gear meshing with the planetary gear, and the sun gear is the output end of the speed increasing device; The transmission ratio of the turntable and the sun gear is N1:N2; The angle detected by the first angle detection unit is A1; the angle detected by the second angle detection unit is A2; The angle calculation method includes: Let the measuring ruler be R, R=360°*(N1/N2), and the measuring ruler R is the minimum range that divides 360° into (N2/N1) on average; M=[A1/R]*R, M is the intermediate value calculated by A1, and M is the integer multiple of R; A0=M+A2*(N1/N2)+A', A0 is the middle angle value, A' is the correction value, and the angle ruler (100) is calibrated before the measurement, so that A'=0; δ=A1-[A1/R]*R, When δ is less than or equal to R/2 and A2 is greater than or equal to 180°, the precise angle measurement value A=A0-R; When δ is greater than R/2 and A2 is less than 180°, the precise angle measurement value is A=A0+R; When (δ-R/2)*(A2-180°) is greater than 0, the precise angle measurement value A=A0.

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