Absolute grating ruler and length measuring device
By using a multi-segment spliced sub-scale structure and an absolute code track design, the high cost and installation difficulties of long grating rulers are solved, realizing a high-precision, low-cost length measuring device suitable for absolute grating rulers and length measuring devices.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Utility models(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-17
- Publication Date
- 2026-03-10
AI Technical Summary
Existing high-precision grating rulers have high processing costs when the length is >30cm, and there are also installation difficulties and measurement errors due to the mismatch of the thermal expansion coefficients of the materials.
By adopting a multi-segment spliced sub-scale structure, combining the first absolute code track of the secondary scale and the incremental code track of the sub-scale, the sub-scale position is located and the moving distance is measured by the code reader, reducing installation requirements and environmental dependence, and achieving high-precision measurement.
It achieves high-precision length measurement, reduces manufacturing costs and installation difficulty, is suitable for mass production, and reduces measurement errors.
Smart Images
Figure CN223985694U_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of optical measurement technology, in particular to an absolute grating ruler and a length measurement device. BACKGROUND
[0002] At present, the known grating rulers are all set in a whole piece, and the machining process of high-precision grating rulers generally uses photoetching, which is not suitable for grating rulers with a length of more than 30 cm and has a high cost. The cost of a one-meter grating ruler on the market is more than 300 yuan.
[0003] The long grating ruler also has a weakness in assembly, that is, the thermal expansion coefficient of the grating ruler does not match the thermal expansion coefficient of the mounting base, and the relative change in a long distance will produce a large stress. For example, the commonly used material of high-precision grating rulers is glass or stainless steel, and the mounting base is preferably made of aluminum alloy. The difference between the thermal expansion coefficients of the two can reach more than 10 ppm / K, and a temperature change of 10° will cause a length difference of 0.1 mm in a distance of 1 m. This puts a great test on the mounting process, and a careless mistake will cause the grating ruler to break or fall off. Even if it does not fall off, it will also produce unpredictable measurement errors. CONTENT OF THE INVENTION
[0004] The purpose of the embodiment of the present application is to provide an absolute grating ruler and a length measurement device, which has high measurement accuracy, is easy to install, has low cost and is convenient for batch production.
[0005] In one aspect of the embodiment of the present application, an absolute grating ruler is provided, which comprises a main ruler used in cooperation with a code reader, the code reader moves along the direction of measuring length of the main ruler, the main ruler comprises a plurality of sub-rulers arranged and spaced apart along the displacement direction of the code reader, and a sub-ruler arranged along the displacement direction of the code reader, at least one first absolute code channel is arranged on the sub-ruler for positioning the position of the corresponding sub-ruler of the code reader, and at least one incremental code channel is arranged on each sub-ruler for reflecting the moving distance of the code reader on the sub-ruler, and the code reader is used for reading the position of the corresponding sub-ruler and measuring the moving distance to obtain a length measurement result.
[0006] Optionally, at least one second absolute code channel is further arranged on the sub-ruler to position the position of the incremental code channel on the sub-ruler.
[0007] Optionally, the code reader has identification areas for identifying minimum continuous code track areas, and at least two of the identification areas are provided on the code reader for identifying code tracks, and the two identification areas are respectively located at two ends of the code reader along the displacement direction; the length of the sub-ruler along the displacement direction is greater than the sum of the center distance between the two identification areas and the width of the identification area along the displacement direction, so that the two identification areas of the code reader can simultaneously cover the same sub-ruler, and the code reader can calibrate the distance between the two identification areas on the absolute grating ruler.
[0008] Optionally, the center distance between the two identification areas of the code reader is greater than the sum of the interval distance between adjacent sub-rulers and the width of the identification area, so that when the code reader is located in the interval area between adjacent sub-rulers, the two identification areas can simultaneously cover the code tracks of adjacent sub-rulers, to ensure the continuity of the reading of the code reader in the interval area.
[0009] Optionally, the code bar fringes of the incremental code track are not perpendicular to the displacement direction of the code reader.
[0010] Optionally, the absolute code track includes pseudo-random coding.
[0011] Optionally, the absolute code track includes at least two code tracks arranged at equal intervals, and the total number of code bars of the two code tracks differs by 1.
[0012] Optionally, the length of the sub-ruler along the displacement direction is not less than the length of the main ruler minus the period of the sub-ruler.
[0013] In one aspect of the embodiments of the present application, a length measurement device is provided, which includes a controller, a base, a code reader, and the above-mentioned absolute grating ruler, the absolute grating ruler is fixed on the base, the code reader is arranged on the absolute grating ruler, the code reader feeds back the code track information of the absolute grating ruler to the controller, and the length measurement result is output by the controller.
[0014] The present application has the following beneficial effects:
[0015] The absolute grating ruler and the length measurement device provided by the embodiments of the present application can locate the position of the current code reader in the sub-ruler through the first absolute code track of the sub-ruler, that is, the first absolute code track of the sub-ruler can locate the serial number of the sub-ruler, and then the moving distance of the code reader on the sub-ruler is obtained through the incremental code track on the sub-ruler, the first absolute code track and the incremental code track are combined to obtain a high-precision measurement length, and a small measurement error is ensured. The sub-ruler spliced by multiple segments in the present application can compress the manufacturing cost, reduce the installation requirements and the requirements for the use environment, and facilitate mass production. BRIEF DESCRIPTION OF DRAWINGS
[0016] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments of this application will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.
[0017] Figure 1 This is one of the structural schematic diagrams of the absolute grating ruler provided in the embodiments of this application;
[0018] Figure 2 This is the second structural schematic diagram of the absolute grating ruler provided in the embodiments of this application.
[0019] Icons: 10-Sub-scale; 101-Incremental code track; 102-Second absolute code track; 11-Secondary scale; 110-First absolute code track; 20-Reader; 201-Identification area; L-Length; D-Width; T1-Interval distance; T2-Center distance; F1-Displacement direction; F2-Vertical direction. Detailed Implementation
[0020] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings.
[0021] In the description of this application, it should be noted that the terms "inner" and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product is in use. They are used only for the convenience of describing this application and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application. Furthermore, the terms "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.
[0022] It should also be noted that, unless otherwise explicitly specified and limited, the terms "setup" and "connection" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.
[0023] In current production, sub-grating rulers are manufactured using a process similar to photolithography, and from a management perspective, it is impossible to produce any number of sub-grating rulers. Absolute grating rulers, on the other hand, require the ability to arbitrarily locate their current position, so it is necessary to be able to determine in real time which segment of the sub-grating ruler the currently read value belongs to, but information from the sub-scale cannot meet this requirement.
[0024] Therefore, please refer to Figure 1 As shown, this application embodiment provides an absolute grating ruler, which includes: a main scale used in conjunction with a code reader 20, the code reader 20 moving along the direction of measuring length along the main scale, the main scale including a plurality of sub-scales 10 arranged and spaced apart along the displacement direction F1 of the code reader 20, and a secondary scale 11 arranged along the displacement direction F1 of the code reader 20, the secondary scale 11 having at least one first absolute code track 110 for locating the position of the sub-scale 10 corresponding to the code reader 20, each sub-scale 10 having at least one incremental code track 101 for reflecting the moving distance of the code reader 20 on the sub-scale 10, the code reader 20 for reading the position of the corresponding sub-scale 10 and the measured moving distance to obtain the length measurement result.
[0025] The main scale is typically mounted and fixed on the base. The barcode reader 20 can be driven by the user's device being measured, sliding along the direction of the measured length on the main scale (displacement direction F1). The vertical direction F2 is... Figure 1 The vertical direction is perpendicular to the displacement direction F1.
[0026] from Figure 1 As can be seen, a row of sub-scales 10 is arranged above the main scale, with multiple sub-scales 10 arranged sequentially according to their numbers, and adjacent sub-scales 10 are spaced apart. For example, the variety of sub-scales 10 is less than the number of sub-scales 10; several types of sub-scales 10 can form a cycle, and multiple sub-scales 10 can be mounted on the same base. In some embodiments, the sub-scales 10 and the base can be fixed with adhesive, with the position and amount of adhesive symmetrical to the center of the sub-scales 10 to avoid displacement of the sub-scales 10's center due to adhesive deformation.
[0027] A secondary scale 11 is set in the area below the main scale. The length of the secondary scale 11 is not less than the length of the main scale minus the period of the sub-scale 10. The period number of the sub-scale 10 can be determined by the first absolute code track 110 of the secondary scale 11.
[0028] Specifically, the subscale 11 has at least one first absolute code track 110, and each subscale 10 has at least one incremental code track 101. The code track is a designed engraving line or pattern, or magnetic field distribution, or dielectric constant distribution, or conductivity coefficient distribution. The smallest scale unit of the code track is a barcode.
[0029] When the code reader 20 slides, it can read the information of the first absolute code track 110 on the secondary scale 11 and the incremental code track 101 on the sub-scale 10. The code reader 20 feeds back the read code track information to the controller, which can calculate the measurement result of the length. The first absolute code track 110 of the secondary scale 11 can be used to locate which sub-scale 10 the code reader 20 is currently located on, that is, the first absolute code track 110 of the secondary scale 11 can locate the sequence number of the sub-scale 10. Then, through the incremental code track 101 on the sub-scale 10, the moving distance of the code reader 20 on that sub-scale 10 can be obtained. The combination of the first absolute code track 110 and the incremental code track 101 can obtain a high-precision measurement length and ensure a small measurement error. This application uses a multi-segment spliced interval sub-scale 10, which can reduce manufacturing costs, while reducing installation requirements and environmental requirements, and facilitating mass production.
[0030] Among them, the absolute code channel can be a pseudo-random code, for example Figure 1 On the sub-scale 11 shown, each code track has a different length and is used for random coding to achieve positioning of the sub-scale 10.
[0031] It could also be Figure 2 A code track consisting of at least two equally spaced tracks with a total number of code bars differing by 1 is called a vernier code.
[0032] For example Figure 2 In the middle, there are two rows of vernier codes on the sub-scale 11. Each row of vernier codes is evenly spaced and the left start end and right end end of the two rows of vernier codes are aligned respectively. There is a phase difference between the middle code tracks of adjacent rows of vernier codes. By coordinating the two rows of vernier codes and comparing the phase difference between the two rows of vernier codes, the specific position of the current sub-scale 10 can be roughly determined, that is, the sequence number of the sub-scale 10 can be determined, and the positioning of the sub-scale 10 can also be achieved.
[0033] Of course, more than two rows of vernier weights can be set on the sub-scale 11, such as three rows, depending on actual needs.
[0034] Based on this, in order to further improve the accuracy of the measurement, at least one second absolute code track 102 can be set on the sub-scale 10 to locate the position of the incremental code track 101 on the sub-scale 10, and then the incremental code track 101 can be used for further subdivision.
[0035] Figure 1In addition to the incremental code track 101, each sub-scale 10 also has a second absolute code track 102. As mentioned above, the function of the absolute code track is positioning. The first absolute code track 110 of the sub-scale 11 locates the specific position of the code reader 20 on which sub-scale 10. The second absolute code track 102 of the sub-scale 10 can further accurately locate the position area of the code reader 20 on which incremental code track 101 on that sub-scale 10, that is, locate the sequence number of the incremental code track 101. Finally, by using the incremental code track 101 of the sub-scale 10 to accurately determine the current position of the code reader 20, a more accurate length measurement result can be obtained.
[0036] When the reader 20 covers the main scale, it has an identification area 201 for identifying the smallest continuous code track area. The reader 20 is provided with at least two identification areas 201 for identifying code tracks. The two identification areas 201 are located at the two ends of the reader 20 along the displacement direction F1. The length L of the sub-scale 10 along the displacement direction F1 is greater than the sum of the center distance T2 of the identification areas 201 and the width D of the identification areas 201 along the displacement direction F1, so that the two identification areas 201 of the reader 20 can cover the same sub-scale 10 at the same time, which is used by the reader 20 to mark the distance between the two identification areas 201 on the absolute grating scale.
[0037] The smallest continuous code track area that the reader 20 can recognize is called a recognition area 201. A sub-scale 10 is simultaneously covered by two recognition areas 201. The thermal expansion and contraction of the reader 20 itself can be accurately determined based on the change in the reading difference between the two recognition areas 201. In other words, the change in the distance between the two recognition areas 201 on a sub-scale 10 can be used to calibrate the change in the distance between the two recognition areas 201 on the absolute grating ruler with temperature and stress.
[0038] At the same time, such as Figure 1 As shown, the center distance T2 between the two recognition areas 201 of the reader 20 is greater than the sum of the interval distance T1 between adjacent sub-scales 10 and the width D of the recognition area 201 along the displacement direction F1, so that when the reader 20 is located in the interval area between adjacent sub-scales 10, the two recognition areas 201 can simultaneously cover the code track (incremental code track 101 and second absolute code track 102) of the adjacent sub-scales 10, so as to ensure the continuity of readings when the reader 20 is in the interval area.
[0039] The two recognition areas 201 of the reader 20 can simultaneously cover the beginning and end segments of the code track of the adjacent sub-scale 10, measure the interval distance T1 between the adjacent sub-scale 10, and simultaneously complete the reading switching and distance splicing when the reader 20 passes the adjacent sub-scale 10, so that the read data is continuous and accurate.
[0040] In this way, when the center distance T2 between the two recognition areas 201 of the reader 20 is greater than the sum of the interval distance T1 between adjacent sub-scales 10 and the width D of the recognition area 201 along the displacement direction F1, at least one recognition area 201 can work when the reader 20 crosses the interval area between adjacent sub-scales 10. There will definitely be two recognition areas 201 recognizing the two adjacent sub-scales 10 respectively. Thus, the phase position between the two sub-scales 10 can be determined based on the distance between the recognition areas 201 obtained above, thereby completing the splicing of adjacent sub-scales 10. This allows the reader 20 to read code track information even when it is located in the interval area between adjacent sub-scales 10, and prevents the reader 20 from reading empty code. In this way, the reading of the reader 20 has continuity, ensuring the accuracy of the final length measurement result.
[0041] In the example of this application, the barcode stripes of the incremental code track 101 are not perpendicular to the displacement direction F1 of the reader 20. The angle between the barcode stripes of the incremental code track 101 and the displacement direction F1 is either all greater than 90° or all less than 90°.
[0042] In other words, since the incremental code track 101 is in the form of a diagonal grating, the reader 20 can compare the measurement differences between the two diagonal code tracks to determine the distance by which the displacement direction F1 of the reader 20 deviates from the axis of symmetry of the two incremental code tracks 101. This allows the positional offset error of the two recognition areas 201 on the reader 20 in the vertical direction F2 to be determined within a sub-scale 10, and further determines the installation error and rotation angle of each sub-scale 10 in the vertical direction F2 of the reader 20.
[0043] The above settings allow for in-depth analysis of installation errors, thermal expansion and contraction, stress and strain during use, and other factors, significantly improving the system's measurement accuracy. The analysis results can be provided to users as functional safety data and for manufacturing error analysis, thereby enhancing customer satisfaction.
[0044] On the other hand, based on the foregoing, this application also provides a length measuring device, including: a controller, a base, a barcode reader 20, and the aforementioned absolute grating ruler. The absolute grating ruler is fixed on the base, and the barcode reader 20 is disposed on the absolute grating ruler. The barcode reader 20 feeds back the code track information of the absolute grating ruler to the controller, and the controller outputs the length measurement result.
[0045] This length measuring device has the same structure and beneficial effects as the absolute grating ruler in the foregoing embodiments. The structure and beneficial effects of the absolute grating ruler have been described in detail in the foregoing embodiments and will not be repeated here.
[0046] The above description is merely an embodiment of this application and is not intended to limit the scope of protection of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.
Claims
1. An absolute grating ruler characterized by, The application relates to an absolute grating ruler and a reading device thereof. The sub-ruler is provided with at least one second absolute code channel for positioning the position of the incremental code channel on the sub-ruler.
2. The absolute encoder scale of claim 1, wherein, The reading device is provided with two identification areas for identifying the minimum continuous code channel area, and the two identification areas are located at the two ends of the reading device along the displacement direction.
3. The absolute encoder scale according to claim 1 or 2, characterized in that The length of the sub-ruler along the displacement direction is greater than the sum of the center distance of the two identification areas and the width of the identification area along the displacement direction, so that the two identification areas of the reading device can simultaneously cover the same sub-ruler, and the reading device can calibrate the distance between the two identification areas on the absolute grating ruler.
4. The absolute encoder of claim 3, wherein, The center distance between the two identification areas of the reading device is greater than the sum of the interval distance between the adjacent sub-rulers and the width of the identification area, so that when the reading device is located in the interval area between the adjacent sub-rulers, the two identification areas can simultaneously cover the code channels of the adjacent sub-rulers, and the continuity of the reading result of the reading device in the interval area is ensured.
5. The absolute encoder of claim 1 or 2, wherein, The code stripe of the incremental code channel is not perpendicular to the displacement direction of the reading device.
6. The absolute encoder of claim 1 or 2, wherein, The absolute code channel comprises pseudo-random code.
7. The absolute encoder of claim 1 or 2, wherein, The absolute code channel comprises at least two equally-spaced code channels with a total code stripe number difference of 1.
8. The absolute encoder of claim 1 or 2, wherein, The length of the sub-ruler along the displacement direction is not less than the length of the main ruler minus the period of the sub-ruler.
9. A length measuring device, characterized in that The application relates to an absolute grating ruler and a reading device thereof. The reading device is provided with two identification areas for identifying the minimum continuous code channel area, and the two identification areas are located at the two ends of the reading device along the displacement direction. The length of the sub-ruler along the displacement direction is greater than the sum of the center distance of the two identification areas and the width of the identification area along the displacement direction, so that the two identification areas of the reading device can simultaneously cover the same sub-ruler, and the reading device can calibrate the distance between the two identification areas on the absolute grating ruler. The center distance between the two identification areas of the reading device is greater than the sum of the interval distance between the adjacent sub-rulers and the width of the identification area, so that when the reading device is located in the interval area between the adjacent sub-rulers, the two identification areas can simultaneously cover the code channels of the adjacent sub-rulers, and the continuity of the reading result of the reading device in the interval area is ensured. The code stripe of the incremental code channel is not perpendicular to the displacement direction of the reading device. The absolute code channel comprises pseudo-random code. The absolute code channel comprises at least two equally-spaced code channels with a total code stripe number difference of 1. The length of the sub-ruler along the displacement direction is not less than the length of the main ruler minus the period of the sub-ruler. The application relates to an absolute grating ruler and a reading device thereof. The reading device is provided with two identification areas for identifying the minimum continuous code channel area, and the two identification areas are located at the two ends of the reading device along the displacement direction. The length of the sub-ruler along the displacement direction is greater than the sum of the center distance of the two identification areas and the width of the identification area along the displacement direction, so that the two identification areas of the reading device can simultaneously cover the same sub-ruler, and the reading device can calibrate the distance between the two identification areas on the absolute grating ruler. The center distance between the two identification areas of the reading device is greater than the sum of the interval distance between the adjacent sub-rulers and the width of the identification area, so that when the reading device is located in the interval area between the adjacent sub-rulers, the two identification areas can simultaneously cover the code channels of the adjacent sub-rulers, and the continuity of the reading result of the reading device in the interval area is ensured. The code stripe of the incremental code channel is not perpendicular to the displacement direction of the reading device. The absolute code channel comprises pseudo-random code. The absolute code channel comprises at least two equally-spaced code channels with a total code stripe number difference of 1. The length of the sub-ruler along the displacement direction is not less than the length of the main ruler minus the period of the sub-ruler. The application relates to an absolute grating ruler and a reading device thereof. The reading device is provided with two identification areas for identifying the minimum continuous code channel area, and the two identification areas are located at the two ends of the reading device along the displacement direction. The length of the sub-ruler along the displacement direction is greater than the sum of the center distance of the two identification areas and the width of the identification area along the displacement direction, so that the two identification areas of the reading device can simultaneously cover the same sub-ruler, and the reading device can calibrate the distance between the two identification areas on the absolute grating ruler. The center distance between the two identification areas of the reading device is greater than the sum of the interval distance between the adjacent sub-rulers and the width of the identification area, so that when the reading device is located in the interval area between the adjacent sub-rulers, the two identification areas can simultaneously cover the code channels of the adjacent sub-rulers, and the continuity of the reading result of the reading device in the interval area is ensured. The code stripe of the incremental code channel is not perpendicular to the displacement direction of the reading device. The absolute code channel comprises pseudo-random code. The absolute code channel comprises at least two equally-spaced code channels with a total code stripe number difference of 1. The length of the sub-ruler along the displacement direction is not less than the length of the main ruler minus the period of the sub-ruler. The application relates to an absolute grating ruler and a reading device thereof. The reading device is provided with two identification areas for identifying the minimum continuous code channel area, and the two identification areas are located at the two ends of the reading device along the displacement direction. The length of the sub-ruler along the displacement direction is greater than the sum of the center distance of the two identification areas and the width of the identification area along the displacement direction, so that the two identification areas of the reading device can simultaneously cover the same sub-ruler, and the reading device can calibrate the distance between the two identification areas on the absolute grating ruler. The center distance between the two identification areas of the reading device is greater than the sum of the interval distance between the adjacent sub-rulers and the width of the identification area, so that when the reading device is located in the interval area between the adjacent sub-rulers, the two identification areas can simultaneously cover the code channels of the adjacent sub-rulers, and the continuity of the reading result of the reading device in the interval area is ensured. The code stripe of the incremental code channel is not perpendicular to the displacement direction of the reading device. The absolute code channel comprises pseudo-random code. The absolute code channel comprises at least two equally-spaced code channels with a total code stripe number difference of 1. The length of the sub-ruler along the displacement direction is not less than the length of the main ruler minus the period of the sub-ruler. The application relates to an absolute grating ruler and a reading device thereof. The reading device is provided with two identification areas for identifying the minimum continuous code channel area, and the two identification areas are located at the two ends of the reading device along the displacement direction. The length of the sub-ruler along the displacement direction is greater than the sum of the center distance of the two identification areas and the width of the identification area along the displacement direction, so that the two identification areas of the reading device can simultaneously cover the same sub-ruler, and the reading device can calibrate the distance between the two identification areas on the absolute grating ruler. The center distance between the two identification areas of the reading device is greater than the sum of the interval distance between the adjacent sub-rulers and the width of the identification area, so that when the reading device is located in the interval area between the adjacent sub-rulers, the two identification areas can simultaneously cover the code channels of the adjacent sub-rulers, and the continuity of the reading result of the reading device in the interval area is ensured. The code stripe of the incremental code channel is not perpendicular to the displacement direction of the reading device. The absolute code channel comprises pseudo-random code. The absolute code channel comprises at least two equally-spaced code channels with a total code stripe number difference of 1. The length of the sub-ruler along the displacement direction is not less than the length of the main ruler minus the period of the sub-ruler. The application relates to an absolute grating ruler and a reading device thereof. The reading device is provided with two identification areas for identifying the minimum continuous code channel area, and the two identification areas are located at the two ends of the reading device along the displacement direction. The length of the sub-ruler along the displacement direction is greater than the sum of the center distance of the two identification areas and the width of the identification area along the displacement direction, so that the two identification areas of the reading device can simultaneously cover the same sub-ruler, and the reading device can calibrate the distance between the two identification areas on the absolute grating ruler. The center distance between the two identification areas of the reading device is greater than the sum of the interval distance between the adjacent sub-rulers and the width of the identification area, so that when the reading device is located in the interval area between the adjacent sub-rulers, the two identification areas can simultaneously cover the code channels of the adjacent sub-rulers, and the continuity of the reading