Guide wheel for push rod type pipeline endoscope
By designing guide wheels with a parallel double-wheel structure, the problem of endoscopes getting stuck in small-diameter pipes was solved, achieving stability and adaptability, reducing costs, and improving safety.
Patent Information
- Application Number
- CN202423034437.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Utility models(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-10
- Publication Date
- 2025-11-04
- Estimated Expiration
- 2034-12-10
AI Technical Summary
The existing guide wheel design makes the endoscope unsuitable for use in small-diameter pipes and it is prone to getting stuck in protrusions or depressions, increasing the cost and risk of use.
The guide wheel adopts a parallel double wheel structure. The side of the guide wheel closer to the endoscope body is composed of a flat surface, and the side farther away from the body is composed of a rounded surface. The guide wheel has a shaft hole and a limiting groove in the middle. The bracket is equipped with a sliding shaft and a fixing screw. The guide wheel can rotate freely. The fixing screw and the limiting groove are in clearance fit to ensure that the guide wheel can resume stable operation under abnormal conditions.
This technology has improved the stability and adaptability of endoscopes in small-diameter pipes, reduced pipe opening size, lowered manufacturing and construction costs, prevented jamming, and improved safety.
Smart Images

Figure CN223513395U_ABST
Abstract
Description
Technical Field
[0001] This utility model relates to the field of pipe endoscopes, and more particularly to a guide wheel for a push rod type pipe endoscope. Background Technology
[0002] The push-rod pipe endoscope is an advanced non-destructive testing device for pipelines, capable of acquiring real-time images of the pipeline interior for accurate assessment of its internal condition. This technology is widely used for pipeline safety inspections in fields such as petroleum, chemical, and urban drainage. The push-rod pipe endoscope consists of three parts: an integrated main controller, a flexible push-rod cable reel, and an endoscope body with a camera. The flexible push-rod cable pushes the camera located at its front end into the pipeline to preview and record images of the internal pipe structure, thus achieving the purpose of inspection.
[0003] In actual pipelines, the working environment of endoscopes is complex. During direct insertion, the camera section may encounter various obstacles, such as protrusions, depressions, or blockages within the pipe. If the external structure of the endoscope is poorly designed, it may get stuck at these obstacles, affecting the movement and use of the endoscope. To solve these problems, many endoscope manufacturers use guide wheels as auxiliary moving parts of the endoscope, making guide wheels an important component. Their main function is to guide the endoscope forward within the pipe, preventing the camera from colliding with or getting stuck against the pipe wall. They also help the endoscope navigate bends in curved pipes.
[0004] However, existing guide wheel technology has some drawbacks, which affect the efficiency and safety of endoscope use. Firstly, current guide wheel designs employ a caster-like structure, evenly distributed along the circumference of the endoscope body, with the number ranging from three to eight sets. This circumferential array guide wheel structure ensures that when the endoscope rotates around its own axis, the guide wheels will first contact the tube wall, effectively preventing the endoscope from directly touching the tube wall. However, this circumferential array of guide wheels increases the overall size of the endoscope. On the one hand, it cannot adapt to small-diameter tubes; on the other hand, the opening for inserting the endoscope into the tube is correspondingly larger, indirectly increasing the cost of use.
[0005] To address the aforementioned issues, smaller circular array guide wheels have emerged on the market. However, in practical applications, it has been found that these smaller guide wheels still experience jamming when larger protrusions or depressions appear inside the pipe. This is especially problematic in environments with high siltation, such as drainage pipes, where the smaller guide wheels not only fail to provide guidance but also become a source of resistance. Therefore, it is necessary to design a new type of guide wheel component that meets the requirements of small size while avoiding the jamming problem. Utility Model Content
[0006] This invention provides a guide wheel for a push-rod type tubular endoscope. This invention prevents the push-rod type tubular endoscope from jamming while also meeting the small size requirement of the endoscope body. See the description below for details:
[0007] A guide wheel for a push rod type tubular endoscope, the guide wheel comprising: a guide wheel, the guide wheel being mounted on a bracket by a fixing nut to form a set of guide wheels, two sets of guide wheels being symmetrically fixed on both sides of the endoscope, and the body of the endoscope being fixed on the two sets of brackets.
[0008] The guide wheel has a flat surface on the side near the endoscope body and an arc surface on the side away from the endoscope body. The guide wheel has a shaft hole and a limiting groove for installing fixing screws in the middle. The limiting groove is concentric with the shaft hole. The flat surface and the arc surface are smoothly transitioned, and the transition surfaces meet to form the outer circle of the guide wheel.
[0009] The arc surface includes: a first arc surface, which is rotationally symmetrical about the center line of the guide wheel, and a cross-section on the guide wheel passing through the center line intersects with the arc surface to form a regular arc or smooth curve; the bracket is provided with a sliding shaft, which is clearance-fitted with the shaft hole on the guide wheel, and the guide wheel rotates freely around the sliding shaft;
[0010] The sliding shaft has a threaded hole at its end for installing a fixing screw, and the bracket also has a semi-circular bracket concave surface with the same outer diameter as the endoscope body, with fixing holes at both ends of the bracket concave surface.
[0011] The fixing screw is cylindrical in shape, with an outer diameter that is the same as the outer diameter of the limiting groove, and is clearance-fitted with the limiting groove. One end of the fixing screw is provided with a fastening screw for connecting to a threaded hole, and the other end is provided with a top arc surface, with a cross groove in the middle of the top arc surface for tightening the fixing screw. The edge of the top arc surface is tangent to the edge of the arc surface.
[0012] The beneficial effects of the technical solution provided by this utility model are:
[0013] 1. By adopting a parallel double wheel design, this guide wheel not only overcomes the problems of traditional circular array guide wheels, but also ensures the stability, guidance, and adaptability of the endoscope during its advancement within the tube.
[0014] 2. Under the premise that the overall outer dimensions of the endoscope do not exceed a certain given diameter, this solution presents the option with the largest guide wheel outer diameter;
[0015] 3. By adopting the guide wheel structure in this solution, the overall peripheral size of the endoscope is small, which not only makes it suitable for small-diameter pipes, but also allows for very small pipe wall openings, enabling the use of smaller delivery devices and saving manufacturing and construction costs.
[0016] 4. The guide wheels adopt guide wheels with different cross-sectional curves. By designing the curvature center position of the cross-sectional curves, the endoscope can always return to a stable operating state no matter how it is tilted, making it possible to replace the traditional circumferential array guide wheel scheme with a guide wheel scheme of parallel double wheels. Attached Figure Description
[0017] Figure 1 This is a schematic diagram of the working condition of the side-by-side guide wheels;
[0018] Figure 2 This is a set of external and sectional views of the guide wheel;
[0019] Figure 3 Rendering of guide wheels installed on an endoscope;
[0020] Figure 4 An exploded view of a set of guide wheels;
[0021] Figure 5 This is a diagram of the guide wheel structure.
[0022] Figure 6 A set of guide wheel sectional views;
[0023] Figure 7 A comparative diagram of guide wheel dimensions given the limitation on the outer dimensions of the endoscope;
[0024] Figure 8 This is a schematic diagram showing the location of the center of curvature of the guide wheel's arc surface;
[0025] Figure 9 shows the force analysis diagram of the guide wheel when it encounters an abnormal state;
[0026] Figure 10 This is a schematic diagram showing the range of the center of curvature when the cross-sectional curve of the circular arc surface is a smooth curve.
[0027] The attached diagram lists the components represented by each number as follows:
[0028] 1: Guide roller; 2: Bracket; 3: Fixing screw; 4: Endoscope; 5: Tube wall;
[0029] 10: Flat surface; 11: Arc surface; 12: Shaft hole; 13: Limiting groove; 14: Outer circle of guide wheel; 15: Groove of guide wheel;
[0030] 16: Center line;
[0031] 20: Sliding shaft; 21: Threaded hole; 22: Bracket concave surface; 23: Fixing hole; 24: Shaft shoulder;
[0032] 30: Fastening screw; 31: Top arc surface; 32: Cross groove;
[0033] 50: Contact point; 51: Dividing line;
[0034] 110: Upper arc surface; 111: Lower arc surface. Detailed Implementation
[0035] To make the objectives, technical solutions, and advantages of this utility model clearer, the embodiments of this utility model will be described in further detail below.
[0036] To achieve better stability, guidance, adaptability, safety, and control performance, push-rod type pipe endoscopes often use a circular array of guide wheels as the guiding structure for the endoscope body, rather than a parallel double-wheel structure. This results in a larger overall endoscope size, making it unsuitable for small-diameter pipes, and requiring a larger opening for inserting the endoscope into the pipe. This is especially problematic when inspecting pressurized pipes, necessitating a heavier insertion device, indirectly increasing operating costs. If a smaller size solution is adopted, each guide wheel would also be smaller. In practical applications, it has been found that these smaller guide wheels can get stuck in slightly larger protrusions or depressions within the pipe, particularly in environments with a lot of silt, such as drainage pipes. In these cases, the smaller guide wheels not only fail to provide guidance but also become a source of resistance. This invention avoids the circular array guide wheel solution, instead employing a parallel double-wheel design. This not only circumvents the problems associated with the circular array guide wheel but also ensures the stability, guidance, and adaptability of the endoscope during its insertion into the pipe.
[0037] Traditionally, it was believed that an endoscope would not always move along the bottom of the tube when moving inside; it would also move along slopes within the tube. In such cases, using parallel wheels as a guide on the endoscope could easily lead to a "tipping" phenomenon, thus compromising the proper functioning of the parallel wheels. For example, the parallel wheels (such as...) could not function properly on a slope. Figure 1 As shown in Figure (a), it is very likely to lose stability and flip 90 degrees (as shown in Figure (a)). Figure 1 As shown in Figure (b), the endoscope loses its guiding function. This situation can be improved by increasing the spacing between the side-by-side wheels, but this means increasing the overall size of the endoscope, which is not a desirable solution. In this invention, the above problem is circumvented by designing guide wheels with arc-shaped surfaces, while providing a guide wheel solution with the maximum diameter under the constraint that the outer dimensions of the endoscope must not exceed a certain value.
[0038] To achieve the above objectives, see [link to relevant documentation]. Figures 1 to 10 This utility model embodiment provides a guide wheel for a push-rod type tubular endoscope, including: a guide wheel 1, a bracket 2, and a fixing screw 3; the guide wheel 1 is mounted on the bracket 2 with a fixing nut 3, forming a set of guide wheels. In use, two sets of guide wheels are symmetrically fixed on both sides of the endoscope 4, and the main body of the endoscope 4 is fixed between the two sets of brackets 2, such as... Figure 2 ,3 As shown.
[0039] like Figure 4 , 5 As shown in Figure 6, the guide wheel 1 has a flat surface 10 on the side near the endoscope 4 body and an arc surface 11 on the side away from the endoscope 4 body. The guide wheel 1 has a shaft hole 12 and a limiting groove 13 for installing the fixing screw 3 in the middle. The limiting groove 13 is concentric with the shaft hole 12. The flat surface 10 and the arc surface 11 have a smooth transition, and the transition surfaces intersect to form the outer circle 14 of the guide wheel. The outer circle 14 refers to the circumferential contour corresponding to the point where the diameter of the guide wheel 1 reaches its maximum. The outer circle 14 is also the part that directly contacts the ground when the endoscope 4 is moving normally. The first arc surface 11 is rotationally symmetrical about the center line 16 of the guide wheel 1, and a cross-section on the guide wheel 1 passing through the center line 16 intersects with the arc surface 11 to form a regular arc or smooth curve. The bracket 2 has a sliding shaft 20, which can be clearance-fitted with the shaft hole 12 on the guide wheel 1, allowing the guide wheel 1 to rotate freely around the sliding shaft 20. The sliding shaft 20 has a threaded hole 21 at its end for installing the fixing screw 3. The bracket 2 also has a semi-circular bracket concave surface 22 with the same outer diameter as the endoscope 4 body. The bracket concave surface 22 has fixing holes 23 at both ends. In use, the endoscope 4 body is clamped between the two sets of bracket concave surfaces 22, and the two sets of brackets 2 are firmly fixed to the endoscope 4 through the fixing holes 23 (e.g., Figure 3 As shown in the figure, fixing hole 23 can be fixed with a standard bolt (the fixing bolt is not shown in the figure).
[0040] The fixing screw 3 is cylindrical in shape, with an outer diameter identical to that of the limiting groove 13, and is clearance-fitted into the limiting groove 13, allowing the fixing screw 3 to be inserted precisely into the limiting groove 13. One end of the fixing screw 3 has a fastening screw 30 for connection to the threaded hole 21, and the other end face has a top arc surface 31 with a cross-shaped groove 32 in the center for tightening the fixing screw 3. The edge of the top arc surface 31 is tangent to the edge of the arc surface 11, and its cross-sectional curve is an extension of the cross-sectional curve of the arc surface 11. Figure 4 , 6 As shown.
[0041] Furthermore, Figure 6A set of cross-sectional views of the guide wheels is given. Point Q is the center point of the concave surface 22 of the support. Because the radius of the concave surface 22 is the same as that of the endoscope 4, the centerline of the endoscope 4 will also pass through point Q. Furthermore, the center point of the concave surface 22 is located on the extension line of the centerline 16 of the guide wheel 1. The flat surface 10 on the guide wheel 1 is either tangential to or spaced from the concave surface 22 of the support, with a gap range of 0.1mm to 1mm. This setting ensures that the diameter of the outer circle 14 of the guide wheel is maximized. For example, when it is required that the overall outer dimension of the endoscope after adding the guide wheel cannot exceed a circle with a diameter of D, such as... Figure 7 As illustrated in the diagram, the outer diameter of the wheel closer to the endoscope is larger (assuming the wheel width is the same). In this embodiment, to maximize the guide wheel's size, the flat surface 10 is tangent to the concave surface 22 of the support, thereby achieving tangency with the outer circle of the endoscope (because the radius of the concave surface 22 of the support is the same as and coincides with the radius of the outer circle of the endoscope). Considering that the support 2 has a certain thickness, to ensure that the flat surface 10 is tangent to the concave surface 22 of the support, a guide wheel groove 15 is provided on the flat surface 10, and the shoulder 24 on the support 2 rests precisely at the bottom of the guide wheel groove 15.
[0042] Figure 6 In the cross-sectional view, the center line 16 of the guide wheel 1 divides the arc surface 11 into an upper arc surface 110 and a lower arc surface 111. The center B of the cross-sectional curve of the upper arc surface 110 (assuming in this embodiment that the cross-sectional curve is a regular arc curve) is located below the center line 16, and the center A of the cross-sectional curve of the lower arc surface 111 is located above the center line 16. Accordingly, as shown... Figure 8 As shown, another set of guide wheels is located on the right side of the endoscope 4, with its center line coinciding with the center line 16 of the first set of guide wheels (left side in the figure). Similarly, the arc surface 11 on the right guide wheel 1 is divided into an upper arc surface 110 and a lower arc surface 111 by the center line 16. The corresponding cross-sectional curve centers are located at point C below the center line 16 and point D above the center line 16, respectively.
[0043] To more clearly illustrate the working process of the guide wheel, Figure 8In the sectional view, draw orthogonal X-axis and Y-axis with center Q as the origin, such that the X and Y axes are exactly the left-right axis of symmetry and the up-down axis of symmetry of the endoscope 4 after the guide wheels are installed. At this time, point Q is not only the geometric center, but also the center of gravity of the endoscope 4. Furthermore, assume that the X and Y axes divide the plane into four quadrants, with the centers of different circular arc surfaces 11 located in one quadrant. Let the quadrant containing center A be the first quadrant, the quadrant containing center B be the second quadrant, the quadrant containing center C be the third quadrant, and the quadrant containing center D be the fourth quadrant. Correspondingly, the arc surface 11 located in the first quadrant is called the first quadrant arc surface, the arc surface 11 located in the second quadrant is called the second quadrant arc surface, the arc surface 11 located in the third quadrant is called the third quadrant arc surface, and the arc surface 11 located in the fourth quadrant is called the fourth quadrant arc surface. Furthermore, it can be seen that the center of the first quadrant arc surface is located in the second quadrant (that is, point B), the center of the second quadrant arc surface is located in the first quadrant (that is, point A), the center of the third quadrant arc surface is located in the fourth quadrant (that is, point D), and the center of the fourth quadrant arc surface is located in the third quadrant (that is, point C).
[0044] In practice, when using parallel double wheels as guide wheels, the normal operating state is when both sets of guide wheels are in contact with the pipe wall and rotate simultaneously. Other states are considered abnormal states. When the guide wheels are running in abnormal states, they are prone to accidents such as "overturning" or jamming. Therefore, the guide wheels are required to have the function of restoring from abnormal states to normal states.
[0045] The following analysis, in conjunction with Figure 9, explains the scenario of the guide wheel encountering an abnormal state in this embodiment. During the endoscope's forward movement, as shown in Figure 9(a), when it encounters a disturbance and tilts to the left, the third quadrant arc surface detaches from the tube wall 5. Only the first quadrant arc surface (arc surface 11 on the left guide wheel 1) contacts the tube wall 5. This contact point is called contact point 50. At this contact point 50, the tube wall 5 applies a force F to the first quadrant arc surface. This force F passes through the center point of the first quadrant arc surface, which is point B. Since point B is in the second quadrant, the extension of force F passes through the first, second, and fourth quadrants. The intersection point Q of the X and Y coordinate axes is located to the right of the extension of force F. Because the endoscope's center of gravity is also at point Q, the endoscope's center of gravity does not coincide with the extension of force F. The endoscope's gravity G generates a rightward rotational torque based on contact point 50. This torque counteracts the external disturbance causing the endoscope to rotate to the left, thus allowing the endoscope to return to a stable operating state. Similarly, when the endoscope encounters a disturbance during its forward movement and tilts to the right, as shown in Figure 9(b), the first quadrant arc surface detaches from the tube wall 5, and only the third quadrant arc surface (arc surface 11 on the right guide wheel 1) contacts the tube wall 5. Through the contact point 50, the tube wall 5 exerts a force F on the third quadrant arc surface. This force F passes through the center of the third quadrant arc surface, i.e., through point D. Since point D is in the fourth quadrant, the extension of force F passes through the third, fourth, and second quadrants. The coordinate axis intersection point Q is located to the left of the extension of force F. Because the endoscope's center of gravity is also at point Q, the endoscope's center of gravity does not coincide with the extension of force F. The endoscope's gravity G, based on the contact point 50, generates a leftward rotational torque. This torque counteracts the external disturbance causing the rightward rotation, thus allowing the endoscope to return to a stable forward movement. The situation where the second and fourth quadrant arc surfaces contact the tube wall 5 is similar to the above analysis and will not be repeated here. Another extreme case is, as shown in Figure 9(c), where the endoscope is rotated 90 degrees. In this case, the extensions of the force F and the gravity G coincide, similar to... Figure 1 The situation in Figure (b) and Figure 1 The difference in Figure (b) is that the end face of the fixing screw 3 on the guide wheel 1 is also an arc surface, so the actual contact area with the tube wall is very small. In addition, the endoscope center Q is located above the contact point 50. In this scenario, the endoscope is very unstable. It will tilt to the left or right with the slightest disturbance, and then return to a stable operating state.
[0046] In another embodiment of this invention, the arc surface 11 of the guide wheel 1 has a curved cross-section that coincides with point Q. In this case, regardless of which direction the endoscope tilts, the extensions of the force F and gravity G always coincide, allowing it to return to stable operation. This situation can be explained by a scenario similar to Figure 9(c). However, in pipes with a lot of silt, the contact area between the guide wheel and the pipe 5 increases, and the endoscope is more likely to remain in the situation shown in Figure 9(c) rather than tilting to one side. Especially when the center point of the arc surface 11 coincides with point Q, the endoscope may remain stable at any tilt angle, thus affecting its normal operation. Therefore, the case where the center point of the arc surface 11 coincides with point Q is suitable for relatively clean pipes, such as urban water supply pipes.
[0047] In another embodiment of this utility model, the cross-sectional curve of the arc surface 11 on the guide wheel 1 is a smooth curve. A smooth curve differs from an arc curve in that the radius of curvature at any point on it can be the same or different. For the arc surface 11 with a smooth cross-sectional curve, the center of curvature corresponding to any point is located above the straight line formed by connecting that point and the center point (Q point) of the concave surface 22 of the support. This line is called the dividing line 51, which divides the cutting plane into upper and lower parts, such as... Figure 10 As shown, assuming contact point 50 is located on the lower arc surface 111 below center line 16, the area above dividing line 51 refers to the area completely encompassing the upper arc surface 110. However, when contact point 50 is located on the upper arc surface 111 above center line 16, the area above dividing line 51 refers to the area completely encompassing the lower arc surface 111. In this embodiment, contact point 50 is located on the lower arc surface 11 (…). Figure 10As shown in the figure, both points B and R are located in the region above the dividing line 51, so they can both serve as the curvature center of the lower arc surface 111 cross-sectional curve. The difference is that point R is farther from the contact point 50 than point B. When the cross-sectional curve at contact point 50 uses point R as the curvature center, its radius of curvature is larger than when point B is the curvature center. This means that the farther the curvature center is from contact point 50, the straighter the curve at contact point 50 is. In the extreme case, point R and all other possible curvature centers are located at infinity. At this time, the radius of curvature of the cross-sectional curve at each contact point 50 on the arc surface 11 is infinitely large. This means that the cross-sectional curve of the arc surface 11 is no longer a curved curve but a straight line. Under this extreme condition, the arc surface 11 on the guide wheel 1 will become a conical surface (not shown in the figure). According to the previous analysis, even in the special case of the arc surface 11 being a conical surface, the guide wheel can still maintain stable operation (see Figure 9). In summary, the arc surface 11 of the guide wheel 1 in this invention has various cross-sectional curve shapes, including arcs, straight lines, or arbitrary curves. As long as the center of curvature at any point on the curve is always above the dividing line 51, or the cross-sectional curve is an arc and the center of curvature coincides with the center of the concave surface 22 of the support, even if the endoscope 4 body faces frequent and complex tilting situations, the guide wheel assembly composed of the guide wheel 1, with its ingenious mechanical design and structural characteristics, can quickly respond to and effectively counteract imbalance interference, ensuring the endoscope 4 returns to a stable operating state. Given this significant advantage, compared to traditional circumferential array guide wheels, the ingeniously designed parallel double-wheel guide wheel scheme of this invention stands out in terms of performance, stability, and adaptability, with undeniable advantages, sufficient to replace it and truly opening a new chapter in the innovative development of endoscope guide structures.
[0048] Unless otherwise specified, the model numbers of the various components in this embodiment of the invention are not limited, and any component that can perform the above functions is acceptable.
[0049] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of a preferred embodiment, and the sequence numbers of the above-mentioned embodiments are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.
[0050] The above description is only a preferred embodiment of the present utility model and is not intended to limit the present utility model. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present utility model should be included within the protection scope of the present utility model.
Claims
1. A guide wheel for a push-rod type tubular endoscope, characterized in that, The guide wheel includes: a guide wheel, The guide wheels are mounted on the bracket with fixing nuts to form a set of guide wheels. The two sets of guide wheels are symmetrically fixed on both sides of the endoscope, and the main body of the endoscope is fixed on the two sets of brackets. The guide wheel has a flat surface on the side near the endoscope body and an arc surface on the side away from the endoscope body. The guide wheel has a shaft hole and a limiting groove for installing fixing screws in the middle. The limiting groove is concentric with the shaft hole. The flat surface and the arc surface are smoothly transitioned, and the transition surfaces meet to form the outer circle of the guide wheel. The arc surface includes: a first arc surface, which is rotationally symmetrical about the center line of the guide wheel, and a cross-section on the guide wheel passing through the center line intersects with the arc surface to form a regular arc or smooth curve; the bracket is provided with a sliding shaft, which is clearance-fitted with the shaft hole on the guide wheel, and the guide wheel rotates freely around the sliding shaft.
2. The guide wheel for a push-rod type tubular endoscope according to claim 1, characterized in that, The sliding shaft has a threaded hole at its end for installing a fixing screw, and the bracket also has a semi-circular bracket concave surface with the same outer diameter as the endoscope body, with fixing holes at both ends of the bracket concave surface.
3. A guide wheel for a push-rod type tubular endoscope according to claim 1, characterized in that, The fixing screw is cylindrical in shape, with an outer diameter that is the same as the outer diameter of the limiting groove, and is clearance-fitted with the limiting groove. One end of the fixing screw is provided with a fastening screw for connecting to the threaded hole, and the other end face is provided with a top arc surface, with a cross groove in the middle of the top arc surface for tightening the fixing screw. The edge of the top arc surface is tangent to the edge of the arc surface.