Miniature self-locking bearing retainer

Abstract

The miniature self-locking bearing retainer comprises an end ring body, a first window beam, a second window beam and a third window beam are evenly distributed on the end ring body, the first window beam and the second window beam are adjacently arranged and are of a mirror symmetry structure, and the first window beam and the second window beam jointly form a window beam unit. The third window beam is arranged between the adjacent window beam units; an arc-shaped window hole is formed between the first window beam and the second window beam, the upper side of the arc-shaped window hole is open, lug structures on the two sides of the arc-shaped window hole can axially limit the balls, the radial projection of the third window beam falls in the center of the arc-shaped window hole, and the third window beam and the adjacent first window beam and second window beam on the two sides form a cylindrical window hole with the upper side open. Compared with the prior art, the characteristic similar to the design of a single-side opening of an existing window hole is kept, the contact area between the window beam and the balls is reduced, the constraint degree on the balls is reduced, and therefore friction resistance borne by the balls in the moving process is effectively reduced.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of bearing retainer, in particular to a micro self-locking bearing retainer. BACKGROUND

[0002] The harmonic reducer mainly consists of wave generator, flexible bearing, flexspline and rigid wheel and other key components. Its core working principle lies in the ingenious use of flexible bearing and flexspline to produce controllable elastic deformation, and then form harmonic motion, so as to realize the speed change function of large transmission ratio. In this complex transmission process, as two flexible components, flexible bearing and flexspline play a crucial role, but at the same time, they are also the key components that are relatively fragile and prone to failure in the harmonic reducer. The structure of flexible bearing is significantly different from that of ordinary bearing. The inner and outer rings are designed very thin. This special structure is to adapt to the working requirements of the harmonic reducer.

[0003] In the operation mechanism of the harmonic reducer, when the wave generator is embedded in the inner ring of the flexible bearing, the flexible bearing will deform with it, showing a non-circular profile consistent with the wave generator, and then forming a long axis and a short axis. At present, in order to meet the elastic deformation requirement, most of the existing harmonic reducer retainers are made of nylon and other materials with certain elasticity. And in order to achieve better elastic deformation effect, the retainer usually adopts the design of single-sided opening of window hole. This design makes the window hole have no axial limiting effect on the ball. On the one hand, it reduces the contact area between the window beam and the ball, reduces the degree of constraint on the ball, and effectively reduces the friction resistance of the ball in the movement process; on the other hand, in the case of high-speed operation or frequent deformation of the flexible bearing, this low-friction design can significantly reduce energy loss and heat generation of the bearing, ensuring the stable operation of the bearing. However, in the running process of the flexible bearing, especially at the position of the long axis of the ellipse, the ball is likely to produce a large amplitude of axial movement due to the large deformation of the flexible bearing. If the balls at the positions near the two long axes all produce a large amplitude of axial movement, it will lead to instability of the retainer, making the retainer prone to shaking and deviation in the movement process, and then causing the change of its position, which not only affects the transmission accuracy of the harmonic reducer, but also may cause damage to the bearing and other related components. But if all the window holes of the retainer are designed to have axial constraint structure, although it can effectively limit the axial movement of the ball, it will greatly increase the contact area and friction resistance between the window beam and the ball, leading to increased energy loss and heat generation of the bearing, affecting the overall performance and service life of the flexible bearing. It is necessary to find a design scheme that can effectively limit the axial movement of the ball and control the friction resistance within a reasonable range. SUMMARY

[0004] The application provides a micro self-locking bearing retainer which can effectively limit the axial movement of the balls and control the frictional resistance within a reasonable range.

[0005] To achieve the above object, the application provides the following technical solutions.

[0006] The micro self-locking bearing retainer comprises an end ring body, and first window beams, second window beams and third window beams are uniformly distributed on the end ring body.

[0007] The first window beams and the second window beams are adjacently arranged and mirror-symmetrically structured, and together form a set of window beam units, and the third window beams are arranged between adjacent window beam units.

[0008] An arc-shaped window hole which is adapted to the balls and has an upper opening is formed between the first window beams and the second window beams, and ear structures which are curved towards the arc-shaped window hole are arranged on the upper sides of the first window beams and the second window beams, and the ear structures can axially limit the balls.

[0009] The third window beams and the first window beams and the second window beams on the two sides form columnar window holes which have upper openings, and the radial projection of the third window beams falls on the central position of the arc-shaped window hole.

[0010] The arc-shaped window hole formed between the first window beams and the second window beams has an upper opening, and the ear structures on the two sides can axially limit the balls, and when the balls have an axial movement tendency during the operation of the flexible bearing, especially at the position of the long axis of the ellipse, the ear structures can block the axial movement of the balls, effectively limit the axial movement amplitude of the balls, the radial projection of the third window beams falls on the central position of the arc-shaped window hole, so that when the long axis of the flexible bearing is deformed, the axial limitation always exists on one side near the long axis position, and the situation that the limitation on both sides is lost does not occur, the control ability of the retainer on the axial movement of the balls is enhanced, the problems of instability, shaking and deviation of the retainer due to the large axial movement of the balls on both sides are avoided, the transmission accuracy of the harmonic reducer is ensured, and the risk of damage to the bearing and other related components is reduced. The third window beams and the first window beams and the second window beams on the two sides form columnar window holes which have upper openings, and the columnar window holes have similar characteristics to the existing window hole single-side opening design, the contact area between the window beams and the balls is reduced, the degree of constraint on the balls is reduced, and thus the frictional resistance suffered by the balls during the movement is effectively reduced. Under the working conditions of high-speed operation or frequent deformation of the flexible bearing, the low-friction design can significantly reduce the energy loss and the heating of the bearing, and ensure the stable operation of the bearing.

[0011] In the preferred implementation mode, a mesa is arranged on the side of the ear structure away from the arc-shaped window hole, and the height of the mesa is lower than the height of the third window beam.

[0012] After the ear structure is provided with a table on the side away from the arc-shaped window hole and the height of the table is lower than the height of the third window beam, a structure with a high side and a low side is formed on the side of the cylindrical window hole. The low side further reduces the contact area between the rolling body and the retainer.

[0013] In the preferred implementation, the total height of the ear structure and the first window beam or the second window beam is equal to the height of the third window beam.

[0014] During rotation, the mass distribution of each part is relatively uniform. When the harmonic reducer is in operation, the retainer rotates at a high speed. The uniform mass distribution can ensure the stability of the rotation, reduce the difference in centrifugal force caused by uneven mass, and thus maintain a good dynamic balance state.

[0015] In the preferred implementation, the first window beam and the second window beam are provided with arc-shaped contact surfaces suitable for the rolling balls on the side facing the cylindrical window hole, and the third window beam is provided with arc-shaped contact surfaces suitable for the rolling balls on the sides facing the cylindrical window beams.

[0016] In the preferred implementation, the ear structure has an arc-shaped surface continuously transitioning with the arc-shaped window hole on the side facing the arc-shaped window hole, and a vertical surface is provided on the upper side of the arc-shaped surface. The distance between adjacent vertical surfaces is less than the diameter of the rolling ball.

[0017] In the preferred implementation, an inclined surface is provided on the upper side of the vertical surface. A gradually narrowing placement space is formed between adjacent inclined surfaces, and the distance between adjacent inclined surfaces is greater than the distance between adjacent vertical surfaces.

[0018] In the preferred implementation, the inner wall surface and the outer wall surface of each of the first window beam, the second window beam, and the third window beam are respectively provided with a sunken groove and a connecting groove connected with the sunken groove. The first window beam, the second window beam, and the third window beam are each separated into two deformation parts capable of independent deformation through the sunken groove and the connecting groove. When the retainer is deformed, one side of the deformation part is in contact with the rolling ball and deforms towards the sunken groove direction to reduce the contact stress of the rolling ball on the inner and outer rings of the bearing.

[0019] In the long axis point position, the beams on both sides of the pocket directly abut the rolling ball and push it radially towards the outer ring, resulting in a relatively large contact stress in this area. In the improved structure, when one side of the deformation part is in contact with the rolling ball and deforms towards the sunken groove direction, the movement of the deformation part towards the sunken groove no longer applies a radial pushing force to the rolling ball, thereby reducing the contact stress of the rolling ball on the unit area of the outer ring of the bearing. The same applies to the short axis point position.

[0020] In the preferred implementation, the sunken groove extends from one end of the window beam to the bottom, and the connecting groove is radially arranged and has the same depth as the sunken groove.

[0021] In the preferred implementation, the cross section of the sunken groove is in the shape of a right-angled trapezoid. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present application and do not constitute an improper limitation of the present invention. In the drawings:

[0023] Figure 1 A schematic diagram of the three-dimensional structure of a schematic embodiment of the miniature self-locking bearing retainer of the present application is depicted;

[0024] Figure 2 A partially enlarged structural diagram of an exemplary embodiment of the present application in which a deformation portion is retained and provided is depicted;

[0025] Description of labels:

[0026] 1. End ring; 2. First window beam; 3. Second window beam; 4. Third window beam; 5. Arc-shaped window hole; 6. Columnar window hole; 7. Ear structure; 70. Table top; 71. Arc-shaped surface; 72. Vertical surface; 73. Inclined surface; 8. Arc-shaped contact surface; 9. Deformation portion; 90. Sink; 91. Connecting groove. DETAILED DESCRIPTION

[0027] Hereinafter, only certain exemplary embodiments are briefly described. As will be appreciated by those skilled in the art, the described embodiments may be modified in various ways without departing from the spirit and scope of the present invention. Therefore, the drawings and description are to be considered as illustrative in nature and not restrictive.

[0028] In the description of the present invention, it should be understood that the terms "center", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "axial", "radial", "circumferential", etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings and are intended only to facilitate the description of the present invention and simplify the description. They do not indicate or imply that the devices or elements referred to must have a specific orientation, be constructed and operate in a specific orientation, and therefore should not be understood as limiting the present invention. In the present invention, unless otherwise expressly specified and limited, a first feature being "up" or "down" a second feature may be such that the first and second features are in direct contact, or the first and second features are in indirect contact through an intermediate medium.

[0029] In the present application, unless otherwise explicitly specified and limited, the terms "mounting", "connecting", "connecting", "fixing" and the like should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or it can be integrated; it can be directly connected, or it can be indirectly connected through an intermediate medium; it can be the internal communication of two elements or the interaction relationship between two elements. However, it is noted that direct connection means that the connection between the two main bodies does not form a connection relationship through an excessive structure, but is connected to form a whole only through the connecting structure. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0030] In the present application, the description such as "first", "second" and the like is only for the purpose of description, and cannot be understood as indicating or implying the relative importance of the indicated technical features or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first", "second" can explicitly or implicitly include at least one of the features.

[0031] The present application will be described below in conjunction with the accompanying drawings.

[0032] The specific scheme adopted is:

[0033] As shown in Figures 1-2 The present application provides a micro self-locking bearing retainer, which comprises an end ring 1 body, on which a first window beam 2, a second window beam 3 and a third window beam 4 are uniformly distributed;

[0034] Among them, the first window beam 2 and the second window beam 3 are arranged adjacent to each other and are mirror-symmetric structures, and together constitute a group of window beam units, and the third window beam 4 is arranged between adjacent window beam units;

[0035] The first window beam 2 and the second window beam 3 form an arc-shaped window hole 5 which is matched with the ball and has an upper opening, and the upper side of the first window beam 2 and the second window beam 3 is provided with an ear structure 7 which is curved towards the arc-shaped window hole 5, and the ear structure 7 can form axial limiting for the ball;

[0036] The third window beam 4 and the first window beam 2 and the second window beam 3 adjacent to both sides form a cylindrical window hole 6 with an upper opening, and the radial projection of the third window beam 4 falls on the center position of the arc-shaped window hole 5.

[0037] The micro self-locking bearing holder of the present application has an arc-shaped window hole 5 formed between the first window beam 2 and the second window beam 3, the upper side of which is open and the ear structures 7 on both sides can form axial limits for the balls. During the operation of the flexible bearing, especially at the long axis position of the ellipse, when the balls have a tendency to move axially, the ear structures 7 can block the axial movement of the balls, effectively limiting the axial movement amplitude of the balls. The radial projection of the third window beam 4 falls on the center position of the arc-shaped window hole 5, so that when the long axis deformation of the flexible bearing occurs, there is always an axial limit on one side near the long axis position, and the situation of losing the limit on both sides will not occur. The control ability of the holder over the axial movement of the balls is enhanced, and the problem of instability, shaking and deviation of the holder caused by the large movement of the balls on both sides is avoided, the transmission accuracy of the harmonic reducer is guaranteed, and the risk of damage to the bearings and other related components is reduced.

[0038] The third window beam 4 forms a cylindrical window aperture 6 with an upper opening, along with the adjacent first and second window beams 2 and 3. This cylindrical window aperture 6 maintains similar properties to existing single-sided window aperture designs, reducing the contact area between the window beam and the ball bearing, lowering the degree of constraint on the ball bearing, and thus effectively minimizing the frictional resistance experienced by the ball bearing during movement. This low-friction design significantly reduces energy loss and bearing heat generation under conditions of high-speed operation or frequent deformation of the flexible bearing, ensuring stable operation.

[0039] As a preferred embodiment of the present application, the ear structure 7 is provided with a table 70 on the side facing away from the curved window 5, with the table 70 being lower than the height of the third window beam 4. With the table 70 provided on the side facing away from the curved window 5 and the table 70 being lower than the height of the third window beam 4, a structure is formed with one side of the cylindrical window 6 being lower and the other side being higher. The lower side further reduces the contact area between the rolling elements and the retainer. Reducing frictional resistance is crucial for harmonic reducers, as they are often used in applications requiring high precision and efficiency, such as robotic joints and aerospace equipment. Lower frictional resistance reduces energy loss, improves transmission efficiency, and enables more stable and efficient operation of the reducer. This design also achieves a certain degree of lightweighting. Reducing the weight of the retainer reduces the inertia of the entire bearing system. The larger oil reservoir formed above the table 70 can store more lubricating oil. This increased lubricating oil ensures that the rolling elements are always adequately lubricated during movement, forming a good oil film, reducing direct contact between the rolling elements and the retainer, as well as between the inner and outer rings, further reducing frictional resistance and wear.

[0040] Further, the total height of the ear structure 7 and the first window beam 2 or the second window beam 3 is equal to the height of the third window beam 4. This makes the mass distribution of each part of the retainer relatively uniform during rotation. When the harmonic reducer is in operation, the retainer rotates at high speed, and the uniform mass distribution can ensure the stability of its rotation, reduce the difference in centrifugal force caused by uneven mass, and thus maintain a good dynamic balance state. If the heights of the several window beams are not uniform, the mass distribution of each part of the retainer will be uneven. When rotating, the part with larger mass will generate larger centrifugal force, while the part with smaller mass will generate smaller centrifugal force. This difference in centrifugal force will cause the retainer to sway and vibrate, thereby destroying its dynamic balance.

[0041] As Figure 1 , the first window beam 2 and the second window beam 3 are provided with arc-shaped contact surfaces on the side facing the cylindrical window hole 6, and the third window beam 4 is provided with arc-shaped contact surfaces on the sides facing the cylindrical window beams. The shape of the arc-shaped contact surface is adapted to the outer contour of the ball, which can make the contact between the ball and the window beam more conformal. Compared with planar contact, this conformal arc surface contact can greatly reduce the stress concentration on the contact area and reduce the pressure per unit area, thereby effectively reducing the friction between the ball and the window beam during movement.

[0042] Further, the ear structure 7 has an arc-shaped surface 71 on the side facing the arc-shaped window hole 5, which continuously transitions with the arc-shaped window hole 5. During operation of the bearing, stress can be uniformly distributed along the arc-shaped surface 71, avoiding stress concentration at the connection. The design of the arc-shaped surface 71 makes the contact between the ball and the ear structure 7 smoother when the ball enters and exits the arc-shaped window hole 5. The distance between adjacent vertical surfaces 72 is less than the diameter of the ball, thereby achieving axial limiting of the ball.

[0043] Further, an inclined surface 73 is provided on the upper side of the vertical surface 72, and a gradually narrowing placement space is formed between adjacent inclined surfaces 73. The distance between adjacent inclined surfaces 73 is greater than the distance between adjacent vertical surfaces 72.

[0044] In actual work process, in view of the unique working characteristics and structural characteristics of flexible rolling bearing, when the flexible bearing is deformed into an elliptical type, the retainer will also be deformed accordingly. At the long axis point position, the distance between the inner side surfaces of the beam on both sides of the pocket is shortened, and the distance between the outer side surfaces is lengthened, which will generate a radial pushing force to the rolling element in the outward direction of the race; while at the short axis point position, the distance between the inner side surfaces of the beam on both sides of the pocket is lengthened, and the distance between the outer side surfaces is also lengthened, thereby generating a radial pushing force to the rolling element in the inward direction of the race. This periodic radial pushing action significantly increases the contact stress between the inner and outer races of the bearing and the rolling elements. Under the action of long-term high contact stress, the material of the contact surface will gradually appear fatigue phenomenon, forming micro cracks. With the extension of running time, these micro cracks continue to expand and spread, and eventually develop into pitting. The occurrence of pitting further destroys the smoothness of the contact surface, leading to accelerated wear, seriously affecting the service life and performance stability of the flexible bearing, and further adversely affecting the normal operation of the entire harmonic reducer and even the industrial robot arm and humanoid robot.

[0045] To solve the above problems, referring to Figure 2 , the inner wall surface and the outer wall surface of each of the first window beam 2, the second window beam 3 and the third window beam 4 are provided with a sink groove 90, and each is provided with a connecting groove 91 facing the window hole surface, the connecting groove 91 being in communication with the sink groove 90; the first window beam 2, the second window beam 3 and the third window beam 4 are each separated into two deformation parts 9 capable of independent deformation by the sink groove 90 and the connecting groove 91; when the retainer is deformed, one side of the deformation part 9 abuts against the ball and deforms towards the sink groove 90 direction to reduce the contact stress of the ball on the inner and outer races of the bearing.

[0046] Specifically, during the operation of the harmonic reducer, the flexible bearing will be deformed into an elliptical type. Due to the close cooperation between the retainer and the flexible bearing, this deformation will be transmitted to the retainer, causing the retainer to also deform accordingly, and the first window beam 2, the second window beam 3 and the third window beam 4 are each separated into two deformation parts 9 capable of independent deformation by the sink groove 90 and the connecting groove 91. When the retainer is deformed, taking the long axis point position as an example, the deformation part 9 on one side of the pocket will abut against the ball. At this time, the deformation part 9 will deform towards the sink groove 90 direction under the combined influence of the force of the ball and the overall deformation of the retainer. The sink groove 90 provides a deformation space for the deformation part 9, so that the deformation part 9 can deform elastically relatively freely without being restricted by too many structures. At the short axis point position, the deformation part 9 on the other side of the pocket will abut against the ball and deform towards the sink groove 90 direction. During the entire operation process, the two deformation parts 9 alternately contact the ball and deform to adapt to the changing geometry of the retainer.

[0047] In the traditional cage structure, when the cage is deformed, the contact surface of the pocket and the ball is relatively fixed, for example, at the long axis point position, the beams on both sides of the pocket directly abut against the ball to push it in the direction of the outer ring, resulting in a relatively large contact stress in this area. In the improved structure, when the deformation part 9 on one side abuts against the ball and deforms in the direction of the sink 90, the movement of the deformation part 9 in the direction of the sink 90 no longer applies a radial pushing force to the roller, thereby reducing the contact stress of the ball on the unit area of the outer ring of the bearing, and the same applies to the short axis point position.

[0048] As a preferred embodiment of the present application, the sink 90 extends from one end of the window beam to the bottom, and the connecting groove 91 is radially arranged and has the same depth as the sink 90. The sink 90 extends from one end of the window beam to the bottom, which provides sufficient deformation space for the deformation part 9. The deformation part 9 needs to withstand the force of the ball and various stresses generated when the cage is deformed. When the thickness of the deformation part 9 is greater than or equal to the thickness of the sink 90, the deformation part 9 can have sufficient strength and rigidity, and will not be easily damaged when subjected to external force, thereby ensuring the overall structural stability of the cage. The connecting groove 91 penetrates the thickness of the deformation part 9 and is arranged in two upper and lower parts, which divides the deformation part 9 into relatively independent parts. When the cage is deformed at the long axis point position, the deformation part 9 on one side is pressed by the ball. Due to the presence of the two connecting grooves 91, the deformation part 9 can independently deform in the direction of the connecting groove 91 and the sink 90, without excessively transmitting stress to the deformation part 9 on the other side and other parts, thereby improving the overall performance and reliability of the cage.

[0049] Further, the cross section of the sink 90 is in the shape of a right-angled trapezoid. The sink 90 with a right-angled trapezoidal cross section makes the deformation part 9 thicker in the middle and thinner at the edges, which can better adapt to stress distribution. When the deformation part 9 is subjected to external force, the thicker middle part can withstand a larger stress, while the thinner edge part can elastically deform to a certain extent, gradually dispersing and relieving the stress. When the pocket of the cage is an arc-shaped window hole 5, the deformation part 9 adopts an arc-shaped design as the other surfaces of the pocket position, which can ensure the consistency and coordination of the overall structure of the cage.

[0050] The places not mentioned in the present application can be realized by using or referring to the existing technology.

[0051] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of various changes or replacements within the technical scope disclosed by the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A miniature self-locking bearing cage, characterized in that: It comprises an end ring body, on which a first window beam, a second window beam and a third window beam are evenly distributed; The first window beam and the second window beam are adjacently arranged and have a mirror-symmetrical structure, and together they constitute a group of window beam units, and the third window beam is arranged between adjacent window beam units; An arcuate window hole adapted for the ball bearing and open on the upper side is formed between the first window beam and the second window beam. The upper sides of the first window beam and the second window beam are both provided with ear structures bent toward the arcuate window hole, and the ear structures can form an axial limit for the ball bearing; The third window beam and the first window beam and the second window beam on two adjacent sides form a cylindrical window hole with an upper side open, and the radial projection of the third window beam falls on the center position of the arc-shaped window hole.

2. The miniature self-locking bearing retainer according to claim 1, characterized in that: A table top is provided on the side of the ear structure facing away from the arc-shaped window hole, and the height of the table top is lower than the height of the third window beam.

3. The miniature self-locking bearing retainer according to claim 2, characterized in that: The total height of the ear structure and the first window beam or the second window beam is equal to the height of the third window beam.

4. The miniature self-locking bearing retainer according to claim 1, characterized in that: The first window beam and the second window beam facing the cylindrical window hole, as well as the cylindrical window beam sides of the third window beam facing both sides, are all provided with arc-shaped contact surfaces adapted to the balls.

5. The miniature self-locking bearing retainer according to claim 1, characterized in that: The ear structure has an arc surface facing the arc window hole, which is in continuous transition with the arc window hole, and a vertical surface is provided on the upper side of the arc surface. The distance between adjacent vertical surfaces is less than the diameter of the ball.

6. The miniature self-locking bearing retainer according to claim 5, characterized in that: An inclined surface is provided on the upper side of the vertical surface, and a gradually narrowing placement space is formed between adjacent inclined surfaces, and the spacing between adjacent inclined surfaces is greater than the spacing between adjacent vertical surfaces.

7. The miniature self-locking bearing retainer according to claim 1, characterized in that: The first window beam, the second window beam, and the third window beam each have a sunken groove on their inner and outer walls, and each have a connecting groove facing the window hole, the connecting groove being connected to the sunken groove; the sunken groove and the connecting groove separate the first window beam, the second window beam, and the third window beam into two independently deformable portions. When the cage is deformed, the deformed portion on one side contacts the ball and deforms toward the groove to reduce the contact stress between the ball and the inner and outer rings of the bearing.

8. The miniature self-locking bearing retainer according to claim 7, characterized in that: The sinking groove extends from one end of the window beam to the bottom, and the connecting groove is arranged in the radial direction and has the same depth as the sinking groove.

9. The miniature self-locking bearing retainer according to claim 1, characterized in that: The cross section of the sink is in the shape of a right-angled trapezoid.

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