CN112747204B

CN112747204B - Surface measuring device

Info

Publication number: CN112747204B
Application number: CN201911054788.3A
Authority: CN
Inventors: 陈世坤; 杨吉康
Original assignee: BYD Co Ltd
Current assignee: BYD Co Ltd
Priority date: 2019-10-31
Filing date: 2019-10-31
Publication date: 2023-06-13
Anticipated expiration: 2039-10-31
Also published as: CN112747204A

Abstract

The invention discloses a surface measuring device, comprising: a rotating frame; a first rotating shaft pivotally provided on the rotating frame, wherein the first rotating shaft is adapted to be provided with a reflecting sheet; at least one base, the base with the turret pivotably links, the pivot axis of base is perpendicular with the pivot axis of first axis of rotation, the base is suitable for adsorbing on the surface of measuring piece. According to the surface measuring device, the rotating frame, the first rotating shaft which is pivotally connected with the rotating frame and the base with the pivot axis perpendicular to the pivot axis of the first rotating shaft are arranged, so that multi-angle measurement is facilitated, and the limitation of the position selection of a measuring and erecting instrument is reduced. In addition, the angle error can be reduced, the authenticity of the measured data is ensured, and the measuring operation efficiency is improved.

Description

Surface measuring device

Technical Field

The invention relates to the technical field of measurement, in particular to a surface measurement device.

Background

In the related art, in the measuring process, the universal reflecting sheet device for measuring the steel structure track beam is required to be placed flatly, the measured surface is required to be flatly and flatly free of iron slag, the magnet surface of the universal reflecting sheet is tightly attached to the measured surface, then the reflecting sheet corresponds to the measured point on the plane projection position, and the center of the reflecting sheet is required to be opposite to the measured point.

However, in the actual measurement process, the reflective sheet is not easy to be placed flat, so that an excessive angle error is easily caused, the center is deviated from the measured point, and the data is lost in reality. Moreover, visual centering can be subject to errors due to the habit of the measuring personnel, and the data can be lost in authenticity. In addition, the steel structure track measurement data has the diversity, and the mode of placing the reflector plate can be changed along with the change of measurement mode, and on average, three times of reflector plates need to be placed for each measurement, so that the measurement operation efficiency is low.

Disclosure of Invention

The present invention aims to solve at least one of the technical problems existing in the prior art. Therefore, an object of the present invention is to provide a surface measuring device, which effectively reduces errors generated by the placement angle, reduces limitations of position selection of a measuring and erecting instrument, improves the measuring operation efficiency, and ensures the accuracy of the coordinates of measuring end points.

According to an embodiment of the present invention, a surface measuring device includes: a rotating frame; a first rotating shaft pivotally provided on the rotating frame, wherein the first rotating shaft is adapted to be provided with a reflecting sheet; at least one base, the base with the turret pivotably links, the pivot axis of base is perpendicular with the pivot axis of first axis of rotation, the base is suitable for adsorbing on the surface of measuring piece.

According to the surface measuring device provided by the embodiment of the invention, the rotating frame, the first rotating shaft which is pivotally connected with the rotating frame and the base with the pivot axis perpendicular to the pivot axis of the first rotating shaft are arranged, so that multi-angle measurement is facilitated, and the limitation of the position selection of a measuring and erecting instrument is reduced. In addition, the angle error can be reduced, the authenticity of the measured data is ensured, and the measuring operation efficiency is improved.

According to some embodiments of the invention, the number of the bases is two, and the adsorption surfaces of the two bases are perpendicular to each other.

According to some embodiments of the invention, each of the bases comprises: the rotating shaft seat is pivotally connected with the rotating frame; the adsorption base is fixedly connected with the rotating shaft seat, and the surface of one side of the adsorption base, which is far away from the rotating shaft seat, is the adsorption surface.

According to some embodiments of the invention, the turret comprises: a first mounting portion, on which the first rotating shaft passes; the two second installation parts are respectively connected to the two ends of the first installation part, the two second installation parts are positioned on the same side of the first installation part, and the two rotating shaft seats are respectively and pivotally connected with the two second installation parts.

According to some embodiments of the present invention, the first rotating shaft is sleeved with a rotating knob, the first rotating shaft comprises a mating shaft section, the outer circumferential surface of the mating shaft section comprises at least one section of plane section, the rotating knob is provided with a mating hole mated with the mating shaft section, the shape of the mating hole is matched with that of the mating shaft section, and rotating the rotating knob drives the first rotating shaft to rotate together with the rotating knob.

According to some embodiments of the present invention, two engaging lugs are disposed on the rotating shaft seat at intervals, one side of each of the second mounting portions, which is far away from the first mounting portion, is provided with an engaging portion, the engaging portion is disposed between the two engaging lugs, a through hole is formed in the engaging portion, a shaft sleeve is disposed in the through hole, and a first threaded fastener passes through one of the two engaging lugs and the shaft sleeve and is in threaded connection with the other of the two engaging lugs.

According to some embodiments of the invention, the adsorption surface of the base is provided with at least one magnetic adsorption piece, and the base is adsorbed on the surface of the piece to be measured through the magnetic adsorption piece.

According to some embodiments of the invention, the adsorption surface of the base is formed with at least one accommodation groove, and the accommodation groove is internally provided with the magnetic adsorption piece.

According to some embodiments of the invention, the magnetic absorbing element is a neodymium magnetic element.

According to some embodiments of the invention, the rotation angle of the first rotation axis is α, and the rotation angle of the base is β, wherein the α, β satisfy: alpha is more than or equal to 0 degree and less than or equal to 360 degrees, and beta is more than or equal to 0 degree and less than or equal to 180 degrees.

Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.

Drawings

The foregoing and/or additional aspects and advantages of the invention will become apparent and may be better understood from the following description of embodiments taken in conjunction with the accompanying drawings in which:

FIG. 1 is an exploded schematic view of a surface measurement device according to an embodiment of the present invention;

fig. 2 is an assembled schematic view of a surface measuring device according to an embodiment of the present invention.

Reference numerals:

100: a surface measuring device;

1: a rotating frame; 11: a first mounting portion; 12: a second mounting portion; 121: a mating portion;

2: a first rotation shaft; 21: a mating shaft section;

3: a base; 31: a rotating shaft seat; 32: an adsorption base; 33: an adsorption surface;

311: a mating ear; 321: a receiving groove;

4: rotating a knob; 41: a mating hole;

5: a shaft sleeve; 6, a magnetic absorption part; 7: a first threaded fastener;

8: a second threaded fastener; 9: a reflector plate.

Detailed Description

Embodiments of the present invention will be described in detail below, by way of example with reference to the accompanying drawings.

A surface measuring device 100 according to an embodiment of the present invention is described below with reference to fig. 1-2. The surface measurement device 100 may be used to measure the surface of a steel structural rail beam. In the following description of the invention, a surface measuring device 100 is illustrated for measuring a steel structural rail beam. Of course, those skilled in the art will appreciate that the surface measuring device may also be used to measure the surface of other structures, and is not limited to steel structure rail beams.

As shown in fig. 1 to 2, a surface measuring device 100 according to an embodiment of the present invention includes: a turret 1, a first rotation shaft 2 and at least one base 3.

Specifically, the first rotating shaft 2 is pivotably provided on the rotating frame 1, wherein the first rotating shaft 2 is adapted to be mounted with a reflective sheet. For example, in the example of fig. 1 and 2, the first rotating shaft 2 is pivotally connected to the rotating frame 1, the first rotating shaft 2 may be rotatable about its own central axis, the central axis of the first rotating shaft 2 is the pivot axis thereof, and the lower end of the first rotating shaft 2 is provided with the reflector plate 9, and the reflector plate is fixed to the reflector plate 9 at the time of measurement. When the first rotation shaft 2 is rotated, the angle of the reflection sheet attaching plate 9 around the central axis of the first rotation shaft 2 can be adjusted.

The base 3 is pivotally connected to the turret 1, the pivot axis of the base 3 being perpendicular to the pivot axis of the first pivot shaft 2, the base 3 being adapted to be attracted to the surface of a piece to be measured, such as a steel structural rail beam. For example, referring to fig. 1 and 2, the base 3 is pivotally connected to the turret 1, and the pivot axis of the base 3 remains perpendicular to the pivot axis of the first rotation shaft 2 at all times. When the bogie 1 rotates about the pivot axis of the base 3, the first rotation axis 2 and the reflector panel 9 thereon can move together with the bogie 1, so that the angle of the reflector panel 9 about the pivot axis of the base 3 can be adjusted. Thus, by arranging the pivot axis of the base 3 perpendicular to the pivot axis of the first rotation shaft 2, multi-angle measurement is facilitated, and limitations in positioning of the measurement setup instrument are reduced. In addition, by arranging the base 3 to be suitable for being adsorbed on the surface of a piece to be measured, such as a steel structure rail beam, the surface measuring device 100 can be effectively ensured to be placed flat, so that the angle error is small, the authenticity of measured data is ensured, the reflecting sheet 9 can be placed once in each measurement, and the measuring operation efficiency is improved.

According to the surface measuring device 100 of the embodiment of the invention, the rotating frame 1, the first rotating shaft 2 which is pivotally connected with the rotating frame 1 and the base 3 of which the rotating axis is perpendicular to the rotating axis of the first rotating shaft 2 are arranged, so that multi-angle measurement is facilitated, and the limitation of the position selection of a measurement erection instrument is reduced. In addition, the angle error can be reduced, the authenticity of the measured data is ensured, and the measuring operation efficiency is improved.

According to some embodiments of the present invention, referring to fig. 1 in combination with fig. 2, there are two bases 3, and the adsorption surfaces 33 of the two bases 3 are perpendicular to each other. For example, in the example of fig. 1 and 2, the suction surfaces 33 of the two bases 3 are at 90 ° to each other. When measurement is required, the suction face 33 of one of the bases 3 may be sucked on the upper surface of the member to be measured such as the steel structure rail beam, and the suction face 33 of the other base 3 may be sucked on the side of the member to be measured such as the steel structure rail beam. In this way, by the adsorption fixation of the two adsorption surfaces 33 perpendicular to each other, the smoothness of the surface measuring device 100 when placed can be further ensured, and thus the authenticity of the measured data can be further ensured.

Specifically, as shown in fig. 1, each base 3 includes: the rotary shaft seat 31 and the adsorption base 32, the rotary shaft seat 31 is pivotally connected with the rotary frame 1, and the adsorption base 32 is fixedly connected with the rotary shaft seat 31. The adsorption base 32 and the rotating shaft seat 31 can be respectively and independently processed and molded, and then are fixedly connected into a whole, and the respective structures of the adsorption base 32 and the rotating shaft seat 31 are simpler, so that the processing difficulty of the base 3 can be reduced, and the cost is saved. Of course, the adsorption base 32 and the rotating shaft seat 31 may be manufactured integrally. The surface of the adsorption base 32 on one side far away from the rotating shaft seat 31 is an adsorption surface 33. Wherein, the upper end of the side of the absorption base 32 near the reflector plate flitch 9 is provided with a section of inclined plane, and the inclined plane can avoid the reflector plate, so that the structure of the surface measuring device 100 is more compact, and the distance between the reflector plate and the surface to be measured, such as a steel structure track beam, can be effectively reduced.

As shown in fig. 2, the base 3 adsorbed on the upper surface of the member to be measured such as a steel structure rail beam is referred to as a vertical adsorption base, and the base 3 adsorbed on the side surface of the member to be measured such as a steel structure rail beam is referred to as a horizontal adsorption base. The side of the vertical adsorption base away from the adsorption surface 33 is called a slope surface, the slope surface is fixedly connected with one end of the rotating shaft seat 31, and the horizontal adsorption base 32 is fixedly connected with the other end of the rotating shaft seat 31. The connecting plate in the middle of the rotating shaft seat 31 is called a rib plate, one end of the rib plate is fixedly connected with the rotating shaft seat 31 fixed on the slope of the adsorption pedestal 32, the lower surface of the rib plate is fixedly connected with the upper surface of the vertical adsorption pedestal, and the other end of the rib plate is fixedly connected with the horizontal adsorption pedestal. The fixing firmness of the rotating shaft seat 31 and the adsorption base 32 is ensured. The lower surface of the horizontal adsorption base is an adsorption surface 33, and the inner side surface of the vertical adsorption base is an adsorption surface 33. The stability of the base 3 is effectively ensured, and the flatness of placement during measurement is improved.

Further, as shown in fig. 1 and 2, the turret 1 includes: a first mounting portion 11 and two second mounting portions 12. The first rotating shaft 2 is arranged on the first mounting part 11 in a penetrating way, the two second mounting parts 12 are respectively connected to two ends of the first mounting part 11, the two second mounting parts 12 are positioned on the same side of the first mounting part 11, and the two rotating shaft seats 31 are respectively and pivotally connected with the two second mounting parts 12. For example, referring to fig. 1 and 2, the turret 1 may have a substantially n-shape, and the first mounting portion 11 may be provided at a central portion of the turret 1, and the reflection sheet attaching plate 9 may be mounted at a lower end of the first mounting portion 11 between the two second mounting portions 12. By the arrangement, in the actual measurement process, the distance between the center of the reflecting sheet and the measured point along the axis direction of the first rotating shaft 2 is 8mm, and the distance between the center of the reflecting sheet and the measured point along the axis direction of the base is 0. The distance between the center of the reflector plate attaching plate 9 and the measured point is effectively shortened, the distance between the reflector plate and the measured point is further shortened, and errors caused by the placement angle are reduced or avoided. Alternatively, the turret 1 is of symmetrical construction.

According to some embodiments of the present invention, referring to fig. 2, two engaging lugs 311 are disposed on the rotating shaft seat 31 at intervals, one side of each second mounting portion 12 far from the first mounting portion 11 is provided with an engaging portion 121, the engaging portion 121 may be disposed near the inner side of the rotating frame 1, the thickness of the engaging portion 121 is smaller than that of the second mounting portion 12, at this time, the outer side of the engaging portion 121 and the outer side of the rotating frame 1 are spaced apart from each other, the engaging portion 121 is disposed between the two engaging lugs 311, a through hole is formed in the engaging portion 121, a shaft sleeve 5 is disposed in the through hole, and when the engaging member is mounted, the outer side of the engaging lug 311 and the outer side of the rotating frame 1 may be disposed in the same plane, and the first threaded fastener 7 passes through one of the two engaging lugs 311 and the shaft sleeve 5 and is in threaded connection with the other of the two engaging lugs 311. By this arrangement, the rotating frame 1 can well rotate relative to the rotating shaft seat 31, and the rotating shaft seat 2 can be limited to axially move along the through hole of the matching portion 121 by adopting the first threaded fastener 7 for fixation, so that the firmness of the fixation of the rotating shaft seat 2 is ensured. Alternatively, the first threaded fastener 7 is a screw or bolt or the like. Here, it should be noted that the direction "in" is understood as a direction toward the middle of the bogie 1, and the opposite direction is defined as "out", i.e., a direction away from the middle of the bogie 1.

Alternatively, referring to fig. 1 and 2, the first rotating shaft 2 is sleeved with a rotating knob 4, the first rotating shaft 2 includes a mating shaft section 21, the outer circumferential surface of the mating shaft section 21 includes at least one plane section, a mating hole 41 mated with the mating shaft section 21 is formed on the rotating knob 4, the shape of the mating hole 41 is matched with the shape of the mating shaft section 21, and the rotating knob 4 drives the first rotating shaft 2 to rotate together with the rotating knob 4. For example, as shown in fig. 1, the cross-sectional shape of the fitting shaft section 21 is rectangular, and accordingly, the shape of the fitting hole 41 of the turning knob 4 is also rectangular, the turning knob 4 is fitted over the fitting shaft section 21, and the fitting shaft section 21 is fitted into the fitting hole 41. When the angle of the reflecting sheet 9 in the horizontal plane needs to be adjusted, the rotating knob 4 can be rotated to drive the reflecting sheet pasting plate 9 on the first rotating shaft 2 to synchronously rotate. It will be appreciated that the specific shape of the mating shaft segment 21 and the mating bore 41 may be specifically set according to the actual requirements to better meet the actual application.

When assembled, as shown in fig. 1 and 2, the second threaded fastener 8 may be threadably coupled to the mating shaft segment 21 at the upper end of the first rotational shaft 2 to define movement of the first rotational shaft 2 in the axial direction thereof. Optionally, the second threaded fastener 8 is a screw or bolt or the like.

According to some embodiments of the invention, the suction surface 33 of the base 3 is provided with at least one magnetic suction member 6, and the base 3 is sucked onto the surface of the member to be measured by the magnetic suction member 6. The number of the magnetic attraction pieces 6 may be specifically set according to the actual measurement environment and the working requirement, and the number of the magnetic attraction pieces 6 on the attraction faces 33 of the two bases 3 is preferably kept consistent, for example, as shown in fig. 1, two magnetic attraction pieces 6 disposed at intervals may be disposed on the attraction face 33 of each base 3, and the two magnetic attraction pieces 6 may be symmetrically disposed about the attraction face 33. This ensures that the base 3 is stably and securely attached to the surface of the object to be measured, such as a steel structure rail beam. Therefore, the operation is simple, the placement is stable, and the cost is reduced.

Further, at least one accommodation groove 321 is formed on the suction surface 33 of the base 3, and the magnetic suction member 6 is provided in the accommodation groove 321. Referring to fig. 1, the suction surface 33 of the base 3 is formed with two receiving grooves 321 recessed upward, and the magnetic suction member 6 is placed in the receiving grooves 321. When the magnetic attraction member 6 is placed in the accommodation groove 321, the surface of the magnetic attraction member 6 may be flush with the surface of the attraction face 33. Thereby, the flatness of the entire suction face 33 can be ensured, and the suction reliability can be ensured.

Optionally, a centering scale is provided on the suction surface 33 of the base 3, and the centering scale is a straight line and is located in the middle of the suction surface 33 of the vertical suction base. Thus, when the groove surface end points are measured, the alignment graduation marks are placed, and the accuracy of placing the surface measuring device 100 is ensured.

Alternatively, the pivot axis of the first rotation shaft 2 is perpendicular to the surface to be measured, and the pivot axis of the base 3 is parallel to the surface to be measured.

Alternatively, the magnetic attraction member 6 is a neodymium magnetic member. The neodymium magnet has the advantages of high temperature resistance, strong magnetic force, hard hardness and the like. Therefore, the surface measuring device 100 can be ensured to measure in a high-temperature environment, the situation that the surface measuring device 100 and the surface of a piece to be measured are instable in adsorption is avoided due to strong magnetic force, and the magnetic adsorption piece 6 is effectively ensured to be not easy to damage.

The magnetic attachment 6 may be a non-permanent magnet, such as an electromagnet, in addition to a permanent magnet of neodymium magnet, specifically, a conductive winding matching the power of the conductive winding is wound around the core, the conductive winding is energized to generate a magnetic force on the core, and the magnetic force on the core is eliminated after the power supply is turned off. When the magnetic attraction piece 6 is an electromagnet, the electromagnet can be electrified after the surface measuring device 100 is placed on the surface to be measured when the surface to be measured needs to be measured, so that the magnetic attraction piece 6 is firmly attracted to the surface to be measured; when the measurement is completed, the power supply can be cut off to power off the electromagnet, and the surface measuring device 100 can be easily removed from the piece to be measured, such as a steel structure rail beam.

According to some embodiments of the present invention, the rotation angle of the first rotation shaft 2 is α, and the rotation angle of the base 3 is β, wherein the α, β satisfy: alpha is more than or equal to 0 degree and less than or equal to 360 degrees, and beta is more than or equal to 0 degree and less than or equal to 180 degrees. The transverse and longitudinal rotation of the surface measuring device 100 is effectively ensured, the multi-angle measurement of the surface measuring device 100 is facilitated, and the accuracy of measured data is improved.

Specifically, for example, referring to fig. 2, when the surface measuring apparatus 100 is used for measurement, the reflection sheet may be mounted on the reflection sheet attaching plate 9, and then the two adsorption bases 32 of the surface measuring apparatus 100 may be adsorbed on the surface to be measured and the side surface adjacent thereto of the piece to be measured, such as the steel structure rail beam, respectively, specifically, one adsorption base 32 is adsorbed on the upper surface of the surface to be measured, and the other adsorption base 32 is adsorbed on the side surface of the surface to be measured; afterwards, the rotating frame 1 is rotated along the central axis of the base 3, the rotating frame 1 is adjusted to a proper position, and the position of the rotating frame 1 is kept still; and then the rotary knob 4 is rotated along the central axis of the first rotary shaft 2 to drive the reflecting sheet on the first rotary shaft 2 to rotate, so that the center of the reflecting sheet is aligned with the point to be measured of the surface to be measured, and finally corresponding data are read by aligning the measuring instrument with the center point of the reflecting sheet.

According to the surface measuring device 100 provided by the embodiment of the invention, the placement is stable, the operation is simple, and the accuracy is high.

In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "axial", "radial", "circumferential", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings are merely for convenience in describing the present invention and to simplify the description, and do not indicate or imply that the device or element being referred to must have a specific orientation, be configured and operated in a specific orientation, and therefore should not be construed as limiting the present invention.

In the description of the present invention, it should be noted that, unless explicitly specified and limited otherwise, the terms "mounted," "connected," and "connected" are to be construed broadly, and may be either fixedly connected, detachably connected, or integrally connected, for example; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art.

In the description of the present specification, reference to the terms "one embodiment," "some embodiments," "illustrative embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples.

While embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A surface measurement device, comprising:

a rotating frame;

a first rotating shaft pivotally provided on the rotating frame, wherein the first rotating shaft is adapted to be provided with a reflecting sheet;

the base is pivotally connected with the rotating frame, the pivot axis of the base is perpendicular to the pivot axis of the first rotating shaft, at least one magnetic adsorption piece is arranged on the adsorption surface of the base, and the base is adsorbed on the surface of the piece to be measured through the magnetic adsorption piece;

wherein the number of the bases is two, and the adsorption surfaces of the two bases are mutually perpendicular;

wherein each of the bases comprises:

the rotating shaft seat is pivotally connected with the rotating frame;

the adsorption base is fixedly connected with the rotating shaft seat, and the surface of one side of the adsorption base, which is far away from the rotating shaft seat, is the adsorption surface;

a connecting plate is arranged between the two rotating shaft seats, and two ends of the connecting plate are fixedly connected with the two rotating shaft seats respectively;

the rotating frame comprises:

a first mounting portion, on which the first rotating shaft passes;

the two second installation parts are respectively connected to two ends of the first installation part, the two second installation parts are positioned on the same side of the first installation part, and the two rotating shaft seats are respectively and pivotally connected with the two second installation parts;

the rotary knob is sleeved outside the first rotary shaft, the first rotary shaft comprises a matched shaft section, the outer peripheral surface of the matched shaft section comprises at least one section of plane section, a matched hole matched with the matched shaft section is formed in the rotary knob, the shape of the matched hole is matched with that of the matched shaft section, and the rotary knob drives the first rotary shaft to rotate along with the rotary knob.

2. The surface measuring device according to claim 1, wherein two engaging lugs are arranged on the rotating shaft seat at intervals, one side of each second mounting portion, which is far away from the first mounting portion, is provided with an engaging portion, the engaging portion is arranged between the two engaging lugs, a through hole is formed in the engaging portion, a shaft sleeve is arranged in the through hole, and a first threaded fastener penetrates through one of the two engaging lugs and the shaft sleeve and is in threaded connection with the other of the two engaging lugs.

3. The surface measuring device of claim 1, wherein the suction surface of the base is formed with at least one receiving groove, and the magnetic suction member is disposed in the receiving groove.

4. A surface measuring apparatus according to claim 3, wherein the magnetic absorbing member is a neodymium magnetic member.

5. The surface measuring device according to claim 1 or 2, wherein the rotation angle of the first rotation axis is α and the rotation angle of the base is β, wherein the α, β satisfy: alpha is more than or equal to 0 degree and less than or equal to 360 degrees, and beta is more than or equal to 0 degree and less than or equal to 180 degrees.