CN211403801U

CN211403801U - Cosecant function definition demonstration and image synthesizer

Info

Publication number: CN211403801U
Application number: CN201921786589.7U
Authority: CN
Inventors: 王书营
Original assignee: Nanjing Institute of Industry Technology
Current assignee: Nanjing Institute of Industry Technology
Priority date: 2019-10-23
Filing date: 2019-10-23
Publication date: 2020-09-01
Anticipated expiration: 2029-10-23

Abstract

The utility model discloses a cosecant function definition demonstration and image synthesizer, the utility model aims at providing a can demonstrate fast the definition of cosecant function on the unit circle, can expand the functional relation under the quadrature with tangent relation on the unit circle, can directly convert definition form into the cosecant curve etc. in the rectangular coordinate system. Including support riser, unit circle cover, rocking pivot pole, can expand lamp plate, radial bull stick, pipe lamp box, shift pipe lamp, image panel, tangential rail board, this device has: the method has the advantages of simple operation, complete functions, capability of finishing the mutual conversion of the circular arc and the straight line, capability of demonstrating the secant function definition through light spot distribution, capability of automatically and synchronously unfolding the single circular arc into the straight line, capability of directly synthesizing the unfolded image into the secant curve, compact structure, low cost and convenient carrying; the applicability is strong, and the method is suitable for teaching, science popularization, environment beautification and the like.

Description

Cosecant function definition demonstration and image synthesizer

Technical Field

The utility model relates to a teaching instrument, especially a cosecant function definition demonstration and image synthesizer.

Background

A trigonometric function is an important tool for solving the relation between circular arcs and straight lines by people at present, and is the most important knowledge which is necessary to be mastered by college students and middle school students, wherein an cotangent function is the most commonly used, the meaning of the cotangent function is the ratio of adjacent sides to opposite sides in a right triangle, a tangent length which is clamped by an arc length which is clamped by a variable angle and an independent variable and a cotangent angle is a dependent variable in a unit circle to form a unitary function, the relation between the arc and the tangent is complex along with the change of the angle, the cotangent curve is in a plane rectangular coordinate system, namely, the arc length is set as a horizontal coordinate tangent length to be set as a vertical coordinate to establish an orthogonal relation, an image in one period is a single increasing curve, the same relation has great reflection difference under two environments, and the relation between the two environments is not clear, great difficulty is brought to the teaching of teachers and the learning application of students, the two environments need to, teachers urgently need scientific teaching aids to assist teaching, students also need easily learned tools, and families and public places also need ornaments expressing scientific principles to beautify the environment.

In order to solve the above problems, a few devices related to the cotangent function are also presented in the near stage, for example, a 'trigonometric function line demonstration instrument' is provided in the document with the patent application number of 201820266760.0, and the device is provided with a transverse slide way, a steel pipe, a sine fixed block and a sine elastic band, wherein the colors of the front and back surfaces of the sine elastic band and the cosine elastic band are different, so that the change of the trigonometric function value in different quadrant signs can be conveniently and visually demonstrated. The device can only express a sine curve through colors, and cannot dynamically demonstrate the definition of the cotangent function in a unit circle, the conversion of the cotangent function into an image in a plane rectangular coordinate system and other problems. The patent application number 201710380616.X discloses a plotter for drawing an overcut curve, which comprises a support, a support frame, a sliding block plate, a rack, a driving gear, a transmission gear, a rolling gear, a first belt pulley and a second belt pulley, wherein the second belt pulley is connected with a painting brush driving gear, so that the overcut curve can be drawn by using a tool, and the defects of the conventional hand-drawing or complex drawing method are overcome. But the problem of how to convert the cotangent function from the definition form in the unit circle to the orthogonal relation of the image in the plane rectangular coordinate system is not solved. The patent application No. 201420122696.0 discloses a tangent cotangent function curve auxiliary drawing instrument, which comprises a drawing board, a sliding plate, a disk, a pulley, a rocker arm, a left driving wire and a right driving wire, wherein a movable pulley and a unit circle are skillfully combined to complete drawing of a tangent cotangent trigonometric function curve, and the characteristic of the movable pulley in the physical subject is utilized, and the concept of the tangent cotangent function in the mathematical subject is also involved. The device can only draw a positive cotangent curve and cannot demonstrate the definition of a cotangent function in a unit circle, the conversion of the cotangent function into an image in a plane rectangular coordinate system and the like. They reflect the problem of the local inability to systematically represent the unity of circular arcs and straight lines globally through motion.

SUMMERY OF THE UTILITY MODEL

For solving the technical problem, the utility model discloses the technical scheme who adopts as follows:

the cosecant function definition demonstration and image synthesizer comprises a support vertical plate, a unit circular sleeve, a rocking shaft lever, an expandable lamp plate, a radial rotating lever, a tubular lamp box, a position-changing tubular lamp, an image display plate and a tangential rail plate, wherein the unit circular sleeve and the image display plate are respectively arranged at the left part and the right part of the support vertical plate;

the technical scheme is further that the position-changing tube lamp comprises a third transparent tube, a square top plate, an eighteenth rectangular plate, a second diode lamp, a reflector and a second optical fiber, wherein the square top plate is arranged at the upper opening of the third transparent tube, a conical hole is formed in the middle of the square top plate, the reflector is arranged in the conical hole, a tenth rectangular groove is formed in the right side face of the third transparent tube, fourth metal sheets are respectively arranged on two walls of the tenth rectangular groove, a fifth sliding block is arranged in the tenth rectangular groove and is a sliding block with a lock, an eighth support rod is arranged in the fifth sliding block, a fourth transparent tube is arranged at the outer end of the eighth support rod, a second diode lamp and a second optical fiber are arranged in the fourth transparent tube, a power line of the second diode lamp is connected with the fourth metal sheets through the fifth sliding block, a ninth rectangular groove is formed in the left side face of the third transparent tube, and the two walls of the ninth rectangular groove are respectively provided with a third metal sheet, the lower end of the third transparent pipe is provided with an eighteenth rectangular plate, a first lead is arranged on the eighteenth rectangular plate, and the two ends of the first lead are respectively connected with the third metal sheet and the fourth metal sheet.

Compared with the prior art, the utility model, its beneficial effect is:

compared with the prior art, the utility model, its beneficial effect is:

1. the utility model discloses a cosecant function definition demonstrates and image synthesizer, easy operation, only need to shake the handle and can accomplish all demonstrations and image synthesizations under initial conditions;

2. the utility model discloses a cosecant function definition demonstration and image synthesizer, it is multiple functional: the method can complete the mutual conversion of the circular arc and the straight line, can demonstrate the cosecant function definition through the light spot distribution, can synchronously expand the unit circular arc into the straight line, and can directly synthesize the expanded image into the cosecant curve. The applicability is strong: can be used for demonstration and image synthesis in various occasions and at any visual angle. Is suitable for teaching, science popularization, environment beautification and the like.

3. At present, no product exists in the market, and the cosecant function definition demonstration and image synthesizer has compact structure, low cost, safety, reliability and light weight.

Drawings

Fig. 1 is a schematic structural diagram of the present invention.

Fig. 2 is a schematic structural view of the vertical plate of the middle support of the present invention.

Fig. 3 is a schematic structural diagram of a unit round sleeve of the present invention.

Fig. 4 is a schematic structural view of the rocking shaft lever of the present invention.

Fig. 5 is a schematic view of the shape of the deployable lamp panel of the present invention.

Fig. 6 is a schematic structural diagram of the first switch of the present invention.

FIG. 7 is a schematic structural view of the middle radial rotating rod of the present invention

Fig. 8 is a schematic structural diagram of the middle tube lamp box of the present invention.

Fig. 9 is a schematic structural view of the position-variable tubular lamp of the present invention.

Fig. 10 is a schematic structural diagram of the image display board of the present invention.

Fig. 11 is a schematic structural view of the tangential rail plate of the present invention.

In the drawings: 1-a support vertical plate, 11-a projection vertical plate, 12-a transverse plate rod, 13-an adjusting support leg, 14-a first screw rod, 15-a first nut, 16-a terrace with edge base, 17-a first scale, 18-a second scale, 19-a first nail hole, 110-a second nail hole, 111-a third nail hole, 112-a first cross hole, 113-a second cross hole, 114-a third cross hole and 115-a fourth cross hole; 2-unit round sleeve, 21-first round tube, 22-first circular ring disc, 23-second round tube, 24-first rectangular hole, 25-conical hole, 26-second screw, 27-angle line, 28-third screw; 3-a rocking shaft lever, 31-a first round shaft lever, 32-a second nut, 33-a second circular disc, 34-a right-angle crank and 35-a four-corner inserted link; 4-expandable lamp panel, 41-elastic lath, 42-first rectangular plate, 43-second rectangular plate, 44-notch inserting plate, 45-screw, 46-first diode lamp, 47-first optical fiber, 48-first rectangular groove, 49-first switch, 410-first rectangular opening, 411-second rectangular opening, 412-battery box, 413-power switch, 414-second switch, 491-trapezoidal bottom plate, 492-second round shaft rod, 493-third round ring disk, 494-forward angle tooth, 495-reverse angle tooth, 496-first supporting rod, 497-second supporting rod, 498-bright and dark inserting plate, 499-first transparent tube, 4910-rectangular transparent tube opening, 4911-second transparent tube, 4912-metal rod, 4913-first metal sheet, U.S. Pat. No. 1, 4914-square head insulating block, 4915-second metal sheet, 4916-first interface, 4917-third rectangular plate, 4918-fourth rectangular plate, 4919-fifth rectangular plate; 5-radial rotating rods, 51-seventh rectangular plates, 52-third circular shaft rods, 53-triangular plates, 54-eighth rectangular plates, 55-ninth rectangular plates, 56-first springs, 57-tenth rectangular plates, 58-second rectangular grooves, 59-third rectangular grooves, 510-fourth rectangular grooves, 511-fifth rectangular grooves, 512-third scales, 513-first sliding blocks, 514-second sliding blocks, 515-third supporting rods, 516-fourth supporting rods, 517-fifth supporting rods, 518-sixth supporting rods, 519-seventh supporting rods and 520-second rectangular holes; 6-tube lamp box, 61-eleventh rectangular plate, 62-twelfth rectangular plate, 63-thirteenth rectangular plate, 64-fourteenth rectangular plate, 65-sliding door baffle, 66-fifteenth rectangular plate, 67-sixteenth rectangular plate, 68-seventeenth rectangular plate, 69-eighteenth rectangular plate, 610-sixth rectangular groove, 611-seventh rectangular groove, 612-third slider, 613-fourth slider, 614-second spring, 615-nineteenth rectangular plate, 616-fourth nail hole, 617-eighth rectangular groove and 618-bolt pin; 7-a position-changing tube lamp, 71-a third transparent tube, 72-a square top plate, 73-an eighteenth rectangular plate, 74-a second diode lamp, 75-a reflector, 76-a second optical fiber, 77-a fifth slider, 78-a fourth transparent tube, 79-a ninth rectangular groove, 710-a conical hole, 711-a tenth rectangular groove, 712-an eighth supporting rod, 713-a first lead, 714-a third metal sheet and 715-a fourth metal sheet; 8-image display board, 81-nineteenth rectangular board, 82-sixth sliding block, 83-ninth supporting rod, 84-fifth scale, 85-eleventh rectangular groove, 86-tenth supporting rod and 87-eleventh supporting rod; 9-tangential rail plate, 91-twentieth rectangular plate, 92-twelfth support rod, 93-sixth scale, 94-seventh scale and 95-twelfth rectangular groove.

Detailed Description

The technical solution of the present invention is explained in detail below, but the scope of protection of the present invention is not limited to the embodiments.

As shown in fig. 1-11, cosecant function definition demonstration and image synthesizer, including support riser 1, unit circle cover 2, rocking pivot pole 3, can expand lamp plate 4, radial bull stick 5, tubular lamp box 6, the tubular lamp 7 that shifts, image panel 8, tangential trackboard 9, the left part and the right part of support riser 1 are arranged respectively in to unit circle cover 2 and image panel 8, rocking pivot pole 3 is located the center of unit circle cover 2, can expand on lamp plate 4 arranges the circumference of unit circle cover 2 in, radial bull stick 5 is arranged in on rocking pivot pole 3, tubular lamp box 6 is arranged in on radial bull stick 5, the tubular lamp 7 that shifts is arranged in tubular lamp box 6, tangential trackboard 9 is arranged in on image panel 8.

As shown in fig. 1 and 2, the vertical stand plate 1 includes a vertical projection plate 11, a cross plate rod 12, and an adjusting leg 13, the projection vertical plate 11 is a rectangular smooth hard plate, the two ends of the lower bottom surface of the projection vertical plate 11 are provided with vertical transverse plate rods 12, two ends of the transverse plate rod 12 are provided with adjusting support legs 13, the adjusting support legs 13 comprise first screw rods 14, first nuts 15 and prismoid bases 16, one end of the first screw 14 is provided with a prismatic table base 16, the other end is fixedly connected with the transverse plate rod 12, a first nut 15 is sleeved in the middle of the first screw 14, a first scale 17 and a second scale 18 are arranged in the middle of the front of the projection vertical plate 11, a first cross hole 112, a second cross hole 113, a first nail hole 19, a second nail hole 110, a third cross hole 114 and a fourth cross hole 115 are sequentially arranged at the left part of the projection vertical plate 11 from top to bottom, and a third nail hole 111 is arranged at the right side of the projection vertical plate 11.

The unit circle cover 2 is arranged in a first nail hole 19 of the support vertical plate 1, the image display plate 8 is arranged in a second nail hole 110 and a third nail hole 111, the rocking and rotating shaft rod 3 is located at the center of the unit circle cover 2, the deployable lamp plate 4 is arranged on the circumference of the unit circle cover 2, the radial rotating rod 5 is arranged on the rocking and rotating shaft rod 3, the tube lamp box 6 is arranged on the radial rotating rod 5, the position-changing tube lamp 7 is arranged in the tube lamp box 6, and the tangential rail plate 9 is arranged in a first cross hole 112, a second cross hole 113, a third cross hole 114 and a fourth cross hole 115.

As shown in fig. 1, 2 and 3, the unit circle sleeve 2 includes a first circular tube 21, a first circular ring disc 22 and a second circular tube 23, the first circular tube 21 is a rigid straight circular tube, the left end of the first circular tube 21 is provided with the first circular ring disc 22, the outer circumference of the first circular ring disc 22 is fixed on the inner side of the first circular tube 21, the first circular ring disc 22 is a thick rigid circular disc, the surface of the first circular ring disc 22 is provided with an angle line 27, the first circular ring disc 22 is provided with a circular hole 25, and the circular hole 25 is internally provided with the second circular tube 23. The side surface of the circumferential surface of the first circular tube 21 is provided with a first rectangular hole 24, the first rectangular hole 24 is positioned at 0 degree, 90 degree, 180 degree, 270 degree and other positions of the front end edge of the first circular tube 21 along the circumference, and the right end of the first circular tube 21 is symmetrically provided with a second screw 26 and a third screw 28.

The unit round sleeve 2 is fixed by inserting the second screw 26 and the third screw 28 into the first nail hole 19 from the front of the projection vertical plate 11 and fixing them with nuts.

As shown in fig. 1, 3 and 4, the rocking shaft lever 3 includes a first circular shaft lever 31, a second nut 32, a second circular disc 33, a right-angle crank 34 and four-corner insertion rods 35, the first circular shaft lever 31 is a rigid straight circular lever, the four-corner insertion rods 35 are disposed at the front end of the first circular shaft lever 31, the second circular disc 33 is disposed at the right end of the first circular shaft lever 31, the inner circumference of the second circular disc 33 is fixed on the first circular shaft lever 31, a thread is disposed at the rear end of the first circular shaft lever 31, the second nut 32 is disposed on the thread, the right-angle crank 34 is disposed at the rear end of the circumferential surface of the first circular shaft lever 31, and the right-angle crank 34 is connected by two perpendicular rigid levers.

The first round shaft rod 31 is inserted into the second round tube 23 of the unit round sleeve 2, and the rear surface of the projection vertical plate 11 is fastened by a second nut 32 in the rocking shaft rod 3.

As shown in fig. 1, 3, 5, and 6, the deployable lamp panel 4 includes an elastic strip 41, a first rectangular plate 42, a second rectangular plate 43, a first diode lamp 46, a first optical fiber 47, and a first switch 49, the elastic strip 41 is a straight strip with greater elasticity, a first rectangular groove 48 is disposed on a front side surface of the elastic strip 41, the first rectangular groove 48 is a through hole, the first rectangular grooves 48 are plural and are equidistantly arranged in a straight line, the first switch 49 is disposed in the first rectangular groove 48,

the first switch 49 comprises a trapezoidal bottom plate 491, a second round shaft rod 492, a third round ring disk 493, a light and dark inserting plate 498 and a square head insulating block 4914, the trapezoidal bottom plate 491 is an insulating plate, the second round shaft rod 492 is arranged at one end of the trapezoidal bottom plate 491, the third round shaft rod 493 is sleeved on the second round shaft rod 492, a reverse angle tooth 495, a forward angle tooth 494, a second supporting rod 497 and a metal rod 4912 are sequentially arranged on the cylindrical surface of the third round ring disk 493 in the anticlockwise direction, the first supporting rod 496 and the metal rod 4912 are perpendicular to each other, the second supporting rod 497 is arranged at the outer end of the first supporting rod 496, the light and dark inserting plate 498 is arranged at the other end of the second supporting rod 497, the light and dark inserting plate 498 is a transparent thin and hard plate strip, a thin film is adhered to one side of the front half part of the light and dark inserting plate, the light and dark inserting plate 498 is provided with a first transparent tube 499, the first transparent tube 498 is rectangular, and a through hole 499 parallel to, the front nozzle is a rectangular transparent nozzle 4910, the outer surface of the first transparent tube 499 is provided with a second transparent tube 4911, two second transparent tubes 4911 are respectively and vertically fixed on the left and right sides and on the same central line, the light and dark inserting plate 498 can freely move in the first transparent tube 499, the front end of the light and dark inserting plate 498 is provided with a third rectangular plate 4917, the left and right ends of the surface of the third rectangular plate 4917 are sequentially provided with a fourth rectangular plate 4918 and a fifth rectangular plate 4919, the middle part of the surface of the third rectangular plate 4917 is provided with a square head insulating block 4914, the left and right sides of the square head insulating block 4914 are respectively provided with a second metal sheet 4915, the fourth rectangular plate 4918 and the fifth rectangular plate 4919 are the same and are parallel to the square head insulating block 4914, and the length is greater than the square head insulating block 4914. A first metal sheet 4913 is disposed near the metal rod 4912, the first metal sheet 4913 is fixed on the trapezoid base plate 491, a first interface 4916 is disposed on an edge of the trapezoid base plate 491, a lead wire in the first interface 4916 is respectively connected to the metal rod 4912, the first metal sheet 4913, and a second metal sheet 4915, the first switch 49 is formed by inserting one end having a reverse angle tooth 495 into a first rectangular slot 48, the reverse angle tooth 495 extends out of a rear opening of the first rectangular slot 48, a first transparent tube 499 is fixed outside the front opening, a first optical fiber 47 is disposed in a second tube 4917 of the first switch 49, the first optical fiber 47 is a line light emitting optical fiber, a second switch 414, a first diode lamp 46, a battery box 412, and a power switch 413 are disposed at a right end of a front side surface of the elastic strip 41, the second switch 414 is formed by detaching a third rectangular plate 49 and a square head insulating block 14 thereon, Fourth rectangular plate 4918 and fifth rectangular plate 4919, said second switch 414 interfacing with the rightmost first optical fiber 47, said first diode lamp 46 being to the right of the second switch 414. A first rectangular plate 42 is arranged on the elastic lath 41, the length of the first rectangular plate 42 is the same as that of the elastic lath 41, the width of the first rectangular plate 42 is larger than that of the elastic lath 41, a first rectangular notch 410 is arranged on the front edge of the first rectangular plate 42, the position of the first rectangular notch 410 is the same as that of a first rectangular groove 48, a second rectangular plate 43 is arranged on the lower surface of the elastic lath 41, the second rectangular plate 43 is completely the same as that of the first rectangular plate 42, a second rectangular notch 411 is arranged at the front edge, the whole body formed by the first rectangular plate 42, the elastic lath 41 and the second rectangular plate 43 is called an inner groove clamping plate, the first rectangular notch 410 above the square head insulating block 4914 in the inner groove clamping plate and the second rectangular notch 411 below form an opening sliding groove, two ends of the inner groove clamping plate are respectively provided with a groove inserting plate 44, a screw 45 is arranged in the groove of the inserting plate 44, the screw 45 is fixed to the inner groove clamp plate.

The deployable lamp panel 4 is formed by respectively inserting two notch insertion plates 44 into two adjacent first rectangular holes 24 on the unit round sleeve 2, the inner slot clamping plate is bent into an arc along the first round pipe 21, and the notch insertion plates 44 can also be slid upwards to reversely place the deployable lamp panel 4 on the unit round sleeve 2.

As shown in fig. 1, 3 and 7, the radial rotating rod 5 includes a seventh rectangular plate 51, a third circular shaft 52, a triangular plate 53, an eighth rectangular plate 54 and a third stay 515, the seventh rectangular plate 51 is a straight hard plate, the right end of the seventh rectangular plate 51 is provided with the triangular plate 53, the triangular plate 53 is an isosceles triangle and is in a plane with the seventh rectangular plate 51, the outer angle represents the arrow direction, the center line of the seventh rectangular plate 51 is provided with a second rectangular slot 58, the second rectangular slot 58 is internally provided with a first slider 513 and a second slider 514, the first slider 513 and the second slider 514 are both provided with a lock and are placed on the right and left, the lower surface of the first slider 513 is provided with the third stay 515, the lower surfaces of the third stay 515 and the second slider 514 are both provided with color marking dots, the rear end surface of the seventh rectangular plate 51 is provided with the third scale 512, the eighth rectangular plate 54 is arranged between the second slider 58 and the third scale 512, the eighth rectangular plate 54 is a transparent straight hard thin plate, a third rectangular groove 59 is arranged at the lower right end of the eighth rectangular plate 54, a vertical third round shaft rod 52 is arranged in the middle of the rear surface of the eighth rectangular plate 54, a ninth rectangular plate 55 is arranged on the upper surface of the eighth rectangular plate 54, a fifth rectangular groove 511 is arranged on the ninth rectangular plate 55, a fourth supporting rod 516 is arranged in the fifth rectangular groove 511, a tenth rectangular plate 57 is arranged at the upper end of the fourth supporting rod 516, a vertical fifth supporting rod 517 is arranged at the lower end of the fourth supporting rod 516, the fifth supporting rod 517 rotates by taking the third round shaft rod 52 as a central axis, a sixth supporting rod 518 and a first spring 56 are respectively arranged at the other end of the fifth supporting rod 517, the upper end of the first spring 56 is vertically fixed below the ninth rectangular plate 55, the sixth supporting rod 518 is vertically downward, a seventh supporting rod 519 vertical to the eighth rectangular plate 54 is arranged at the lower end of the sixth supporting rod 518, the seventh stay rod 519 is formed by connecting two stay rods, one side of the connecting part is connected with an elastic metal sheet, one stay rod is fixed with the other stay rod and can be bent towards one side of the metal sheet but cannot be bent in the reverse direction, the seventh stay rod 519 penetrates through the third rectangular groove 59, and the upward part of the seventh stay rod 519 is a straight stay rod and the downward front end stay rod can be bent. A fourth rectangular groove 510 is arranged in front of the second rectangular groove 58 at the left part of the seventh rectangular plate 51. The left end of the seventh rectangular plate 51 is provided with a second rectangular hole 520, and the second rectangular hole 520 is a square hole.

The radial rotating rod 5 is formed by sleeving a second rectangular hole 520 on the four-corner inserting rod 35 of the rocking shaft rod 3, and the surface where the third scale 512 is located faces forward.

As shown in fig. 1, 7 and 8, the tubular lamp box 6 includes an eleventh rectangular plate 61, a twelfth rectangular plate 62, a thirteenth rectangular plate 63, a fourteenth rectangular plate 64, a sliding door stopper 65, a second spring 614, a twelfth rectangular plate 62 is arranged on the right edge of the eleventh rectangular plate 61, the front-back length of the twelfth rectangular plate 62 is smaller than that of the eleventh rectangular plate 61, a sixth rectangular groove 610 is arranged at the front end of the twelfth rectangular plate 62, a third sliding block 612 is arranged in the sixth rectangular groove 610, a fifteenth rectangular plate 66 is arranged on the outer surface of the third sliding block 612, a seventh rectangular groove 611 is arranged on the fifteenth rectangular plate 66, a fourth sliding block 613 is arranged in the seventh rectangular groove 611, a lock is arranged on each of the third sliding block 612 and the fourth sliding block 613, a sixteenth rectangular plate 67 is disposed on a lower surface of the fourth slider 613, and the sixteenth rectangular plate 67 is a hard thin plate. The fifteenth rectangular plate 66 is provided with a bolt pin 618 at the rear end of the seventh rectangular groove 611. The rear ends of the twelfth and eleventh

rectangular plates

62 and 61 are provided with thirteenth rectangular plates 63, a second spring 614 is provided in the middle of the front surface of the thirteenth rectangular plate 63, nineteenth rectangular plates 615 are provided at the upper ends of the thirteenth and twelfth

rectangular plates

63 and 62, the left ends of the eleventh rectangular plate 61, the thirteenth rectangular plate 63 and the nineteenth rectangular plate 615 are provided with a fourteenth rectangular plate 64, the fourteenth rectangular plate 64 is the same as the twelfth rectangular plate 62, and has an eighth rectangular slot 617 at the front end of the right side, the eighth rectangular trough 617 is an impermeable groove, a sliding door baffle 65 is arranged in the eighth rectangular trough 617 and the sixth rectangular trough 610, the front portion of the fourteenth rectangular plate 64 outside is provided with a seventeenth rectangular plate 68, the other end of the seventeenth rectangular plate 68 is provided with an eighteenth rectangular plate 69, and the eighteenth rectangular plate 69 is provided with a fourth nail hole 616.

The tube lamp box 6 is fixed in the fourth rectangular groove 510 on the radial rotating rod 5 through the fourth nail hole 616 by screws, and the twelfth rectangular plate 62 is close to the deployable lamp plate 4 on the unit round sleeve 2.

As shown in fig. 1, 8 and 9, the position-changing lamp 7 includes a third transparent tube 71, a square top plate 72, an eighteenth rectangular plate 73, a second diode lamp 74, a reflective mirror 75 and a second optical fiber 76, wherein the third transparent tube 71 is a square tube made of a hard thin transparent plate, the square top plate 72 is disposed at the upper opening of the third transparent tube 71, a conical hole 710 is disposed at the middle of the square top plate 72, a reflective mirror 719 is disposed in the conical hole 710, and the inner mirror surface of the reflective mirror 719 is a paraboloid of revolution. A tenth rectangular groove 711 is arranged on the right side surface of the third transparent tube 71, fourth metal sheets 715 are respectively arranged on two walls of the tenth rectangular groove 711, a fifth slider 77 is arranged in the tenth rectangular groove 711, the fifth slider 77 is a slider with a lock, an eighth support rod 712 is arranged in the fifth slider 77, a fourth transparent tube 78 is arranged at the outer end of the eighth support rod 712, a second diode lamp 74 and a second optical fiber 76 are arranged in the fourth transparent tube 78, a power line of the second diode lamp 74 is connected with the fourth metal sheets 715 through the fifth slider 77, and the second optical fiber 76 is a line light-emitting optical fiber. The left side face of the third transparent tube 71 is provided with a ninth rectangular groove 79, two walls of the ninth rectangular groove 79 are respectively provided with a third metal sheet 714, the lower end of the third transparent tube 71 is provided with an eighteenth rectangular plate 73, the eighteenth rectangular plate 73 is wider than the front and back of the square top plate 72, the eighteenth rectangular plate 73 is provided with a first lead 713, and two ends of the first lead 713 are respectively connected with the third metal sheet 714 and the fourth metal sheet 715. The fifth slider 77 is slid to the top second diode lamp 74 just at the focal point of the mirror 75.

In the position-changing lamp 7, the third transparent tube 71 is placed in the lamp box 6, or the third transparent tube 71 is placed in an opening sliding groove formed by the first rectangular opening 410 and the second rectangular opening 411 on the deployable lamp panel 4, the first switch 49 is switched on, the square-head insulating block 4914 is automatically inserted into the ninth rectangular groove 79, the second metal sheet 4915 is in contact with the third metal sheet 714, and the first diode lamp 46, the first optical fiber 47, the second diode lamp 74 and the second optical fiber 76 are all on.

As shown in fig. 1, 2, and 10, the image displaying board 8 includes a nineteenth rectangular board 81, a sixth sliding block 82, a ninth stay 83, a fifth scale 84, and a tenth stay 86, an eleventh rectangular groove 85 is provided in the middle of the nineteenth rectangular board 81, the sixth sliding block 82 is provided in the eleventh rectangular groove 85, the sixth sliding block 82 is a sliding block with a lock, the ninth stay 83 is provided in the middle of the upper surface of the sixth sliding block 82, the fifth scale 84 is provided at the front end of the upper surface of the nineteenth rectangular board 81, and the tenth stay 86 and the eleventh stay 87 are provided at the left and right ends of the rear side surface of the nineteenth rectangular board 81 in sequence.

The tenth brace 86 and the eleventh brace 87 are inserted into the second nail hole 110 and the third nail hole 111 of the projection vertical plate 11 in sequence and fixed on the image display plate 8.

As shown in fig. 1, 2 and 11, the tangential rail plate 9 includes a twenty-fourth rectangular plate 91 and a twelfth brace 92, the nineteenth rectangular plate 91 is a hard plate strip, a twelfth rectangular groove 95 is arranged in the middle of the twentieth rectangular plate 91, the right end of the twelfth rectangular groove 95 is a notch, a sixth scale 93 and a seventh scale 94 are sequentially arranged on the upper edge and the lower edge of the front surface of the twentieth rectangular plate 91, and the twelfth brace 92 is arranged on the left side surface of the twentieth rectangular plate 91.

The tangential rail plate 9 is formed by inserting the twelfth support rod 92 into the first cross hole 112, the second cross hole 113, the third cross hole 114 and the fourth cross hole 115 on the stand vertical plate 1.

The utility model discloses a cosecant function definition demonstration and image synthesizer's theory of operation is, and the circular arc curve according to the constant curvature expandes the straight line for zero curvature, turns into the curve light ring to the light that has the rectilinear propagation through optic fibre, utilizes the projection cylinder to realize the conversion between the figure. The method is characterized in that: the operation is simple, and all demonstration and image synthesis can be completed only by rocking the handle under the initial condition; the functions are complete: the method can complete the mutual conversion of the circular arc and the straight line, can demonstrate the cosecant function definition through the light spot distribution, can synchronously expand the unit circular arc into the straight line segment, and can directly synthesize the expanded image into the cosecant curve. The structure is compact, the cost is low, and the carrying is convenient; the applicability is strong: can be used for demonstration and image synthesis in various occasions and at any visual angle. Is suitable for teaching, science popularization, environment beautification and the like.

The utility model discloses a cosecant function definition demonstration and image synthesizer has the function that demonstrates secant function y ═ cscx definition in unit circle, and operating procedure is:

firstly, assembling an instrument, 1] placing a prismatic table base 16 of a support vertical plate 1 on a stable horizontal plane, screwing a first nut 15 to enable the support vertical plate 1 to be in a stable state, and adjusting a projection vertical plate 11 to be in a vertical state. 2, the unit round sleeve 2 is arranged on the vertical plate 1 of the bracket, and the directions of 0-degree and 90-degree lines in the angle adjusting line 27 are respectively consistent with the first scale 17 and the second scale 18 and then fixed. And 3, placing the image display plate 8 on the vertical plate 1 of the bracket, and adjusting the transverse center line of the nineteenth rectangular plate 81 to be consistent with the direction of the second scale 18 and then fixing. Four extendable lamp panels 4 are taken, a battery closing power switch 413 is installed in the battery box 412, two counterclockwise direction switches are respectively arranged in the second quadrant and the fourth quadrant on the unit round sleeve 2, the other two clockwise direction switches are respectively arranged in the first quadrant and the third quadrant on the unit round sleeve 2, and the first switch 49 is adjusted to be in a closed state. And 5, inserting two tangential rail plates 9 into a first cross hole 112 and a second cross hole 113 respectively, enabling the opening of the twelfth rectangular groove 95 to be outward, and similarly inserting the two tangential rail plates 9 into a third cross hole 114 and a fourth cross hole 115 respectively. 6] the rocking shaft lever 3 is placed on the unit round sleeve 2. And 7, taking down the door moving baffle 65 on the first tubular lamp box 6, placing N position-changing tubular lamps 7 in the door moving baffle 65, inserting the door moving baffle 65, and similarly taking N position-changing tubular lamps 7 to be placed in the second tubular lamp box 6. 8, a first tubular lamp box 6 provided with a position-changing tubular lamp 7 is arranged on the radial rotating rod 5. 9] place radial bull stick 5 on rocking axis pole 3, adjust first slider 513 and make third vaulting pole 515 place in the twelfth rectangular slot 94 of first tangential rail board 9, third slider 612 on the adjusting tube lamp box 6 makes seventeenth rectangular board 68 press close to the outside of deployable lamp board 4, adjust fourth slider 613 makes sixteenth rectangular board 67 behind deployable lamp board 4, adjust first slider 513 and make third vaulting pole 515 place in the twelfth rectangular slot 94 of first tangential rail board 9, fix with bolt pin 618.

Setting symbols: 1]The coordinate system in which the unit circle sleeve 2 is located is set as O₁ty₁The center of the unit circle is O₁Which is the projection point of the common center of the first circular tube 21 and the first circular ring disc 22 on the projection vertical plate 11. The 0 deg. line is the beginning edge of the angle, and the center line of the first rectangular groove 48 on the radial rotating rod 5 is the end edge of the angle. Center line of the first optical fiber 47 on the unit round jacket 2 to the point O₁The curve of the first optical fiber 47 when lit forms a unit circle when the distance of (d) is set to one unit. Four can expand lamp plate 4, four tangential trackboards 9 and all sort according to their quadrant that belongs to, if the interior deployable lamp plate 4 of first quadrant is called first can expand lamp plate 4, the tangential trackboard 9 of first quadrant is called first tangential trackboard 9. Each expandable lamp plate 4 is provided with N sections of first optical fibers 47, the first optical fibers 47 have the same length and are arranged in a counterclockwise direction, the first optical fibers 47 on the first expandable lamp plate 4 are the first, second, … and N sections, the second, third and fourth optical fibers on the expandable lamp plate 4 are marked as the N +1, N +2, …, 2N +1, …, 3N +1, … and 4N in a counterclockwise direction, and the serial numbers are used for the diode lamps, switches and other devices contained in the lamps. The radial rotating rod 5 rotates counterclockwise from the starting edge to form a variable angle arc degree of x, and the arc length reaching the end of the mth first optical fiber 47 is x_m。m＝1,2，…，4N。2]The closed end of the center line of the twelfth rectangular groove 95 on the first tangential rail plate 9 and the second tangential rail plate 9 is positioned at O₁ty₁The middle point A has coordinates of zero and one, the sixth scale 93 on the first tangential rail 9 is above, the scale value represents positive, the seventh scale 94 on the second tangential rail is above, the scale value represents negative, the color mark dots on the third supporting rod 515 are located at the points B, ∠ AO₁B is x, cscx is O₁B, the opening end of the twelfth rectangular groove 95 is positioned at point C, and cscx is set_n＝O₁C or cscx_N+n＝O₁C。3]The coordinate system on the image display plate 8 is set as Oxy, the ninth stay bar 83 is a straight line parallel to the Oy axis, and the length of the main lamp light on the displacement tube lamp 7 represents the cosecant function value. 4]The N position-changing tubular lamps 7 in the first tubular lamp box 6 are arranged inwards from the sliding door baffle 65The numbers of the tube lamps 7 are N, N-1, …, two and one displacement tube lamp, and the numbers of the tube lamp box 6 are N +1, N +2, … and 2N displacement tube lamps 7.

Thirdly, adjusting the initial position: 1]Adjusting the light length, taking out the Nth position-changing tubular lamp 7 in the first tubular lamp box 6, sliding the fifth slide block 77 to make the light length equal to cscx₁And (4) fixing, and sequentially adjusting the light lengths of the Nth-1, the … and the Nth, the Nth-N-1, the Nth-N-2, the … and one of the lights to the maximum by the same method. The N +1, N +2, …, and 2N displacement tube lamps 7 in the second tube lamp box 6 were adjusted to be the same as the N, N-1, …, two, and one, respectively, in the same way. 2]Collecting the position-changing tubular lamps 7, sequentially placing the first, second, …, N-1 and N position-changing tubular lamps 7 in the first tubular lamp box 6 in the right direction of the left tenth rectangular groove 711 according to the ninth rectangular groove 79, pressing tightly and sealing by using a door-moving baffle 65, placing the first tubular lamp box 6 on the radial rotating rod 5, sequentially pushing the 2N, 2N-1, …, N +2 and N +1 position-changing tubular lamps 7 into the second tubular lamp box 6 to be pressed tightly by using the same method, and sealing by using the door-moving baffle 65 for standby. 3]The adjustment angle is 90 ° and the secant function value is one, open bolt pin 618, wave right-angle crank 34 and rotate radial rotating rod 5 to coincide with 90 ° line and lock, adjust fourth slider 613 to make sixteenth rectangular plate 67 press close to the rear side of deployable lamp panel 4, adjust second slider 514 to make the color marking dot aim at first optical fiber 47. 4]The first tangential rail panel 9 is adjusted so that the color-coded dots on the third brace 515 are in front of the nineteenth rectangular panel 91.

Fourthly, defining and demonstrating a cosecant function on the unit circle: 1]Interval [0 °,90 ° ]]The demonstration of the function is that the power switch 413 on the first expandable lamp plate 4 is turned on, the door moving baffle 65 on the first tube lamp box 6 is pulled out, the Nth tube lamp 7 with the displacement is popped out to the front of the second rectangular groove 58, the right side of the Nth tube lamp is blocked by the ninth rectangular plate 55, the back of the Nth tube lamp is close to the front edge of the first expandable lamp plate 4, the seventh support rod 519 is arranged in the front of the Nth tube lamp, the bolt pin 618 is opened, the right-angle crank 34 is shaken anticlockwise, the radial rotating rod 5 rotates clockwise, the second switch 414 is turned on, the first diode lamp 45 and the Nth section of first optical fiber 47 emit light, the included angle is 90 degrees, the right-angle crank 34 is shaken continuously, and the color mark round dotsThe circular motion, the color mark dot on the third supporting rod 515 moves to the right, and when the radial rotating rod 5 reaches the end point of the Nth segment of the first optical fiber 47, the rotating angle is x_NThe included angle of the cosecant function is 90-x_NThe first diode lamp 45 faces the open chute, the Nth switch 49 is turned on, the square-head insulating block 4914, the fourth rectangular plate 4918 and the fifth rectangular plate 4919 extend forward to push the tenth rectangular plate 57 to move forward, the seventh stay rod 519 moves backward to push the Nth position-changing tube lamp 7 to enter the open chute, and the Nth position-changing tube lamp 7 is clamped by the fourth rectangular plate 4918 and the fifth rectangular plate 4919 to form an arc upper point of 90-x_NThe normal line is normal line, the square head insulating block 4914 is inserted into the ninth rectangular groove 79, the Nth deflection tubular lamp 7 and the N-1 st section of the first optical fiber 47 emit light, and the main light length of the Nth deflection tubular lamp 7 is csc (90-x)_N) The value of (c). The right-angle crank 34 is further shaken, the tenth rectangular plate 57 departs from the Nth position-changing tubular lamp 7 to be rebounded to the original position and enters the front of the Nth-1 position-changing tubular lamp 7, and when the radial rotating rod 5 reaches the end point of the Nth-1 section of the first optical fiber 47, the rotating angle is x_N-1The first switch 49 of the N-1 th switch is turned on, the second position-changing tubular lamp 7 is pushed into the opening chute and emits light, and the length of the light is csc (90-x)_N-1) The value of (c). When the right-angle crank 34 is further shaken to lead the radial rotating rod 5 to reach the end point of the first optical fiber 47 of the Nth-nth section, the rotating angle is x_N-nThe N-N first switch 49 is turned on, the color mark dot on the third supporting rod 515 is close to the highest point, the N-N displacement tubular lamps 7 are pushed into the opening chute to emit light, and the lamp length is csc (90-x)_N-n) The third support bar 515 of the right-angle crank 34 is swung to be separated from the first tangential rail plate 9, the rest of the position-changing tubular lamps 7 are pushed into the open chute in sequence and emit light, and the length of a light beam on the position-changing tubular lamps 7 and the length of a light beam emitted by the reflector 75 are considered to be csc (90-x)_N-n-1)，…，cscx₁The value of (c). When the angle reaches 0 degree, the right-angle crank 34 stops shaking and is locked by the bolt pin 618, the length of the light beam on the position-changing tubular lamp 7 arranged on the first expandable lamp panel 4 in the counterclockwise direction sequentially shows that the angle is 0 degree and 90 degrees]The value of the cosecant function cscx. 3]Interval [90 °,180 ° ]]Demonstrating the upper function, namely dismounting the first tubular lamp box 6, rotating the radial rotating rod 5 clockwise to coincide with a 90-degree line and then locking, and adjusting the second tangential rail plate 9 to enable the color mark on the third support rod 515The dots are in front of a nineteenth rectangular plate 91. A second tubular lamp box 6 is arranged on the radial rotating rod 5, a power switch 413 on a second expandable lamp panel 4 is turned on to imitate [0 degrees, 90 degrees ]]The demonstration method comprises the steps of shaking the right-angle crank 34 anticlockwise, completing corresponding operation until the line reaches 180 degrees, and then fixing, wherein the length of the light spot and the light column of the position-changing tubular lamp 7 in the anticlockwise direction on the second extensible lamp plate 4 represents that the angle is [90 degrees ], 180 degrees]The cosecant function value of (1).

The utility model discloses an after-cut function definition demonstration and image synthesizer can expand the after-cut function relation of definition in the unit circle and become the after-cut curve on the rectangular coordinate system, synthesizes the image that after-cut function y is cscx with light spot or light beam, and the operating procedure is:

firstly, assembling an instrument: as defined by the demonstration cosecant function.

Setting symbols: as defined by the demonstration cosecant function.

Thirdly, adjusting the initial position: 1-4 ] are the same as defined by the demonstration cosecant function. And 5, the ninth brace 83 is moved to the middle point of the fifth scale 84 and fixed, and the abscissa is pi/2.

Fourthly, defining and demonstrating the secant function in the unit circle: as defined by the demonstration cosecant function.

Fifthly, unfolding the unit circular arc into a straight line segment: 1]The rocking shaft lever 3 and the radial rotating lever 5 thereon are removed. 2]Expand first deployable lamp plate 4, lift off first deployable lamp plate 4 from unit circle cover 2 and expand for the flat board, N tube lamp 7 and the light beam that shifts on it are parallel to each other, arrange first deployable lamp plate 4 in image panel 8 eleventh rectangle groove 85 along with tube lamp 7 forward that shifts, originally in the one end of 90 lines near ninth vaulting pole 83 the left side and fixed, this point is exactly pi/2 radian point, originally the one end of 0 lines is fixed with sixth slider 82 with the left side, this point is 0 radian point. 3]Unfolding a second expandable lamp panel 4, detaching the second expandable lamp panel 4 from the unit round sleeve 2, expanding the second expandable lamp panel 4 into a flat plate, enabling the N position-changing tubular lamps 7 and the light columns on the second expandable lamp panel to be parallel to each other, placing the second expandable lamp panel in an eleventh rectangular groove 85 of the image display panel 8 in the forward direction, enabling one end of the original 90-degree line to be close to and fixed to the right side of a ninth support rod 83, marking the point as a pi/2 radian point, and enabling one end of the original 180-degree line to be fixed by a sixth sliding block 82 on the right sideThis point is then the pi radian point. 4]O₁ty₁The upper half circular arc of the middle unit circular sleeve 2 is expanded into an interval [0, pi ] of the Oxy axis in the Oxy]The height of the light beam of the 2N deflection tubular lamps 7 above the Ox axis is cscx-1, and the height of the light beam below the Ox axis is 1.

Sixthly, synthesis of a cosecant curve: the bottoms of the position-changing tube lamps 7 in the interval [0, pi ] are pushed upwards one by one vertically to be flush with the lower surface of the expandable lamp plate 4, the height of a light beam on 2N position-changing tube lamps 7 is the value of the cosecant function, the bright spots at the highest points of the position-changing tube lamps are the image contour of the cosecant function on the interval [0, pi ] on the projection vertical plate 11, and the connecting points are the cosecant curve y ═ cscx, [0, pi ].

The definition demonstration, the circular arc expansion, the function value translation and the curve synthesis on the interval [ pi, 2 pi ] can refer to the operation on the interval [0, pi ], and only the curve is positioned below.

The utility model discloses economic value and application prospect of cosecant function definition demonstration and image synthesizer: with the technical progress and economic development, advanced equipment is required to improve the teaching effect and the environment beautifying level more and more, a cosecant function definition demonstration and image synthesizer which is simple to operate and convenient to use is urgently needed, only the aspects of higher education and middle education, tens of thousands of schools are shared in the whole country, numerous families and exhibition places are also needed, the quantity is considerable, the market prospect is very wide, and good economic benefits and social benefits are achieved.

The utility model discloses the part that does not relate to all is the same with prior art or can adopt prior art to realize.

As mentioned above, although the present invention has been shown and described with reference to certain preferred embodiments, it should not be construed as limiting the invention itself. Various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims

1. Cosecant function definition demonstration and image synthesizer, its characterized in that: including support riser, unit circle cover, rocking pivot pole, can expand lamp plate, radial bull stick, tubular lamp box, the tubular lamp that shifts, image panel, tangential trackboard, the left part and the right part of support riser are arranged respectively in to unit circle cover and image panel, rocking pivot pole is located the center of unit circle cover, can expand on the circumference of unit circle cover is arranged in to the lamp plate, radial bull stick is arranged in on the rocking pivot pole, tubular lamp box is arranged in on the radial bull stick, the tubular lamp that shifts is arranged in the tubular lamp box, the tangential trackboard is arranged in on the image panel.

2. The cosecant function definition presentation and image synthesizer of claim 1, wherein: the position-changing tube lamp comprises a third transparent tube, a square top plate, an eighteenth rectangular plate, a second diode lamp, a reflector and a second optical fiber, wherein the square top plate is arranged at the upper opening of the third transparent tube, a conical hole is formed in the middle of the square top plate, the reflector is arranged in the conical hole, a tenth rectangular groove is formed in the right side surface of the third transparent tube, fourth metal sheets are respectively arranged on two walls of the tenth rectangular groove, a fifth sliding block is arranged in the tenth rectangular groove and is a sliding block with a lock, an eighth support rod is arranged in the fifth sliding block, a fourth transparent tube is arranged at the outer end of the eighth support rod, a second diode lamp and a second optical fiber are arranged in the fourth transparent tube, a power wire of the second diode lamp is connected with the fourth metal sheets through the fifth sliding block, a ninth rectangular groove is formed in the left side surface of the third transparent tube, and third metal sheets are respectively arranged on two walls of the ninth rectangular groove, the lower extreme of third hyaline tube is equipped with eighteenth rectangular plate, be equipped with first wire above the eighteenth rectangular plate, first wire both ends link to each other with third sheetmetal and fourth sheetmetal respectively.