CN110718121A - Cosine function definition demonstration and image synthesizer - Google Patents

Abstract

The invention provides a method for rapidly demonstrating the definition of a cosine function in a unit circle, which can expand the cosine relation in the unit circle into an orthogonal function relation and can directly synthesize a cosine curve and the like in a rectangular coordinate system. The device comprises a support vertical plate, a transverse pallet, a diameter chord plate, an arc display plate, an inner inserted tube lamp, a rotating mechanism, a measuring angle disc, a radial rotating rod and a tangential display plate. The device comprises: the operation is simple, and all demonstration and image synthesis can be completed only by rocking the handle or pushing the roller under the initial condition; the functions are complete: the method can complete the mutual conversion of circular arcs and straight lines, demonstrate the definition of cosine functions through light spot distribution, expand unit circles by using the rolling of a disc, and directly synthesize expanded images into cosine curves. 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.

Description

Cosine function definition demonstration and image synthesizer

Technical Field

The invention relates to a teaching instrument, in particular to a cosine 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.

Disclosure of Invention

In order to solve the technical problems, the technical scheme adopted by the invention is as follows:

the cosine function definition demonstration and image synthesizer comprises a support vertical plate, a unit circular roller, a radius chord plate, an arc display plate, an inserted tube lamp, a rotating mechanism, a protractor disc, a radial rotating rod and a tangential pallet, wherein the unit circular roller and the tangential pallet are respectively arranged on the left part and the right part of the support vertical plate;

according to the further technical scheme, a disc lamp holder is arranged on the upper surface of the directional base block in the arc display board, the middle of the disc lamp holder is provided with a positive pole and a negative pole of a lead, a transparent circular tube is arranged on the disc lamp holder, and two ends of a third circular tube are arranged on the front side wall and the rear side wall of the second rectangular groove in the rotating lamp holder;

according to the technical scheme, the inner tube inserting lamp comprises a rubber tube plug, a third transparent tube, a fourth transparent tube, a yellow diode lamp, a green diode lamp and a second optical fiber, the third transparent tube is arranged on the lower bottom surface of the rubber tube plug, a pin lock is arranged on the circumferential surface of the lower end of the third transparent tube, one end of the pin lock penetrates through the third transparent tube, the fourth transparent tube is arranged at the lower end of the third transparent tube, a first disc is arranged at the opening of the tail end of the fourth transparent tube, the green diode lamp and a third conducting wire are arranged on the upper surface of the first disc, and the third conducting wire is connected with the green diode lamp. The middle of the rubber pipe plug is provided with a sixth round hole, a second optical fiber is arranged in the sixth round hole, the upper surface of the rubber pipe plug is provided with a yellow diode lamp and a third plastic pipe, a metal sheet is arranged in the third plastic pipe, and the metal sheet in the third plastic pipe is connected with a third lead.

Compared with the prior art, the invention has the beneficial effects that:

1. the cosine function definition demonstration and image synthesis instrument is simple to operate, and can complete all demonstration and image synthesis only by rocking the handle or pushing the roller under the initial condition;

2. the cosine function definition demonstration and image synthesizer of the invention has complete functions: the method can complete the mutual conversion of circular arcs and straight lines, demonstrate the definition of cosine functions through light spot distribution, expand unit circles by using the rolling of a disc, and directly synthesize expanded images into cosine curves. 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 cosine function definition demonstration and image synthesizer has a compact structure, low cost, safety, reliability and light weight.

Drawings

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

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

FIG. 3 is a schematic view of a unit circle roller according to the present invention.

FIG. 4 is a schematic view of the construction of the radius chords of the present invention.

Fig. 5 is a schematic structural view of the arc display board of the present invention.

Fig. 6 is a schematic diagram of the structure of the bidirectional switch of the present invention.

FIG. 7 is a schematic view of an inner cannula lamp according to the present invention.

Fig. 8 is a schematic structural view of the rotating mechanism in the present invention.

Fig. 9 is a schematic view of the construction of the protractor disk according to the present invention.

Fig. 10 is a schematic structural view of the radial rotating rod of the present invention.

Fig. 11 is a schematic view of the tangential pallet configuration 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 prism table base, 17-a first scale, 18-a second scale, 19-a first groove, 110-a second groove, 111-a first nail hole, 112-a second nail hole, 113-a third nail hole, 114-a fourth nail hole, 115-a first round hole, 116-a second round hole, 117-a third round hole, 118-a fourth round hole and 119-a fifth round hole; 2-unit round roller, 21-first round pipe, 22-second round pipe, 23-first spoke plate, 24-second spoke plate, 25-first spoke plate, 26-second spoke plate, 27-first elastic bolt, 28-first round gear ring, 29-first rectangular hole, 210-right angle baffle, 211-first spring plate, 212-first rectangular plate, 213-fifth nail hole, 214-sixth nail hole, 215-seventh nail hole, 216-eighth nail hole, 217-first gap, 218-second nut; 3-radius chord plate, 31-second rectangular plate, 32-positioning sliding plate, 33-first rectangular groove, 321-third rectangular plate, 322-first circular ring piece, 323-first circular shaft rod, 324-fourth rectangular plate, 325-fifth rectangular plate, 326-first spring and 327-elastic lockset; 32-positioning slide 324-fourth rectangular plate; 4-circular arc exhibition plate, 41-sixth rectangular plate, 42-second rectangular groove, 43-rotary lamp holder, 44-third rectangular groove, 45-fourth rectangular groove, 46-sixth rectangular groove, 47-red diode lamp, 48-first optical fiber, 49-bidirectional switch, 410-battery box, 411-power switch, 412-fifth rectangular groove, 413-seventh rectangular groove, 431-third circular tube, 432-directional base block, 433-disc lamp holder, 434-transparent circular tube, 491-switch bottom plate, 492-second circular shaft rod, 493-first circular disc, 494-forward angular tooth, 495-reverse angular tooth, 496-first supporting rod, 497-second supporting rod, shading film-transparent thin plate, 499-rotary lamp holder, 44-third rectangular groove, 45-fourth rectangular groove, 46-sixth rectangular groove, 47-red diode lamp, 48-first optical fiber, 49-bidirectional switch, 410-battery box, 411-power switch, 412-fifth rectangular groove, 413-seventh rectangular, 4910 metal fork, 4911 first plastic tube, 4912 first lead, 4913 second plastic tube, 4914 second lead, 4915 eighth rectangular groove, 4916 first transparent tube, 4917 second transparent tube, 4918 first baffle, 4919 second baffle, 4920 eighth nail hole; 5-inner inserted tube lamp, 51-rubber tube plug, 52-third transparent tube, 53-fourth transparent tube, 54-yellow diode lamp, 55-green diode lamp, 56-second optical fiber, 57-pin lock, 58-third plastic tube, 59-sixth round hole, 510-third wire, 511-first disc; 6-a rotating mechanism, 61-a third round shaft rod, 62-a fourth round pipe, 63-a second round disc, 64-a right-angle crank, 65-a second round disc, 66-a seventh rectangular plate, 67-an eighth rectangular plate and 68-a ninth nail hole; 7-angle measuring disc, 71-transparent circular plate, 72-fifth circular tube, 73-second circular gear ring, 74-second elastic bolt, 75-seventh circular hole, 76-tenth nail hole, 77-eleventh nail hole and 78-angle line; 8-radial rotating rods, 81-ninth rectangular plate, 82-semicircular plate, 83-third triangular plate, 84-tenth rectangular plate, 85-fourth circular shaft rod, 86-cambered plate, 87-ninth rectangular groove, 88-tenth rectangular groove, 89-first sliding block, 810-second sliding block, 811-third scale, 812-twelfth nail hole, 813-circular roller and 814-bolt lock; 9-a tangential pallet, 91-an eleventh rectangular plate, 92-a first straight rack, 93-a second straight rack, 94-a third straight rack, 95-a fourth straight rack, 96-a fourth scale, 97-an eleventh rectangular groove, 98-a twelfth rectangular groove, 99-a thirteenth rectangular groove, 910-a third elastic bolt, 911-a fourth elastic bolt, 912-a first support rod, 913-a second support rod;

Detailed Description

The technical solutions of the present invention are further described below with reference to the accompanying drawings.

As shown in fig. 1-11, the cosine function definition demonstration and image synthesizer includes a support vertical plate 1, a unit circle roller 2, a radius chord plate 3, an arc exhibition plate 4, an inserted tube lamp 5, a rotation mechanism 6, a protractor 7, a radial rotating rod 8, and a tangential pallet 9, wherein the unit circle roller 2 and the tangential pallet 9 are respectively disposed on the left and right portions of the support vertical plate 1, the radius chord plate 3, the protractor 7, and the rotation mechanism 6 are respectively disposed on the unit circle roller 2, the arc exhibition plate 4 is arc-shaped and is respectively disposed on the circumference of the unit circle roller 2, the radial rotating rod 8 is disposed on the rotation mechanism 6, and the inserted tube lamp 5 is disposed between the arc exhibition plate 4 and the radius chord plate 3.

As shown in fig. 1 and 2, the upright support plate 1 includes a vertical projection plate 11, a horizontal plate rod 12, and adjusting legs 13, the vertical projection plate 11 is a rectangular smooth hard plate, the horizontal plate rods 12 are disposed at two ends of a lower edge of the vertical projection plate 11, the adjusting legs 13 are disposed at two ends of the horizontal plate rod 12, each adjusting leg 13 includes a first screw 14, a first nut 15, and a prism base 16, the first nut 15 is sleeved in the middle of the first screw 14, the prism base 16 is disposed at a lower end of the first screw 14, and the adjusting legs 13 fix an upper end of the first screw 14 on the horizontal plate rod 12. The middle of projection riser 11 surface is equipped with vertical first scale 17, the right-hand member in the middle of first scale 17 is equipped with horizontal second scale 18, second scale 18 right-hand member is equipped with first nail hole 111, the left end is equipped with second nail hole 112, fourth nail hole 114, first round hole 115, third nail hole 113 from a left side to the right side respectively in the middle of first scale 17, first round hole 115 is circular nail hole, first nail hole 111, second nail hole 112 are the rectangle, third nail hole 113, fourth nail hole 114 are oval nail hole, projection riser 11 right-hand member is from last to being equipped with first slot 19 and second slot 110 down, both ends are equipped with second round hole 116, third round hole 117 respectively about first slot 19, both ends are equipped with fourth round hole 118, fifth round hole 119 respectively about second slot 110.

As shown in fig. 1 to 3, the unit round roller 2 includes a first round tube 21, a second round tube 22, a first spoke plate 23, a second spoke plate 24, a first spoke plate 25, a second spoke plate 26, a first elastic bolt 27, and a first round gear ring 28, the first round tube 21 and the second round tube 22 are rigid round tubes, a first notch 217 is provided at the front end of the second round tube 22, a second nut 218 is provided at the rear end of the second round tube 22, and a thread is provided on the outer surface of the front end of the second round tube 22. Be equipped with first spoke board 23 and second spoke board 24 from a left side to the right side on the 22 horizontal line of second pipe, from last to being equipped with first spoke board 25 and second spoke board 26 down on the vertical line, surface is equipped with right angle baffle 210 about first spoke board 25 and the second spoke board 26 other end, right angle baffle 210 includes the right angle edge board that two rectangle hardboards link firmly perpendicularly, right angle baffle 210 uses first spoke board 25 and second spoke board 26 to indulge the symmetrical structure of spoke board for the symmetry axis, forms the inner grooved rail. The front side surface of the first spoke plate 23 is sequentially provided with a fifth nail hole 213 and a seventh nail hole 215 from left to right, the second spoke plate 24 is sequentially provided with a sixth nail hole 214 and an eighth nail hole 216 from right to left, the rear surface of the spoke plate is provided with a first circular tube 21, the first circular tube 21 and the second circular tube 22 are concentric circles, the rear end of the circumferential surface of the first circular tube 21 is provided with a first circular gear ring 28, the front end edge of the circumferential surface of the first circular tube 21 is provided with a first rectangular hole 29, the first rectangular hole 29 is arranged at a position opposite to each spoke plate, the first rectangular hole 29 is internally provided with a first elastic bolt 27, the first elastic bolt 27 comprises a first spring piece 211 and a first rectangular plate 212, the first spring piece 211 is provided with a vertical first rectangular plate 212, the first spring piece 211 is fixed on the inner wall of the first circular tube 21, and the first rectangular plate 212 penetrates out of the first rectangular hole 29, the unit round roller 2 is formed by inserting the rear end of the second round pipe 22 into the first round hole 115 from the front of the projection vertical plate 11, fixing the rear end of the projection vertical plate 11 by the second nut 218, and connecting the seventh nail hole 215 and the eighth nail hole 216 sequentially by passing through the third nail hole 113 and the fourth nail hole 114 by screws.

As shown in fig. 1, 3 and 4, the radius chord 3 includes a second rectangular plate 31 and a positioning sliding plate 32, the second rectangular plate 31 is a rigid straight plate, a first rectangular groove 33 is formed in the middle of the second rectangular plate 31, the positioning sliding plate 32 is disposed in the first rectangular groove 33, the positioning sliding plate 32 includes a third rectangular plate 321, a first circular ring piece 322, a first circular shaft 323, a fourth rectangular plate 324, a fifth rectangular plate 325 and a first spring 326, the first circular ring piece 322 is disposed at two ends of the surface of the third rectangular plate 321, a first circular shaft 323 is disposed in the first circular ring piece 322, the first circular shaft 323 is sleeved with the first spring 326 at two ends, the fourth rectangular plate 324 and the fifth rectangular plate 325 are sleeved at the middle of the first circular shaft 323, the fourth rectangular plate 324 and the fifth rectangular plate 325 are perpendicular to each other, the fifth rectangular plate 325 can rotate with the first circular shaft 323 when the fourth rectangular plate 324 is pushed reversely, the edge of the third rectangular plate 321 is provided with an elastic lock 327, and the radius chord 3 is formed by inserting two ends of the second rectangular plate 31 into the groove tracks formed by the two right-angle baffles 210 on the same side of the first spoke plate 25 and the second spoke plate 26 on the unit round roller 2.

As shown in fig. 1, 3, 5-6, the circular arc expansion plate 4 comprises a sixth rectangular plate 41, a rotating lamp holder 43, a red diode lamp 47, a first optical fiber 48, and a bidirectional switch 49, the sixth rectangular plate 41 is an elastic thick plate, the sixth rectangular plate 41 is provided with a second rectangular groove 42, the rotating lamp holder 43 comprises a third circular tube 431, an orientation base block 432, a disk lamp holder 433, and a transparent circular tube 434, two ends of the third circular tube 431 are provided on an inner wall of the second rectangular groove 42, the middle of the third circular tube 431 is provided with an orientation base block 432, the orientation base block 432 is a cylinder with a planar upper surface and lower surface, the third circular tube 431 and the orientation base block 432 are concentric circles, the upper surface of the orientation base block 432 is provided with a disk lamp holder 433, the middle of the disk lamp holder 433 is provided with positive and negative leads, the disk of a transparent thin plastic tube 4947, the rotating plastic tube 43 is provided with a transparent thin plate 491, the transparent thin plate 431, a transparent thin plate 491 is provided with a transparent thin plate 491, a transparent thin plate 491, a transparent thin plate 491, a transparent thin plate 26, a transparent thin plate 16, a transparent thin plate 26, a transparent thin plate 20, a transparent thin plate 16 is provided with a transparent thin plate, a transparent thin plate 16, a transparent thin plate 16 is provided, a transparent thin plate 16, a transparent thin plate 16 is provided, a transparent thin plate 16 is provided, a transparent thin plate 16 is provided, a transparent thin plate, a transparent thin plate plug is provided, a transparent thin plate plug is provided, a transparent thin plate is provided, a transparent thin plate 16 is provided, a transparent thin plate plug is provided, a transparent thin plate plug is provided, a transparent thin plate plug is provided, a transparent thin plate plug is provided, a transparent thin plate plug is.

As shown in fig. 1, 5 and 7, the inner tube inserted lamp 5 includes a rubber tube plug 51, a third transparent tube 52, a fourth transparent tube 53, a yellow diode lamp 54, a green diode lamp 55 and a second optical fiber 56, the rubber tube plug 51 is a truncated cone-shaped rubber block, the third transparent tube 52 is disposed on the lower bottom surface of the rubber tube plug 51, a pin lock 57 is disposed on the circumferential surface of the lower end of the third transparent tube 52, the pin lock 57 is T-shaped, one end of the pin lock passes through the third transparent tube 52, the fourth transparent tube 53 is disposed on the inner side of the lower end of the third transparent tube 52, the third transparent tube 52 and the fourth transparent tube 53 are both rigid transparent tubes, the fourth transparent tube 53 can move up and down in the third transparent tube 52 when the pin lock 57 is opened, the fourth transparent tube 53 is fixed when the pin lock 57 is closed, a first circular disc 511 is disposed at the opening of the end of the fourth transparent tube 53, the upper surface of the first circular disc 511 is disposed with the green diode lamp 55 and a third conducting wire 510, the third wire 510 is connected to the green diode lamp 55. A sixth round hole 59 is formed in the middle of the rubber pipe plug 51, a second optical fiber 56 is arranged in the sixth round hole 59, and the second optical fiber 56 extends into the fourth transparent pipe 53. The upper surface of the rubber tube plug 51 is provided with a yellow diode lamp 54 and a third plastic tube 58, a metal sheet is arranged in the third plastic tube 58, the metal sheet in the third plastic tube 58 is connected with a third lead 510, the inner insertion tube lamp 5 is formed by inserting the rubber tube plug 51 into a transparent circular tube 434 of the rotary lamp holder 43, and two third plastic tubes 58 are respectively sleeved on a positive electrode and a negative electrode on the disc lamp holder 433.

As shown in fig. 1, 3 and 8, the rotating mechanism 6 includes a third circular shaft rod 61, a fourth circular shaft rod 62, a second circular disc 63, a right-angle crank 64 and a second circular disc 65, the third circular shaft rod 61 is a hard circular rod, the circumferential surface of the third circular shaft rod 61 is respectively provided with the second circular disc 63 and the fourth circular pipe 62 from left to right, the fourth circular pipe 62 is sleeved at the right end of the first circular shaft rod 61, the circumferential surface of the fourth circular pipe 62 is symmetrically provided with a seventh rectangular plate 66 and an eighth rectangular plate 67, the second circular disc 63 and the third circular shaft rod 61 are concentric circles, the second circular disc 63 is provided with a ninth nail hole 68, the end of the third circular shaft rod 61 is provided with the second circular disc 65, the diameter of the second circular disc 65 is larger than the inner diameter of the fourth circular pipe 62, the front end of the third circular shaft rod 61 is provided with the right-angle crank 64, the right-angle crank 64 is formed by vertically fixing two hard rods, the fourth circular tube 62 swings the right-angle crank 64, the third circular shaft rod 61 drives the second circular disc 63 to rotate in the fourth circular tube 62, the rotating mechanism 6 is used for inserting the fourth circular tube 62 into the second circular tube 22, and the seventh rectangular plate 66 and the eighth rectangular plate 67 are inserted into the first notch 217.

As shown in fig. 1, 3 and 9, the angle measuring disc 7 includes a transparent circular plate 71, a fifth circular tube 72, a second circular gear ring 73 and a second elastic bolt 74, the transparent circular plate 71 is a thin transparent hard circular plate, a seventh circular hole 75 of a concentric circle is formed in the center of the transparent circular plate 71, the fifth circular tube 72 perpendicular to the transparent circular plate 71 is formed on the rear surface of the transparent circular plate 71, the second circular gear ring 73 is formed at the left end of the circumferential surface of the fifth circular tube 72, the second elastic bolt 74 is formed at the right end of the circumferential surface of the fifth circular tube 72, and the fifth circular tube 72 has the same structure as the first circular tube 21, the second circular gear ring 73, the first circular gear ring 28 and the second elastic bolt 74 as the first elastic bolt 27. An angle line 78 is arranged on the front side face of the transparent circular plate 71, a tenth nail hole 76 and an eleventh nail hole 77 are sequentially arranged on the horizontal line from left to right, the seventh circular hole 75 is sleeved on the second circular tube 22 in the unit circular roller 2 by the angle measuring disc 7, pins are sequentially and respectively fixed on the fifth nail hole 213 and the sixth nail hole 214 through the tenth nail hole 76 and the eleventh nail hole 77, and the fifth circular tube 72 is identical to the first circular tube 21. The second resilient latch 74 may be inserted into the fifth rectangular slot 412 and the seventh rectangular slot 413.

As shown in fig. 1, 9 and 10, the radial direction rotating lever 8 includes a ninth rectangular plate 81, a semicircular ring plate 82, a third triangular plate 83, a tenth rectangular plate 84 and a circular roller 813, the ninth rectangular plate 81 is a transparent straight hard plate strip, the right side surface of the ninth rectangular plate 81 is provided with the third triangular plate 83, the third triangular plate 83 is an isosceles triangle and is in the center line with the ninth rectangular plate 81, and the outer angle represents the arrow direction. The right end of the ninth rectangular plate 81 is provided with a ninth rectangular groove 87, a first sliding block 89 is arranged in the ninth rectangular groove 87, the first sliding block 89 is provided with a tenth rectangular plate 84, the upper top surface of the tenth rectangular plate 84 is provided with an arched plate 86, the middle of the tenth rectangular plate 84 is provided with a tenth rectangular groove 88, the tenth rectangular groove 88 is internally provided with a second sliding block 810, the side surface of the second sliding block 81 is provided with a fourth round shaft rod 85, and the tail end of the fourth round shaft rod 85 is provided with a round roller 813. The left end of the ninth rectangular groove 87 is provided with a third scale 811 along the center line, the left side surface of the ninth rectangular plate 81 is provided with a semicircular ring plate 82, the middle of the semicircular ring plate 82 is provided with a twelfth nail hole 812, the radial rotating rod 8 is formed by sleeving the semicircular ring plate 82 on a third round shaft rod 61 of the rotating mechanism 3, a pin penetrates through the twelfth nail hole 812 and the second round disc 65 to be fixed, and the surface where the third scale 811 is located faces forward.

As shown in fig. 1, 2 and 11, the tangential pallet 9 comprises an eleventh rectangular plate 91, a first straight rack 92, a second straight rack 93, a third straight rack 94, a fourth straight rack 95, a third elastic latch 910 and a fourth elastic latch 911, wherein the eleventh rectangular plate 91 is a transparent straight rack without elasticity, the bottom surface of the eleventh rectangular plate 91 is sequentially provided with the third straight rack 94 and the fourth straight rack 95 from front to back, the upper surface of the eleventh rectangular plate 91 is sequentially provided with an eleventh rectangular groove 97, a second straight rack 93, a fourth scale 96, a first straight rack 92 and a twelfth rectangular groove 98 from front to back, the second straight rack 93 and the first straight rack 92 are respectively arranged at corresponding positions of the third straight rack 94 and the fourth straight rack 95, the thirteenth rectangular groove 99 is arranged between the fourth scale 96 and the first straight rack 92, and the thirteenth rectangular groove 99 is sequentially arranged in the fourth scale 96 from left to right and is 0, Pi/2, 3 pi/2 and 2 pi, a third elastic bolt 910 and a fourth elastic bolt 911 are respectively arranged in the thirteenth rectangular slot 99, the third elastic bolt 910 and the fourth elastic bolt 911 have the same structure as the first elastic bolt 27, a base point of the third elastic bolt 910 is fixed on the bottom surface of the eleventh rectangular plate 91, and a base point of the fourth elastic bolt 911 is fixed on the upper surface of the eleventh rectangular plate 91. Both ends are equipped with first vaulting pole 912 and second vaulting pole 913 in proper order about the eleventh rectangular plate 91 trailing flank, tangential pallet 9 is in inserting second nail hole 112 and the first nail hole 111 on the projection riser 11 respectively with first vaulting pole 912 and second vaulting pole 913 in proper order and fixed.

The invention discloses a cosine function definition demonstration and image synthesizer, which adopts the working principle that light with linear propagation is converted into a curved aperture through an optical fiber according to the fact that an arc curve with equal curvature is expanded into a straight line with zero curvature, and the conversion between graphs is realized by utilizing a projection cylindrical surface. The method is characterized in that: the device comprises: the operation is simple, and all demonstration and image synthesis can be completed only by rocking the handle or pushing the roller under the initial condition; the functions are complete: the method can complete the mutual conversion of circular arcs and straight lines, demonstrate the definition of cosine functions through light spot distribution, expand unit circles by using the rolling of a disc, and directly synthesize expanded images into cosine curves. 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 invention discloses a cosine function definition demonstration and image synthesizer, which has the function of demonstrating cosine function definition in a unit circle, and comprises the following operation steps:

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 roller 2 is arranged on the vertical plate 1 of the bracket. 3] a first radius chord plate 3 is arranged on the right side of a first longitudinal spoke plate 25, a second radius chord plate 3 and three radius chord plates 3 are sequentially arranged on the left sides of the first longitudinal spoke plate 25 and the second longitudinal spoke plate 26, a fourth radius chord plate 3 is arranged on the right side of the second longitudinal spoke plate 26, and the closing direction of a fourth rectangular plate 324 on a positioning sliding plate 33 in the four radius chord plates 3 is clockwise. 4] placing a first circular arc board 4 on the first circular tube 21 between the second transversal bar 24 and the first longitudinal bar 25, placing a battery in the battery box 410 with one end of the power switch 411 at the second transversal bar 24, turning off the power switch 411, turning off the two-way switch 49 to the off position, i.e. with the forward corner teeth 494 inside the outer reverse corner teeth 495, with the side of the red diode light 47 and the first optical fiber 48 facing forward, similarly placing a second circular arc board 4 on the first circular tube 21 between the first transversal bar 23 and the first longitudinal bar 25, placing one end of the power switch 411 at the first longitudinal bar 25, placing a third circular arc board 4 on the first circular tube 21 between the first transversal bar 23 and the second longitudinal bar 26, placing one end of the power switch 411 at the first transversal bar 23, placing a fourth circular arc board 4 on the first circular tube 21 between the second transversal bar 24 and the second longitudinal bar 26, the power switch 411 is connected to the second spoke plate 26, and the first optical fibers 48 on the four circular arc panels 4 surround a circle. And 5] inserting the first tube inserting lamp 5 into the rotary lamp holder 43 at the lowest edge of the first circular arc exhibition board 4, opening the pin lock 57, adjusting the position and the angle between the third transparent tube 52 and the fourth transparent tube 53, fixing and closing the pin lock 57 by using the positioning slide plate 32 at the lowest edge when the central lines of the third transparent tube 52 and the fourth transparent tube 53 are perpendicular to the first radius chord board 3 and the first disc 511 is close to the first longitudinal spoke board 25, placing the remaining second, third, … and N tube inserting lamps 5 into the remaining rotary lamp holder 43 on the first circular arc exhibition board 4 by the same method, placing the N tube inserting lamps 5 on the second circular arc exhibition board 4 in sequence from top to bottom, and similarly placing 2N tube inserting lamps 5 on the third and fourth circular arc exhibition boards 4 respectively. 6, the angle measuring disc 7 is arranged on the unit round roller 2, the adjusting transparent round plate 71 is parallel to the projection vertical plate 11, and the second elastic bolt 74 is inserted into the fifth rectangular groove 412 and the seventh rectangular groove 413 of the arc display plate 4. 7, placing the rotating mechanism 6 on the unit round roller 2. 8] the radial rotating rod 8 is arranged on the rotating mechanism 6, the positions of the first sliding block 89 and the second sliding block 810 are adjusted, so that the round roller 813 is positioned behind the transparent round plate 71 of the angle measuring disc 7 and can roll along the angle measuring disc 7 along with the rotation of the radial rotating rod 8, the outer end of the arched plate 86 can touch the forward angle teeth 494 and the reverse angle teeth 495 of the arc display plate 4, and finally, the bolt lock 814 is used for fixing. 9, the tangential pallet 9 is arranged on the projection vertical plate 11, and the interval [0,2 pi ] between the tangential pallet 9 and the projection vertical plate 11 is adjusted to be aligned and then fixed.

Adjusting the initial position: 1] the bolt lock 814 is opened, and the right-angle crank 64, 2 is shaken to align the center line of the radial rotating rod 8 with the 0 DEG line of the protractor plate 7, and then the bolt lock 814 is rotated and fixed.

Thirdly, symbol setting: the center of the unit circle 1 is set to be O1, which is the projection point of the common center of the third circular shaft 61, the first circular tube 21 and the second circular tube 22 on the projection vertical plate 11. 2O 1 is the top point of the upper corner of the angle disc 7, the 0 degree line of the angle disc 7 is the initial side of the corner, and the central line of the radial rotating rod 8 is the final side of the corner. 3] the distance from the center line of the first optical fiber 48 to the point O1 on the circular arc board 4 is set to one unit, i.e., the first optical fiber 48 constitutes a unit circle. 4, the arc degree of the angle change formed by the rotation of the radial rotating rod 8 is x, and the corresponding arc length on the unit circumference is x. 5] the distance between the yellow diode lamp 54 and the green diode lamp 55 on the interior inserted tube lamp 5, that is, the length of the second optical fiber 56, represents the cosine function value, the first and the four circular arc display boards 4 are positive, and the second and the three circular arc display boards 4 are negative. The yellow diode lamp 54 is located at point a, the green diode lamp 55 is located at point B, the ABO1 is a right triangle, and AB is cosx. The serial number of the inner tube lamp 5 also represents the serial number of all the devices at the position of the inner tube lamp, namely, the serial numbers are marked as the first, the second, the … and N by counterclockwise on the first arc exhibition board 4 in the first quadrant, the serial numbers are marked as the N +1, the N +2, the …, the 2N +1, the …, the 3N +1, the … and the 4N by counterclockwise on the second, the third and the four arc exhibition boards 4 in the second, the third and the fourth quadrants, and the serial numbers are used by the yellow diode lamp 54, the green diode lamp 55, the two-way switch 49, the positioning sliding plate 32 and other devices at which the inner tube lamp 5 is positioned.

Fourthly, cosine function definition demonstration in the unit circle: 1] turn on the power switch 411, release the bolt lock 814. 2] slowly rock the quarter crank 64 counterclockwise, when the radial turn bar 8 reaches the end of the first length of the first optical fiber 48, the first bi-directional switch 49 is turned on, the first section of the first optical fiber 48, the yellow diode lamp 54, the green diode lamp 55 and the second optical fiber 56 of the first inner plug lamp 5 all illuminate, the first optical fiber 48 illuminates with an arc length x1, the second optical fiber 56 illuminates with a straight line segment cosx1, the right-angle crank 64 continues to be rocked, when the radial rotating rod 8 reaches the end point of the second section of the first optical fiber 48, the second two-way switch 49 is opened, the arc length of the first optical fiber 48 of the first and second sections is x2, the straight line segment of the second optical fiber 56 on the second inner tube inserting lamp 5 is cosx2, …, when the end point of the nth section of the first optical fiber 48 is reached, the nth two-way switch 49 is opened, the arc length of the first optical fiber 48 of the first to nth sections is xN, and the straight line segment of the second optical fiber 56 on the nth inner tube inserting lamp 5 is cosxN. 3] continue anticlockwise to wave right angle crank 64, radial bull stick 8 gets into the demonstration of second quadrant after the 90 line of excessive angle dish 7, when reaching the terminal point of the first optic fibre 48 of the (N + 1) th section, the (N + 1) th two-way switch 49 is opened, the first optic fibre 48 and the first interior intubate lamp 5 of the (N + 1) th section get into operating condition, the arc length that first optic fibre 48 shines is xN +1, the straight-line segment that the second optic fibre 56 that is located shines is in the below, record as the negative value, its size is xN +1, continue to wave right angle crank 64, stop after reaching 360 lines of angle dish 7, fix with bolted lock 814.

Fifthly, finishing the demonstration: 1] release the boltworks 814. 2] the right-angle crank 64 is rocked clockwise, the radial rotating rod 8 turns off the 4N, 4N-1, …, N +1, N, …,2 and 1 bidirectional switches 49 in sequence, the display lamps on the radial rotating rod are turned off in sequence, and finally the radial rotating rod 8 is fixed on the 0-degree line of the angle measuring disc 7. And 3, turning off the power switch 411, and returning the demonstration instrument to the initial state.

The invention discloses a cosine function definition demonstration and image synthesizer, which can expand the cosine function relation defined in a unit circle into a cosine curve on a rectangular coordinate system, namely, the non-orthogonal relation between a circular arc and a half-chord on the unit circle is converted into the orthogonal relation in the rectangular coordinate system, and a light spot or a light column is used for synthesizing an image of the cosine function, wherein the operation steps are as follows:

firstly, instrument assembly, secondly, initial position adjustment and demonstration cosine function definition are the same.

Thirdly, symbol setting: 1-6 is the same as that defined by demonstration cosine function, 7 is a rectangular coordinate system xOy on the projection vertical plate 11, the central line of the tangential pallet 9 is consistent with the horizontal axis Ox, and the length unit is consistent with that on the radial rotating rod 8.

And fourthly, the demonstration of the cosine function definition in the unit circle is the same as that of the demonstration of the cosine function definition.

Fifthly, equivalent movement of unit circle: 1] the rotational system composed of the rotational mechanism 6 and the radial direction rotary rod 8 is detached by adjusting the positions of the first slider 89 and the second slider 810. 2] the second nut 218 is removed, and the screw connected to the seventh nail hole 215 and the eighth nail hole 216 is unscrewed. 3, a unit round roller wheel vehicle is formed by drawing out a whole body consisting of the unit round roller wheel 2, the radius chord plate 3, the circular arc display plate 4, the inserted tube lamp 5 and the angle measuring disc 7 from the first round hole 115.

Sixthly, unit circle expansion and cosine curve synthesis: 1] the rear end of the second circular tube 22 of the unit circular roller car is inserted into the second circular hole 116 from the front of the projection vertical plate 11, and the second nuts 218 are screwed to the two ends of the second circular tube 22 respectively but not tightened. 2, the 0-degree line of the angle measuring disc 7 on the unit roller vehicle is vertical to the eleventh rectangular plate 91 on the tangential pallet 9, the first circular gear ring 28 is meshed with the first straight rack 92, the second circular gear ring 73 is meshed with the second straight rack 93, the first elastic bolt 27 and the second elastic bolt 74 at the 0-degree line on the unit roller vehicle are respectively aligned to the two third elastic bolts 910 at the 0 point on the eleventh rectangular plate 91, and the starting end of the first circular arc exhibition plate 4 is switched to the tangential pallet 9 by pressing force. 3] the two hands respectively grab the second nuts 218 to push rightwards, the unit circle roller vehicle rolls along the first straight rack 92 and the second straight rack 93, the rotating lamp holder 43 on the circular arc exhibition board 4 is pressed by the eleventh rectangular board 91, the rotating lamp holder 43 and the inner insertion tube lamp 5 thereof automatically turn to become vertical to the eleventh rectangular board 91, the first circular arc exhibition board 4 is pasted on the eleventh rectangular board 91 to be continuously unfolded and straightened, when the first circular arc exhibition board 4 is completely unfolded, the first circular arc exhibition board 4 is stopped and fixed by using two third elastic bolts 910 at the anti-thrust pi/2 position to switch, the unfolding of the interval [0, pi/2 ] is completed, and the light spots emitted by the first, second, … and N green diode lamps 55 are completely above the horizontal axis Ox. 4] the second nut 218 is screwed onto each end of the second round tube 22, and the unit round roller car is pulled out from the third round hole 117. 5] the front end of the second circular tube 22 of the unit circular roller car is inserted into the fourth circular hole 118 from the front of the projection vertical plate 11, and the second nuts 218 are screwed to the two ends of the second circular tube 22 respectively but not tightened. The operations 2 and 3 are repeated to complete the expansion of the second and the third arc display boards 4 in the interval [ pi/2, 3 pi/2 ], and the light spots emitted by the N +1, N +2, … and 3N green diode lamps 55 are all below the horizontal axis Ox. And 5, unloading the unit circular roller vehicle, repeating the operations 1-4 to finish the expansion of the fourth circular arc display plate 4 in the interval [3 pi/2, 2 pi ], wherein the light spots emitted by the 3N +1, 3N +2, … and 4N green diode lamps 55 are completely above the horizontal axis Ox. 6] the light spot emitted by the green diode lamp 55 of the 4N interpolation tube lamps 5 projected on the projection vertical plate 11 is a cosine curve, i.e. an image of the function.

Seventhly, finishing the demonstration: the power switch 411 is turned off and the demonstrator reverts to the initial state.

The cosine function definition demonstration and image synthesizer of the invention has economic value and application prospect: 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 cosine 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 are achieved, the whole country shares tens of thousands of schools, numerous families and exhibition places are provided, the number is considerable, the market prospect is very wide, and good economic benefit and social benefit are achieved.

The parts not involved in the present invention are the same as or can be implemented using the prior art.

As noted above, while the present invention has been shown and described with reference to certain preferred embodiments, it is not to be construed as limited thereto. 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 (3)

1. The cosine function definition demonstration and image synthesizer is characterized in that: including support riser, unit circle gyro wheel, radius chord plate, circular arc panel, interior pinup lamp, slewing mechanism, volume angle dish, radial bull stick, tangential pallet, two parts about support riser are arranged respectively to unit circle gyro wheel and tangential pallet, radius chord plate, volume angle dish, slewing mechanism are arranged in respectively on the unit circle gyro wheel, the circular arc panel is circular-arcly and arranges in on the circumference of unit circle gyro wheel respectively, slewing mechanism is arranged in to radial bull stick, interior pinup lamp is arranged in between circular arc panel and the radius chord plate.

2. The cosine function definition presentation and image synthesizer of claim 1, wherein: the circular arc panel is characterized in that a disc lamp holder is arranged on the upper surface of the directional base block, the middle of the disc lamp holder is provided with a positive electrode and a negative electrode of a lead, a transparent circular tube is arranged on the disc lamp holder, and the lamp holder is rotated to place the two ends of a third circular tube on the front side wall and the rear side wall of the second rectangular groove.

3. The cosine function definition presentation and image synthesizer of claim 1, wherein: the inner tube inserting lamp comprises a rubber tube plug, a third transparent tube, a fourth transparent tube, a yellow diode lamp, a green diode lamp and a second optical fiber, the third transparent tube is arranged on the lower bottom surface of the rubber tube plug, a pin lock is arranged on the periphery of the lower end of the third transparent tube, one end of the pin lock penetrates through the third transparent tube, the fourth transparent tube is arranged at the lower end of the third transparent tube, a first disc is arranged at an opening at the tail end of the fourth transparent tube, the green diode lamp and a third conducting wire are arranged on the upper surface of the first disc, and the third conducting wire is connected with the green diode lamp. The middle of the rubber pipe plug is provided with a sixth round hole, a second optical fiber is arranged in the sixth round hole, the upper surface of the rubber pipe plug is provided with a yellow diode lamp and a third plastic pipe, a metal sheet is arranged in the third plastic pipe, and the metal sheet in the third plastic pipe is connected with a third lead.

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