CN212289317U

CN212289317U - Negative quadratic power function demonstration and image drawing instrument

Info

Publication number: CN212289317U
Application number: CN202022075290.XU
Authority: CN
Inventors: 王书营
Original assignee: Nanjing Vocational University of Industry Technology NUIT
Current assignee: Nanjing Vocational University of Industry Technology NUIT
Priority date: 2020-09-21
Filing date: 2020-09-21
Publication date: 2021-01-05
Anticipated expiration: 2030-09-21

Abstract

The demonstration of the power function of the inverse square and image drawing appearance, characterized by, including: support, steering wheel, directional cursory, subtend painting brush, drawing board and cuboid deformer, the support lower part is arranged in to the steering wheel, the cuboid deformer is arranged in above the steering wheel, directional cursory is arranged in on the cuboid deformer, subtend painting brush is arranged in on the directional cursory, the support middle part is arranged in to the drawing board, and is multiple functional: the system can complete the relation demonstration, the characteristic analysis and the image drawing of a function y-cx-2 in a controllable numerical range, and intuitively express the actual meaning of the function property and the parameter; the structure is compact, the cost is low, the carrying is convenient, the precision is high, and the time and the labor are saved; the applicability is strong: the drawing can be demonstrated in various occasions.

Description

Negative quadratic power function demonstration and image drawing instrument

The technical field is as follows:

the utility model belongs to the teaching field, concretely relates to negative second power function demonstration and image drawing appearance.

Background art:

the function with the analytical expression of y-cx-2 is the most basic function which is discovered by human beings at the earliest and is continuously used in the future, is the most main content of medium mathematics and high mathematics research, has important characteristics, and is easy to cause the natural isolation of function forming reasons and function images because a teacher does not have a proper entity teaching aid and geometric scenes for guidance during teaching, so that a plurality of students feel very arduous during learning, and the double difficulties of teaching and learning are aggravated. At present, only a few demonstration devices of simple power functions are available in the market, and no special teaching aid about the function of the inverse second power exists. Therefore, a device capable of demonstrating the functional relationship and synchronously drawing a continuous function curve through the deformation phenomenon of equal volume of liquid according to the geometric shape of the liquid container is needed.

The utility model has the following contents:

in order to solve the technical problem, the utility model discloses the demonstration of negative second power function and image drawing appearance, include: 1. support, steering wheel, directional cursory, subtend painting brush, drawing board and cuboid deformer, the support lower part is arranged in to the steering wheel, the cuboid deformer is arranged in above the steering wheel, directional cursory is arranged in on the cuboid deformer, subtend painting brush is arranged in on the directional cursory, the support middle part is arranged in to the drawing board.

The orthogonal decomposer comprises a main push-pull device, a branch push-pull device, a fixed-shaft ring disc, a tangential baffle and a toothed belt wheel, wherein the main push-pull device comprises a box-type rail frame, a spur rack, a first round shaft rod, a gear and a stepping motor, the box-type rail frame comprises a cuboid box frame which is surrounded by four rectangular hard plates and is provided with an opening on the left side and the front side, the spur rack is arranged on the inner side of a rear vertical plate of the box-type rail frame, grooves are respectively arranged on an upper plate rod and a lower plate rod of the box-type rail frame, a third sliding block and a fourth sliding block are sequentially arranged in the upper groove and the lower groove, the first round shaft rod which is rotatably connected with the third sliding block and the fourth sliding block and extends out of two ends of the third sliding block and the fourth sliding block, the first round shaft rod is respectively provided with the gear and the stepping motor, the gear is meshed with the spur rack in the middle, the stepping motor is fixed on the outer side, the branch push-pull device is completely the same as the main push-pull device, the branch push-pull device is characterized in that an upper plate rod and a lower plate rod at the opening end of a box-type rail frame on the branch push-pull device are respectively and vertically fixed on a third slide block and a fourth slide block in the main push-pull device, two stepping motors are arranged on the same side, a first circular pipe fixedly sleeved outside a first circular shaft rod is arranged below the fourth slide block of the branch push-pull device, a first pressure rod and a second pressure rod are respectively arranged on two sides of a groove where the fourth slide block is located, a fixed shaft circular disc is arranged below the fourth slide block of the main push-pull device, the fixed shaft circular disc is a circular pipe fixed on the inner circumference of a circular disc with the outer circle radius of R, the circular pipe is sleeved outside the first circular shaft rod, the other end of the circular pipe is fixed below the fourth slide block, a tangential baffle plate is arranged on the fixed shaft circular disc, and the tangential baffle is, the cylindrical surface on the tangential baffle is smooth, other outer side surfaces are provided with sealing gaskets, the tangential baffle is used for fixing the arc at the upper end of the cylindrical surface on the outer circumference of the fixed-axis circular ring disc in a superposition manner, the right-angle plane at the outer side is respectively in parallel and perpendicular to the groove line where the fourth sliding block is located, the lower end of the first circular shaft rod is provided with a toothed belt wheel which rotates coaxially, and the toothed belt wheel can be meshed with the second toothed belt plate or the first toothed belt plate.

According to the technical scheme, the opposite direction painting brush comprises a second round tube, a round tube sleeve, a cross beam, a third round tube and the painting brush, wherein the round tube sleeve is arranged outside the second round tube, the round tube sleeve is a round tube with a pin on the outer surface and smooth in inner wall, the round tube sleeve is provided with a vertical cross beam, the outer end of the cross beam is provided with the vertical third round tube, the other end of the third round tube is provided with the vertical painting brush, and the painting brush is an elastic telescopic pen point pointing to the second round tube.

Compared with the prior art, the beneficial effects of the utility model are that:

1. the utility model discloses an appearance is drawn to negative second power function demonstration and image, easy operation as long as open the motor control key and just can accomplish whole work.

2. The utility model discloses an appearance is drawn to negative second power function demonstration and image, it is multiple functional: the system can complete the relation demonstration, the characteristic analysis and the image drawing of a function y-cx-2 in a controllable numerical range, and intuitively express the actual meaning of the function property and the parameter; the applicability is strong: the drawing demonstration device can demonstrate drawing in various occasions and is suitable for teaching, exhibitions and the like.

3. At present, no product exists in the market, and the negative second power function demonstration and image drawing instrument has a compact structure, low cost, safety, reliability and light weight.

Description of the drawings:

the accompanying drawings are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, together with the description of embodiments of the invention, serve to explain, without limitation, the invention in which:

fig. 1 is a schematic structural diagram of the present invention;

FIG. 2 is a schematic structural view of a bracket according to the present invention;

FIG. 3 is a schematic structural view of a steering wheel according to the present invention;

FIG. 4 is a schematic structural view of a barrel rack according to the present invention;

fig. 5 is a schematic structural view of the auxiliary chute of the present invention;

FIG. 6 is a schematic structural diagram of the orthogonal decomposition machine of the present invention;

FIG. 7 is a schematic structural view of the directional float of the present invention;

FIG. 8 is a schematic diagram of a structure of an opposite direction brush of the present invention;

fig. 9 is a schematic structural diagram of the drawing board of the present invention.

In the drawings are labeled: 1-bracket, 11-bracket bottom plate, 12-bracket top plate, 13-upright rod, 14-adjusting ground foot, 15-rectangular groove, 16-round shaft hole and 17-steering alignment line; 2-a steering wheel, 21-a steering wheel base plate, 22-a square supporting plate, 23-a round solenoid, 24-a hexagonal nut and 25-a crank; 3-a deformed bucket rack, 31-a bucket rack bottom plate, 32-a first vertical plate, 33-a second vertical plate, 34-a first toothed belt plate, 35-a second toothed belt plate, 36-a hinge, 37-a first scale, 38-a second scale, 39-a third scale, 310-a second clamp, 341-a positioning end plate, 342-a grid plate, 343-a guiding end plate, 344-a first clamp, 345-a cylindrical groove, 3421-a grid plate base plate, 3422-a grid plate auxiliary plate, 3423-an auxiliary plate cover sleeve, 3424-a sealing adhesive tape and 3425-a toothed lath; 4-auxiliary slideway, 41-first slideway rod, 42-second slideway rod, 43-first slide block, 44-second slide block and 45-slideway supporting rod; 5-orthogonal decomposer, 51-main push-pull device, 52-branch push-pull device, 53-fixed-axis circular disc, 54-tangential baffle, 55-toothed belt wheel, 56-first circular tube, 57-first pressure lever, 58-second pressure lever, 511-box rail frame, 512-straight rack, 513-third slide block, 514-fourth slide block, 515-first circular shaft rod, 516-gear, 517-stepping motor; 6-directional float, 61-directional base plate, 62-directional vertical plate, 63-float, 64-float stay bar, 65-fifth slide block, 66-supporting plate, 67-directional top plate, 68-fixed pulley, 69-upper directional hole, 610-lower directional hole, 611-counterweight with rope, 612-indicator light; 7-opposite brush, 71-second round tube, 72-round tube sleeve, 73-beam, 74-third round tube and 75-brush; 8-a drawing board, 81-a transparent bottom plate, 82-a paper clip, 83-a supporting plate supporting rod, 84-a fourth scale and 85-a fifth scale; 9-cuboid deformer.

The specific implementation mode is as follows:

as shown in the figure, the apparatus for demonstrating the inverse power function and drawing the image comprises: the device comprises a support 1, a steering wheel 2, a directional float 6, an opposite painting brush 7, a painting board 8 and a cuboid deformer 9. The steering wheel 2 is arranged in 1 lower part of support, 2 higher sides are arranged in steering wheel to cuboid deformer 9, directional cursory 6 is arranged in on cuboid deformer 9, directional cursory 6 is arranged in to painting brush 7 on, 1 middle part of support is arranged in to drawing board 8.

Support 1 includes support bottom plate 11, support roof 12, pole setting 13 and adjusts lower margin 14, support bottom plate 11 and support roof 12 are the same rectangle hardboard, the outer angle department of support bottom plate 11 and support roof 12 is equipped with vertically pole setting 13, the lower extreme of four pole settings 13 is equipped with respectively adjusts lower margin 14, support roof 12 front portion is equipped with rectangle groove 15, be equipped with round shaft hole 16 on the support bottom plate 11 respectively and turn to guideline 17, turn to guideline 17 relative with rectangle groove 15, the diameter of round shaft hole 16 with turn to guideline 17 coincidence.

The steering wheel 2 comprises a steering wheel base plate 21, a square supporting plate 22, a round solenoid 23 and a crank 25, the steering wheel base plate 21 is a hard disc with the diameter larger than that of a round shaft hole 16, the steering wheel base plate 21 is provided with the fixed square supporting plate 22, the square supporting plate 22 is a thick square hard plate with a baffle at the upper edge, one corner of the square supporting plate 22 is located at the circle center of the round surface on the steering wheel base plate 21, the fixed round solenoid 23 is arranged below the steering wheel base plate 21, the thread of the round solenoid 23 passes through the circle center of the steering wheel base plate 21 on the outer side axis, the diameter of the round solenoid 23 is the same as that of the round shaft hole 16, and the upper end and the outer end of the round solenoid 23 are respectively provided with a hexagon nut 24 and the crank 25.

The deformed barrel frame 3 comprises a barrel frame bottom plate 31, a first vertical plate 32, a second vertical plate 33, a first toothed belt plate 34 and a second toothed belt plate 35 which are enclosed to form an open barrel-shaped container, the barrel frame bottom plate 31 is a square hard plate with a smooth surface, a vertical first vertical plate 32 is arranged on the rear edge of the barrel frame bottom plate 31, the first vertical plate 32 is a rectangular transparent hard plate with a smooth inner surface, a first scale 37 and a second scale 38 are respectively arranged at the left edge and the lower edge of the rear surface of the first vertical plate 32, the first toothed belt plate 34 is arranged in front of the first vertical plate 32, the first toothed belt plate 34 comprises a positioning end plate 341, a grid plate 342 and a guide end plate 343, the positioning end plate 341 is a cuboid hard plate strip, a first clamp 344 is arranged at one side of the positioning end plate 341, a fixed grid plate 342 is arranged at the other side of the positioning end plate 341, the grid plate 342 comprises a grid plate base 3421, a grid plate 342, The fence comprises a fence auxiliary plate 3422 and a toothed lath 3425, wherein the fence base 3421 is a rectangular thin hard lath, the outer side surface of the fence base 3421 is respectively provided with the fence auxiliary plate 3422 and a sealing adhesive tape 3424, the fence auxiliary plate 3422 is a rectangular hard lath with a section length and width smaller than that of the fence base 3421 and is fixed in the middle, a half of the sealing adhesive tape 3424 with certain elasticity is closely attached to the rest side of the fence auxiliary plate 3422, the fence auxiliary plate 3422 is provided with a rectangular open auxiliary plate cover 3423, the auxiliary plate cover 3423 is sleeved on the fence auxiliary plate 3422 to form a rectangular sealing lath which is the same as the outer side surface of the fence base 3421, the middle part and the edge of the inner side surface of the fence base 3421 are respectively provided with the fixed toothed lath 3425 and a hinge 36, and the toothed lath 3425 is a gear-shaped lath with a tooth root thickness smaller. More than one grid plate 342 is mutually linked to form a toothed belt-shaped grid which can be folded or unfolded in a one-way mode, the inner sides of two adjacent grid plates 342 are linked through a hinge 36, the maximum opening angle is a flat angle, the outer sides of the two adjacent grid plates 342 are hermetically connected through a sealing adhesive tape 3424, the outer side surfaces of all the grid plates 342 are connected into a rectangular closed plane when the flat angle is formed, toothed laths 3425 on the inner side surfaces form toothed teeth, a fixed guide end plate 343 is arranged at the grid plate 342 at the tail end, the guide end plate 343 is a cuboid hard lath of which the outer side surface is attached with a sealing gasket, and a cylindrical groove 345 is. The first toothed belt plate 34 is formed by fixing a positioning end plate 341 on the right edge of the first vertical plate 32 by using a first clamp 344, the straightened outer side surface and the straightened lower bottom surface are respectively superposed with the inner sides of the first vertical plate 32 and the barrel frame bottom plate 31, the left edge of the barrel frame bottom plate 31 is provided with a vertical second vertical plate 33, the second vertical plate 33 is the same as the first vertical plate 32, the rear edge is vertically connected with the first vertical plate 33, the outer lower edge of the second vertical plate 33 is provided with a third scale (39), three orthogonal axes of a common ridge space orthogonal coordinate system in which the first scale 37, the second scale 38 and the third scale (39) are positioned are arranged, an intersection point O is an original point, the inner side of the second vertical plate 33 is provided with a second toothed belt plate 35, the second toothed belt plate 35 is almost the same as the first toothed belt plate 34, only the upper and lower width values of the toothed belt plate are larger than those of the first toothed belt plate 34, the left and right width values of the guide end plate 35 of the second toothed belt plate 343 are smaller than those of the first toothed belt plate, the second fixture 310 is arranged on the outer edge of the inner side of the guide end plate 343 of the second toothed belt plate 35. The second toothed belt plate 35 is mounted on the second vertical plate 33 in the same manner as the first toothed belt plate 34, the guide end plate 343 is located at one end of the origin O, the deformed barrel frame 3 is internally provided with the auxiliary chute 4, and the orthogonal decomposition machine 5 and the displaced orthogonal decomposition machine 5 are respectively arranged on a box frame consisting of the deformed barrel frame 3 and the auxiliary chute 4.

The auxiliary slideway 4 comprises a first slideway rod 41, a second slideway rod 42 and a slideway stay rod 45, the upper end of the slideway stay rod 45 is respectively provided with the first slideway rod 41 and the second slideway rod 42 which are perpendicular to each other, the first slideway rod 41 and the second slideway rod 42 are both rectangular hard plate rods provided with grooves, and a first sliding block 43 and a second sliding block 44 are respectively arranged in the grooves of the first slideway rod 41 and the second slideway rod 42.

The orthogonal decomposition machine 5 comprises a main push-pull device 51, a branch push-pull device 52, a fixed-axis circular disc 53, a tangential baffle 54 and a toothed belt wheel 55. The main puller 51 comprises a box rail frame 511, a spur rack 512, a first round shaft 515, a gear 516 and a stepping motor 517. The box-type rail frame 511 is a cuboid box frame which comprises four rectangular hard plates and is enclosed by the four rectangular hard plates, the left surface and the front surface of the box-type rail frame 511 are open, a spur rack 512 is arranged on the inner side of a rear vertical plate of the box-type rail frame 511, grooves are respectively arranged on an upper plate rod and a lower plate rod of the box-type rail frame 511, a third sliding block 513 and a fourth sliding block 514 are sequentially arranged in the upper groove and the lower groove, a first round shaft rod 515 which is connected in a rotating manner and extends out of two ends is arranged on the third sliding block 513 and the fourth sliding block 514, a gear 516 and a stepping motor 517 are respectively arranged on the first round shaft rod 515, the gear 516 is in the middle and is meshed with the spur rack 512, the stepping motor 517 is fixed on the outer side of the third sliding block 513, the rotating shaft of the stepping motor is connected with the upper end of the first round shaft rod 515, a branch push-pull device 52 is arranged on the main push-pull device 51, the branch push-pull device 52 is completely identical with the main, the two stepping motors 517 are arranged on the same side, a first circular tube 56 fixedly sleeved outside a first circular shaft rod 515 is arranged below a fourth sliding block 514 of the branch push-pull device 52, a first pressing rod 57 and a second pressing rod 58 are respectively arranged on two sides of a groove where the fourth sliding block 514 is located, a fixed-axis circular disc 53 is arranged below the fourth sliding block 514 of the main push-pull device 51, the fixed-axis circular disc 53 is a circular disc with an outer circle radius of R, a section of circular tube is fixed on the inner circumference of the circular disc, the circular tube is sleeved outside the first circular shaft rod 515, the other end of the circular tube is fixed below the fourth sliding block 514, a tangential baffle 54 is arranged on the fixed-axis circular disc 53, the tangential baffle 54 is one of four corner cylinders left after an inscribed cylinder is removed from a regular four-square prism body with a side length of 2R, sealing gaskets are arranged on other smooth outer side surfaces of the tangential baffle 54, and the tangential baffle 54 is used for fixing the upper end of an arc, the right-angle plane of the outer side is respectively in parallel and perpendicular to the straight line of the groove where the fourth sliding block 514 is located, the lower end of the first round shaft lever 515 is provided with a gear belt wheel 55 which rotates coaxially, and the gear belt wheel 55 can be meshed with the second gear belt plate 35 or the first gear belt plate 34.

The directional float 6 comprises a directional base plate 61, a directional vertical plate 62, a float 63 and a float stay bar 64, the directional base plate 61 is a rectangular hard thin plate, a lower directional hole 610 is arranged at one end edge of the directional base plate 61, the float stay bar 64 is arranged in the lower directional hole 610, the vertical supporting plate 66 and the float 63 are respectively arranged at the upper end and the lower end of the float stay bar 64, the float 63 is provided with an indicator lamp 612, the vertically fixed directional vertical plate 62 is arranged in the middle of the upper surface of the directional base plate 61, the directional vertical plate 62 is a hard plate strip with a groove in the middle, a fifth sliding block 65 is arranged in the groove of the directional vertical plate 62, the fifth sliding block 65 is connected with the supporting plate 66, the upper end of the directional vertical plate 62 is provided with a vertical directional top plate 67, the directional top plate 67 is respectively provided with a fixed pulley 68 and an upper directional hole 69, the fixed pulley 68 is provided with a rope counterweight 611, and the rope, for balancing the pressure in the up-and-down floating of the buoy 63, the outer end of the soft rope with the rope counterweight 611 is connected to the supporting plate 66 through the fixed pulley 68 and the upper directional hole 69, and the upper directional hole 69 is consistent with the lower directional hole 610.

The opposite direction painting brush 7 comprises a second round pipe 71, a round pipe sleeve 72, a cross beam 73, a third round pipe 74 and a painting brush 75, wherein the round pipe sleeve 72 is arranged outside the second round pipe 71, the round pipe sleeve 72 is a round pipe with a pin on the outer surface and smooth inner wall, the vertical cross beam 73 is arranged on the round pipe sleeve 72, the vertical third round pipe 74 is arranged at the outer end of the cross beam 73, a vertical painting brush 75 is arranged at the other end of the third round pipe 74, and the painting brush 75 is an elastic telescopic pen point pointing to the second round pipe 71.

Drawing board 8 includes transparent bottom plate 81, paper clip 82, layer board branch 83, fourth scale 84 and fifth scale 85, transparent bottom plate 81 is the hard sheet metal of smooth transparent rectangle, be equipped with paper clip 82, fourth scale 84, fifth scale 85 on transparent bottom plate 81's the smooth surface respectively, fourth scale 84, fifth scale 85 mutually perpendicular intersect at the middle part, be equipped with layer board branch 83 on a set of parallel arris of transparent bottom plate 81 respectively.

The working principle is as follows:

the utility model discloses an inverse square power function demonstration and image drawing appearance's theory of operation is, according to the certain bottom surface area of cuboid volume and high between inverse ratio, and with bottom surface square side length square inverse ratio, utilize the cylinder forming method to carry out the cuboid closed container that perpendicular isometric separation structure height invariable bottom surface square side length changes with the rectangle plane of two couples of coincidence and quadrature, deformation principle formation measurement system and motion change relation with the help of quantitative liquid, the constant velocity rate through a plurality of motors rotates the synthesis and the synchronous image drawing of accomplishing the moving point. The method is characterized in that: the operation is simple, and all work can be completed only by starting the motor control key. The functions are complete: the system can complete the relation demonstration, the characteristic analysis and the image drawing of a function y-cx-2 in a controllable numerical range, and intuitively express the actual meaning of the function property and the parameter; the structure is compact, the cost is low, the carrying is convenient, the precision is high, and the time and the labor are saved; the applicability is strong: the drawing can be demonstrated in various occasions.

The utility model discloses an appearance is drawn to negative second power function demonstration and image, have demonstration function y ═ x-2 function of relation, the operating procedure is:

firstly, assembling an instrument: 1, the bracket 1 is placed on a stable plane, the anchor feet 14 are rotated and adjusted to enable the upright rod 13 to be in a vertical state, and the bracket bottom plate 11 is in a horizontal state. 2, the steering wheel 2 is arranged on a bracket bottom plate 11 of the bracket 1, and a crank 25 is shaken to enable the front edge of the square supporting plate 22 to be superposed with the right side of the steering alignment line 17 and then fixed by a hexagon nut 24. And 3, fixing the assembled cuboid deformer 9 on the steering wheel 2, wherein the second vertical plate 33 is parallel to the steering alignment line 17. 4] the directional float 6 is placed on a second decomposer of the cuboid deformer 9. And 5, placing the drawing board 8 on the support 1 in a vertical state, wherein the fourth scale 84 and the original point O are respectively consistent with the third scale 39 and the angular point O on the cuboid deformer 9. 6] place opposing brush 7 on directional float 6 with brush 75 in front of panel 8, with the tip of brush 75 pointing towards indicator 612 and making sliding contact with panel 8 when extended.

II, explanation and symbol setting: let H denote the inverse quadratic power function demonstration and image drawing instrument, the cuboid formed by the liquid container in the cuboid deformer 9 is denoted as W, the cuboid of the liquid in W is denoted as W, the side length of the square on the bottom surface of W is x, the height is y, the volume of W is x2y, when x2y is 1, y is x-2, and x is not equal to 0. The volume of the inner float 63 in 1W below the liquid level is ignored, the horizontal section is as small as possible, and the sliding friction force between the painting brush 75 and the painting board 8 can be ignored or fine adjustment of the weight 611 with a rope is included. 2] the indicator 612 moves horizontally along with the tangential baffle 54 (i.e. the length x is the same as the side length x) and also moves up and down synchronously with the liquid level (i.e. the height y is the same as the side length x), when the float 63 moves horizontally along the upper transverse axis of the drawing board 8, the position change of the point P projected by the indicator 612 on the first vertical plate 32 or the second vertical plate 33 represents the locus of the moving point, when the first vertical plate 32 or the second vertical plate 33 is parallel to the drawing board 8, the third scale 39 and the first scale 37 represent the first quadrant of the coordinate system Oxy, and the first scale 37 and the second scale 38 represent the second quadrant of the coordinate system Oxy. 3] the movement of the pen tip of the brush 75 coincides with the indicator light 612. 4] coordinate system on drawing board 8 is set to O1xy, and contact point of brush 75 pen tip on drawing board 8 is Q. When drawing, O1xy and Oxy are overlapped, and the projection of the point P is the point Q on the image. And 5] the liquid level is kept horizontal all the time when the liquid in the tank deforms. All the stepping motors 517 comprise a switch K for control, the side length of the bottom surface of the W is increased when the K is in a positive gear, the side length of the bottom surface of the W is decreased when the K is in a negative gear, and the side length of the bottom surface of the W is unchanged when the K is in a zero gear.

Thirdly, adjusting the initial position: 1 important points Q1(b, b-2), Q2(-b, b-2), Q3(1,1), Q4(-1, -1), Q5(a, a-2), Q6(-a, a-2),0< b <1, a >1 are drawn in O1xy in front of transparent bottom plate 81 of drawing board 8. 2] detach the tip of the brush 75 from the palette 8. And 3, opening the switch K to adjust the unfolded surfaces of the tangent baffles 54 on the second decomposer and the orthogonal decomposer 5 to be positioned at the positions of the third scale 39 and the scale value of the second scale 38 which are both 1. 4] the liquid is injected into the space W, and the injection is stopped when the liquid level reaches the scale value 1 of the first scale 37. 5] the float 63 is adjusted to be in a natural floating state on the liquid surface by using the string-type balance weight 611.

Fourthly, demonstrating functional relation: 1] see through panel 8 that the back projected point of indicator 612 on panel 8 is at point Q3, where w is a square with a unit of edge length. 2] the switch K is in the positive gear, the liquid level in the W is reduced along with the increase of the side length of the negative square of the bottom surface, the indicator lamp 612 starts to move from a point Q3 to a point Q5 towards the right lower part, when the indicator lamp 612 reaches a point Q5, the K is in the zero gear, and the process shows that the height y of the W is rapidly reduced along with the increase of the x. 3] the switch K is in the negative gear, the indicator lamp 612 starts from the point Q5 and returns to the upper left point Q3, continues to move to the upper left point Q1 after passing through the point Q3, and when the indicator lamp 612 reaches the point Q1, the switch K is in the zero gear, which indicates that the height y of w is rapidly increased as x is decreased.

Fifthly, finishing the demonstration: h is restored to the initial state.

The utility model discloses an appearance is drawn to negative second power function demonstration and image has analytical function y ═ x-2 characteristic and draws the function of image, and the operating procedure is:

firstly, assembling an instrument: the operation steps are the same as those of the function of demonstrating functional relationship.

II, explanation and symbol setting: the operation steps are the same as those of the function of demonstrating functional relationship.

Thirdly, adjusting the initial position: 1] A coordinate system O2xy and important points Q1(b, b-2), Q2(-b, b-2), Q3(1,1), Q4(-1, -1), Q5(a, a-2), Q6(-a, a-2),0< b <1, a >1 are drawn on the paper M. 2-4 ] is the same as the operation steps with the function of demonstrating functional relations. 5] sheet M is placed on palette 8, O2xy coincides with O1xy, and the important point also coincides.

Fourthly, analyzing functional characteristics and drawing an image: 1] the tip of the brush 75 is extended and located at point Q3, where w is a square with a single unit of edge length. 2] with switch K in the forward position, brush 75 moves from point Q3 to the lower right point Q5 and draws a curve, and when brush 75 reaches point Q5, with K in the zero position, we see a monotonically decreasing course from Q3 to Q5. And 3] when the switch K is in the negative gear, the brush 75 returns from the point Q5 to the point Q3 along the original path, the brush is continuously reversely increased to the point Q1 after passing through the point Q3, when the point Q1 is reached, the K is in the zero gear, and the pen point of the brush 75 is retracted to be separated from the drawing board 8. 4] plot a curve Q1Q5 for x >0 on M, where point Q3 indicates w is a square with a ridge length of 1, and if the curve continues to run in the positive direction when reaching point Q5 or in the negative direction when reaching point Q1, the curve Q1Q5 will run in opposite directions, approaching but not intersecting the positive direction of axes O2x and O2y, respectively. And 5, detaching the directional float 6 and the opposite painting brush 7, and shaking the crank 25 anticlockwise to enable the first vertical plate 32 on the cuboid deformer 9 to be superposed with the left side of the turning alignment line 17 and then fixing the cuboid deformer by using a hexagonal nut 24. 6] the directional float 6 is placed on the orthogonal decomposer 5 of the rectangular parallelepiped deformer 9 with the tip of the brush 75 extended and located at point Q2 on M. 7] with switch K in the forward position, brush 75 moves from point Q2 to point Q6 to the lower left and past point Q4 to draw a curve, which reaches point Q6 with K in the zero position and the tip of brush 75 retracted away from palette 8. 8] plot a curve Q2Q6 for x <0 on M, where point Q4 indicates w is a cube with a ridge length of 1, curve Q2Q6 is symmetric about axis O2y with curve Q1Q5, and other characteristics are similar to those of x > 0.

Fifthly, finishing the demonstration drawing: the paper sheet M is removed to restore H to the original state.

The utility model discloses an appearance is drawn to power of negative second function demonstration and image has demonstration, analysis, drawing function y the function of cx-2 image, and operating procedure and function y are the almost the same of cx-2, and the liquid level reachs the scale interval of first scale 37 and stops when stopping pouring into when the difference lies in to pouring into liquid in W when being c, and c >0, other are identical.

The utility model relates to an economic value and application prospect of negative second power function demonstration and image drawing appearance: along with the technical progress and economic development, advanced equipment is required to improve the teaching effect and the social service quality, and particularly, a tool which is simple to operate and convenient to use and can comprehensively express the negative quadratic power function relationship and properties and draw images is urgently needed for basic course teaching and middle school mathematics teaching of colleges and universities, only thousands of schools are shared in the nation of advanced education, and a plurality of middle schools, vocational schools and the like are available, so that the quantity is considerable, the market prospect is very wide, and good economic benefits and social benefits are achieved.

The technical means disclosed by the scheme of the utility model is not limited to the technical means disclosed by the technical means, but also comprises the technical scheme comprising the equivalent replacement of the technical features. The present invention is not to be considered as the best thing, and belongs to the common general knowledge of the technicians in the field.

Claims

1. The demonstration of the power function of the inverse square and image drawing appearance, characterized by, including: support, steering wheel, directional cursory, subtend painting brush, drawing board and cuboid deformer, the support lower part is arranged in to the steering wheel, the cuboid deformer is arranged in above the steering wheel, directional cursory is arranged in on the cuboid deformer, subtend painting brush is arranged in on the directional cursory, the support middle part is arranged in to the drawing board.

2. The inverse power function presentation and image rendering instrument of claim 1, wherein: the orthogonal decomposition machine comprises a main push-pull device, a branch push-pull device, a fixed shaft circular disc, a tangential baffle and a toothed belt wheel, wherein the main push-pull device comprises a box-type rail frame, a straight rack, a first circular shaft rod, a gear and a stepping motor, the box-type rail frame comprises a rectangular box frame with a left surface surrounded by four rectangular hard plates and an opening in the front surface, the straight rack is arranged on the inner side of a rear vertical plate of the box-type rail frame, grooves are respectively arranged on an upper plate rod and a lower plate rod of the box-type rail frame, a third sliding block and a fourth sliding block are sequentially arranged in the upper groove and the lower groove, the first circular shaft rod which is rotationally connected with the third sliding block and the fourth sliding block and extends out of two ends is arranged on the third sliding block and the fourth sliding block, the gear and the stepping motor are respectively arranged on the first circular shaft rod, the gear is meshed with the straight rack in the middle part, the stepping motor is fixed on the, the branch push-pull device is completely the same as the main push-pull device, the branch push-pull device is characterized in that an upper plate rod and a lower plate rod at the opening end of a box-type rail frame on the branch push-pull device are respectively and vertically fixed on a third slide block and a fourth slide block in the main push-pull device, two stepping motors are arranged on the same side, a first circular pipe fixedly sleeved outside a first circular shaft rod is arranged below the fourth slide block of the branch push-pull device, a first pressure rod and a second pressure rod are respectively arranged on two sides of a groove where the fourth slide block is located, a fixed shaft circular disc is arranged below the fourth slide block of the main push-pull device, the fixed shaft circular disc is a circular pipe fixed on the inner circumference of a circular disc with the outer circle radius of R, the circular pipe is sleeved outside the first circular shaft rod, the other end of the circular pipe is fixed below the fourth slide block, a tangential baffle plate is arranged on the fixed shaft circular disc, and the tangential baffle is, the cylindrical surface on the tangential baffle is smooth, other outer side surfaces are provided with sealing gaskets, the tangential baffle is used for fixing the arc at the upper end of the cylindrical surface on the outer circumference of the fixed-axis circular ring disc in a superposition manner, the right-angle plane at the outer side is respectively in parallel and perpendicular to the groove line where the fourth sliding block is located, the lower end of the first circular shaft rod is provided with a toothed belt wheel which rotates coaxially, and the toothed belt wheel can be meshed with the second toothed belt plate or the first toothed belt plate.

3. The inverse power function presentation and image rendering instrument of claim 1, wherein: subtend painting brush includes second pipe, pipe box, crossbeam, third pipe and painting brush, the second pipe is equipped with the pipe box outward, the pipe box is that its outside has the smooth pipe of inner wall of pin, the pipe is sheathe in and is equipped with the vertically crossbeam, the outer end of crossbeam is equipped with the vertically third pipe, the other end of third pipe is equipped with the vertically painting brush, the painting brush is the directional second pipe of elastic telescopic nib.