CN106945436B - Compound function space-time is demonstrated and Image Rendering instrument - Google Patents

Abstract

The invention discloses a compound function four-dimensional space demonstration and image drawing instrument; the technical problem to be solved is that the instruments in the prior art mentioned in the background technology cannot demonstrate four-dimensional mapping, space curved surface, complex variable function and draw the corresponding complex plane curve technical problems. The technical solution adopted: a compound function four-dimensional space demonstration and image drawing instrument, including a bracket, a projection plane, an upper section plane, a generating complex plane, a real part surface, an imaginary part surface, a sliding round rod, a moving bracket, a drawing mechanism, and a connection system. The invention has the advantages of simple operation, demonstration and drawing can be performed as long as the handle on the device is pushed; complete functions: it can demonstrate the changes of multiple space curved surfaces and draw their corresponding curves on the complex plane, and can also be used to analyze complex variable functions Experiments such as analysis and integration; strong applicability: choosing different forms of spatial surfaces can be demonstrated and drawn on various occasions.

Description

Composite function four-dimensional space demonstration and image plotter

technical field

The invention relates to a compound function four-dimensional space demonstration and image drawing device, which is to place two moving points on the same straight line on two real curved surfaces u=f(x, y), v=g(x, y) The vertical displacement of , respectively mapped to the real axis and imaginary axis on another complex plane through the synthesis mechanism, and draws the corresponding plane curve, specifically a method that can demonstrate that the change of two real functions in the complex variable function leads to The change of points on another complex plane, especially the movement of points on different real surfaces can be transformed into the trajectory of points on the complex plane, which truly reflects the four-dimensional space characteristics formed between the two complex planes.

Background technique

With technological progress and economic development, higher education needs more and more advanced equipment to improve teaching effects and practical training. Knowledge of complex variable functions, mapping, and spatial analytic geometry is an important content of university study in my country. Due to the influence of real variable functions and Due to the influence of geometric meaning, it is extremely difficult to express multiple functions in one system at the same time. The teaching mainly relies on description or illustration with two simple plane figures, which is not easy for junior college students who are limited to two-dimensional or three-dimensional real space. Understand that some physical devices are urgently needed in teaching to truly represent what has been learned.

For a long time, no model or device that reflects the four-dimensional complex plane with a space surface has been found, but some similar devices that reflect the local area have appeared; The transparent conical shell is injected with water, and there are a number of fluorescent particles floating on the water surface. The conical shell can be directly irradiated with a light source, and the various formation processes of the conic curve can be displayed according to the distribution of fluorescent particles in the conical shell. This achievement is completely based on the distribution of fluorescent particles. Displaying conic curves without spatial curves on real surfaces cannot simultaneously demonstrate projected curves.

The document with the patent application number CN200820069548.1 provides a "conic curve demonstration instrument", which combines a magnet and a thin wire, winds the pen around the thin wire, and turns the screw to adjust the length of the thin wire to accurately draw an ellipse or Hyperbola, this achievement is mainly to draw curves and lacks the mapping function of four-dimensional space, so it is difficult to reflect the formation process of complex variable functions.

The patent application number is 201420395360.1, which provides a "conic curve plotter", including a longitudinal base frame, a transverse base frame, a sliding plate, a slider, a wire winding device, a first rope, and a second rope; the longitudinal base frame It is vertically connected with the transverse base frame, and the side connected with the transverse base frame is provided with a sliding groove. This achievement is mainly for drawing curves and lacks the functions corresponding to two complex planes, so it is difficult to reflect the process of complex variable functions.

Contents of the invention

The technical problem to be solved by the present invention is: aiming at the technical problem that the instruments in the prior art mentioned in the background technology cannot demonstrate four-dimensional mapping, space curved surface, complex variable function and draw corresponding complex plane curves.

In order to overcome the functions that are lacking or not available in existing instruments and devices, the purpose of the present invention is to provide a compound function four-dimensional space demonstration and image plotter that can demonstrate four-dimensional mapping, space surfaces, complex variable functions and draw corresponding complex plane curves ; Composite function four-dimensional space demonstration and image plotting instrument is the vertical displacement of two moving points on the same straight line on two real curved surfaces u=f(x, y), v=g(x, y), through The synthetic mechanism is respectively mapped to the real axis and the imaginary axis on another complex plane, and the corresponding plane curve is drawn, specifically, it is a method that can demonstrate that the change of two real functions in the complex variable function results in another complex plane The change of the upper point, especially the movement of points on different real surfaces can be transformed into the motion trajectory of points on the complex plane, which truly reflects the four-dimensional space characteristics formed between the two complex planes.

In order to solve the problems of the technologies described above, the technical solution adopted in the present invention is:

A compound function four-dimensional space demonstration and image plotter, including a bracket, a projection plane, an upper section plane, a generating complex plane, a real part surface, an imaginary part surface, a sliding round rod, a moving bracket, a drawing mechanism, and a connection system,

The bracket includes a baffle and four uprights, each upright is a straight cylindrical rod, the baffle is a rectangular hard plate, and the four uprights are vertically fixed on the four right angles of the baffle respectively, and each upright is provided with a Taper feet, with suction cups inside the taper legs, and adjusting nuts between each vertical rod and the taper legs;

The upper sectional plane is fixed on the upper end of the pole;

The projection plane is fixed on the middle and lower part of the pole and is between the upper section plane and the baffle;

The real part surface is fixed on the upper plane of the projection plane;

The imaginary part surface is fixed on the lower base of the upper section plane;

The sliding rod passes through the real part surface and the imaginary part surface, and the lower and upper ends are respectively connected with the projection plane and the upper sectional plane;

The mobile bracket is fixed on the upper end of the sliding rod;

The generated complex plane is fixed on the mobile support, and the drawing mechanism is connected to the generated complex plane;

The drawing mechanism, the real part surface, the imaginary part surface, and the sliding round bar form a moving unity through a connection system.

As an improvement to the technical solution of the present invention, the upper sectional plane includes a transparent hard plate, a groove slider and a pipe shaft,

There are curve L21 groove and curve L22 groove on the transparent hard board, the curve L21 groove and the curve L22 groove intersect, the groove slider is embedded in the curve L21 groove or the curve L22 groove, and the groove slider There is a tube shaft inside; there are many square holes on the transparent hard plate, and ring clamps are set on the four right angles of the transparent hard plate;

The upper sectional plane is inserted into the four vertical rods on the support one by one through the four ring clamps and is located at the upper ends of the four vertical rods.

As a further improvement to the above technical solution, the imaginary part surface includes the upper kerf line, the curve L41 slide rail, the curve L42 slide rail, the white line net and the second slider with the card,

The upper kerf line is a closed coil made of hard metal wire. The two ends of the curve L41 slide rail and the curve L42 slide rail are respectively fixed on the upper kerf line. The curve L41 slide rail curve L42 slide rail and the upper kerf edge The lines are connected by a white wire net, the curve L41 slide rail and the curve L42 slide rail intersect, and the second belt card slider is arranged on the curve L41 slide rail or the curve L42 slide rail, and the second belt card slider is provided with a connecting ring There are a plurality of ring-shaped fixing cards on the ridge line of the upper kerf, and each ring-shaped fixing card is provided with a pin hole;

The opening of the imaginary part curved surface is arranged upwards, and the imaginary part curved surface is fixed on the lower bottom surface of the upper sectional plane through a plurality of annular fixing clips provided.

As a further improvement to the above technical solution, the projection plane includes a rectangular hard board, a curved L11 slide rail, a curved L12 slide rail, a ball slider and a cylindrical fixture,

The curve L11 slide rail and the curve L12 slide rail are respectively fixed on the top of the rectangular hard plate, the curve L11 slide rail and the curve L12 slide rail intersect, and the ball slider is embedded in the curve L11 slide rail or the curve L12 slide rail, on the ball slider A cylindrical jack is provided; a space coordinate system is provided at one right-angle end of the rectangular hard board, a plurality of round holes are opened on the rectangular hard board, and cylindrical fixtures are arranged on four right angles of the rectangular hard board;

The surface of the curved L11 slide rail and the curved L12 slide rail is set on the projection plane, and the projection plane is inserted into the four poles on the bracket one by one through four cylindrical clamps and is located at the middle and lower positions of the four poles. , the projection plane is located between the baffle inside the bracket and the upper sectional plane.

As a further improvement to the above technical solution, the real part of the curved surface includes a cylindrical lower kerf line, a curved L31 slide rail, a curved L32 slide rail, a red line net and the first slider with a card,

The cylindrical lower kerf line is a closed coil made of hard metal wire. The two ends of the curved L31 slide rail and the curved L32 slide rail are respectively fixed on the cylindrical lower kerf ridge line. The curved L31 slide rail and the curved L32 slide rail It is connected with the ridge line of the lower sectional edge of the column with a red line network, and the curve L31 slide rail intersects with the curve L32 slide rail. The slide block is provided with a connection ring, and a plurality of square fixing cards are arranged on the ridge line of the lower sectional edge of the column, and each square fixing card 57 is provided with a screw hole;

The opening of the real part of the curved surface is set downward, and the real part of the curved surface is fixed on the upwardly set surface of the projection plane through a plurality of square fixing clips provided.

As a further improvement to the above technical solution, the sliding round rod includes a shaft tube, a lower insertion rod shaft, a lower sliding collar, an upper sliding collar and a push-and-turn handle,

The shaft of the lower plunger is vertically fixed on the lower end plane of the shaft tube. The lower sliding collar and the upper sliding collar are respectively sleeved on the shaft tube and can rotate and move up and down. There is a one-to-one correspondence between the lower sliding collar and the upper sliding collar. There is a lower collar card and an upper collar card. The lower collar card and the upper collar card are respectively provided with a yellow indicator light and a green indicator light. A lower left pulley and a lower right pulley are arranged at the bottom of the shaft tube. The upper part is respectively provided with a push-turn handle and a first pin hole;

One end of the lower plunger shaft on the sliding rod passes through the gap of the curved slide rail on the surface of the real part, and is inserted into the cylinder socket on the ball slider on the projection plane. The connecting rings on the first clamped slider in the real part of the surface meet.

As a further improvement to the above technical solution, the mobile bracket includes a bracket shaft tube, a horizontal left strut, a horizontal right strut, a longitudinal front strut, a longitudinal rear strut and an inner inserting rod,

Horizontal left struts, horizontal right struts, longitudinal front struts and longitudinal rear struts are evenly distributed on the upper outer surface of the bracket shaft tube, and horizontal shaft tubes are respectively arranged on the inner and outer ends of the horizontal left struts The pulley and the horizontal left end pulley are respectively provided with a horizontal lower pulley and a horizontal right end pulley at the inner and outer ends of the horizontal right strut, and are respectively provided with a vertical lower pulley and a horizontal right end pulley at the inner and outer ends of the longitudinal front strut. The longitudinal front pulley is provided with a longitudinal shaft tube pulley and a longitudinal rear end pulley respectively at the inner and outer ends of the longitudinal rear strut, and an inner insertion rod and a second pin hole are provided at the lower section of the bracket shaft tube;

The mobile bracket is provided with an inner insertion rod and a second pin hole connected to the first pin hole in the sliding round bar through the lower section of the bracket shaft tube.

As a further improvement to the above technical solution, the generated complex plane includes a square flat plate, a vertical slide, a vertical slide, a horizontal left slide and a horizontal right slide,

The vertical slideway and the vertical upper slideway are respectively fixed on the front and rear edges of the square plate, and the horizontal left slideway and the horizontal right slideway are respectively fixed on the left and right edges of the square plate.

A vertical lower slider and a vertical upper slider are respectively arranged on the vertical slideway and the vertical upper slideway, and a horizontal left slider and a horizontal right slider are respectively arranged on the horizontal left slideway and the horizontal right slideway. , there are multiple jammers on the square plate;

The complex plane is generated by connecting the vertical front pulley, the longitudinal rear pulley, the horizontal left end pulley and the horizontal right end pulley respectively in the moving bracket through the vertical lower slider, the vertical upper slider, the horizontal left slider and the horizontal right slider.

As a further improvement to the above-mentioned technical scheme, the drawing mechanism includes a chute longitudinal bar, a chute cross bar and a paintbrush,

A horizontal slider is arranged in the chute of the cross bar of the chute, and a longitudinal slider is arranged in the chute of the longitudinal bar of the chute, and the cross bar of the chute and the longitudinal bar of the chute form a cross through the horizontal slider and the longitudinal slider connect;

The vertical slide block and the horizontal slide block are connected by a pin shaft arranged vertically, a paintbrush is arranged at the lower end of the pin shaft, a spring is arranged between the paintbrush and the pin shaft, and a red indicator light is arranged at the upper end of the pin shaft; The ends of the two wide sides of the vertical rod of the chute are respectively provided with a lower socket and an upper socket correspondingly, and a left wire ring and a right wire ring are respectively provided with a one-to-one correspondence on both sides of the middle part of the long side of the vertical rod of the chute. ;The ends of the two wide sides of the cross bar of the chute are respectively provided with a left jack and a right jack corresponding to each other, and the two sides of the middle part of the long side of the cross bar of the chute are respectively provided with a lower thread ring and an upper thread respectively. ring.

As a further improvement to the above technical solution, the connection system includes a real axis left pull wire, a real axis right pull wire, a virtual axis pull wire and a virtual axis upper pull wire,

The lower end of the real shaft left pull wire is connected to the lower collar clip, and the upper end passes through the lower right pulley, the horizontal shaft tube pulley, and the horizontal left end pulley in turn to connect with the left wire ring on the longitudinal bar of the chute; the lower end of the real shaft right pull wire is connected to the lower collar clip On the top, the upper end passes through the horizontal lower pulley in turn, and the horizontal right end pulley is connected to the right wire ring on the longitudinal bar of the chute; the lower end of the virtual axis pull line is connected to the upper collar card, and the upper end passes through the longitudinal lower pulley and the longitudinal front end pulley in turn It is connected with the lower wire ring on the cross bar of the chute; the lower end of the upper pull wire on the virtual axis is connected to the upper collar card, and the upper end passes through the lower left pulley, the longitudinal shaft tube pulley, the longitudinal rear end pulley and the cross bar on the chute in turn. The upper line ring is connected.

The present invention compares with prior art, and its beneficial effect is:

1. The compound function four-dimensional space demonstration and image drawing instrument of the present invention can demonstrate four-dimensional mapping, space curved surface, complex variable function and draw corresponding complex plane curves.

2. The compound function four-dimensional space demonstration and image drawing instrument of the present invention has complete functions: it can demonstrate the changes of multiple space surfaces and draw their corresponding curves on the complex plane, and can also be used to analyze the analysis and integration of complex functions and other experiments .

3. The compound function four-dimensional space demonstration and image plotter of the present invention has strong applicability: different forms of space surfaces can be selected for demonstration and drawing in various occasions.

4. There is no such product on the market at present; the compound function four-dimensional space demonstration and image plotting instrument has simple structure, multiple functions, safety, reliability, easy operation, and light device.

Description of drawings

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

Fig. 2 is a schematic structural view of the stent in the present invention.

Fig. 3 is a schematic structural diagram of a projection plane in the present invention.

Fig. 4 is a schematic structural view of the upper sectional plane of the present invention.

Fig. 5 is a schematic structural diagram of generating a complex plane in the present invention.

Fig. 6 is a schematic structural diagram of a real part curved surface in the present invention.

Fig. 7 is a structural schematic diagram of the imaginary part curved surface in the present invention.

Fig. 8 is a structural schematic diagram of a sliding round rod in the present invention.

Fig. 9 is a schematic structural diagram of the mobile support in the present invention.

Fig. 10 is a schematic structural diagram of the drawing mechanism in the present invention.

Fig. 11 is a schematic structural diagram of the connection system in the present invention.

In the figure: 1—bracket, 11—pole, 12—conical foot, 13—suction cup, 14—adjusting nut, 15—baffle; 2—projection plane, 21—rectangular hard board, 22—curve L11 slide rail, 23—curve L12 slide rail, 24—ball slider, 25—cylindrical socket, 26—space coordinate system, 27—round hole, 28—cylindrical fixture; 3—upper section plane, 31—transparent hard board, 32— Curve L21 groove, 33—curve L22 groove, 34—groove slider, 35—pipe shaft, 36—square hole, 37—ring clamp; 4—generate complex plane, 41—square plate, 42—longitudinal slide , 43—vertical lower slider, 44—vertical upper slider, 45—longitudinal upper slider, 46—horizontal left slider, 47—horizontal left slider, 48—horizontal right slider, 49—horizontal right slider, 410—paper jammer; 5—real part surface, 51—lower kerf line, 52—curve L31 slide rail, 53—curve L32 slide rail, 54—red line net, 55—first slider with card, 56 —connecting ring, 57—square fixing card, 58—screw hole; 6—imaginary part surface, 61—upper cut edge, 62—curve L41 slide rail, 63—curve L42 slide rail, 64—white line net, 65—Second slider with card, 66—Connecting ring clip, 67—Annular fixed clip, 68—Pin hole; 7—Sliding round rod, 71—Axis tube, 72—Lower inserting rod shaft, 73—Lower sliding collar , 74—lower collar clip, 75—upper sliding collar, 76—upper collar clip, 77—lower left pulley, 78—lower right pulley, 79—pin hole, 710—green indicator light, 711—yellow indicator light ;8—moving bracket, 81—bracket shaft tube, 82—horizontal left strut, 83—horizontal right strut, 84—horizontal lower pulley, 85—transverse shaft tube pulley, 86—longitudinal front strut, 87—longitudinal slide Wheel, 88—longitudinal rear strut, 89—longitudinal shaft tube pulley, 810—inner rod, 811—transverse left end pulley, 812—transverse right end pulley, 813—longitudinal front end pulley, 814—longitudinal rear end pulley, 815—pin Hole; 9—drawing mechanism, 91—chute longitudinal bar, 92—chute cross bar, 93—horizontal slider, 94—longitudinal slider, 95—pin shaft, 96—painting brush, 97—lower jack, 98— Upper jack, 99—left jack, 910—right jack, 911—left wire ring, 912—right wire ring, 913—down wire ring, 914—up wire ring, 915—red indicator light; 10—connection system, 101—real axis left pull wire, 102—real axis right pull wire, 103—imaginary axis pull wire, 104—imaginary axis upper pull wire.

Detailed ways

The technical solutions of the present invention will be described in detail below, but the protection scope of the present invention is not limited to the embodiments.

In order to make the content of the present invention more obvious and comprehensible, further description will be made below in conjunction with the drawings 1-11 and specific implementation methods.

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

Example:

As shown in Figures 1 to 11, the compound function four-dimensional space demonstration and image plotter of the present invention, the device includes a support 1, a projection plane 2, an upper section plane 3, a generating complex plane 4, a real part curved surface 5, and an imaginary part curved surface 6. Sliding round rod 7, mobile bracket 8, drawing mechanism 9, connection system 10. Both the projection plane 2 and the upper section plane 3 are fixed on the vertical pole of the support 1, the real part curved surface 5 is fixed on the upper plane of the projection plane 2, the imaginary part curved surface 6 is fixed on the lower plane of the upper section plane 3, and the sliding round rod 7 Passing through the real part curved surface 5 and the imaginary part curved surface 6, the lower and upper ends are respectively connected with the projection plane 2 and the upper sectional plane 3, the mobile bracket 8 is fixed on the upper end of the sliding rod 7, and the generated complex plane 4 is fixed on the mobile bracket 8, Above the generating complex plane 4 is the drawing mechanism 9, and the drawing mechanism 9, the real part curved surface 5, the imaginary part curved surface 6, and the sliding round rod 7 form a kinematic unity through the connection system 10.

As shown in Figures 1 and 2, the bracket 1 includes a baffle plate 15 and four vertical rods 11, each vertical rod 11 is a straight cylindrical rod, the baffle plate 15 is a rectangular hard plate, and the four vertical rods 11 are vertically fixed on the baffle plate respectively. On the four right angles of the plate 15, the lower end of each vertical rod 11 is provided with a conical surface leg 12, and the inside of the conical surface leg 12 is provided with a suction cup 13, and an adjusting nut 14 is arranged between each vertical rod 11 and the conical surface leg 12 .

As shown in FIGS. 1 and 3 , the projection plane 2 includes a rectangular hard plate 21 , a curve L11 slide rail 22 , a curve L12 slide rail 23 , a ball slider 24 and a cylindrical clamp 28 .

The curve L11 slide rail 22 and the curve L12 slide rail 23 are respectively fixed on the rectangular hard plate 21, the curve L11 slide rail 22 and the curve L12 slide rail 23 intersect, and the ball slider 24 is embedded in the curve L11 slide rail 22 or the curve L12 slide rail 23, a cylindrical socket 25 is provided on the ball slider 24; a space coordinate system 26 is provided at a right-angled end of the rectangular hard plate 21, and a plurality of round holes 27 are opened on the rectangular hard plate 21, and the rectangular hard plate Column clamps 28 are provided on the four right angles of the plate 21 .

The surface of the curve L11 slide rail 22 and the curve L12 slide rail 23 is set on the projection plane 2 facing upwards, and the projection plane 2 is inserted into the four vertical rods 11 on the bracket 1 one by one through four cylindrical clamps 28 and located on the four At the middle and lower part of the pole 11 , the projection plane 2 is located between the inner baffle plate 15 of the bracket 1 and the upper sectional plane 3 .

As shown in FIGS. 1 and 4 , the upper sectional plane 3 includes a transparent hard plate 31 , a groove slider 34 and a pipe shaft 35 .

Curve L21 groove 32 and curve L22 groove 33 are opened on transparent hard board 31, curve L21 groove 32 and curve L22 groove 33 intersect, groove slider 34 is embedded in curve L21 groove 32 or curve L22 groove 33, a pipe shaft 35 is provided inside the groove slider 34; a plurality of square holes 36 are provided on the transparent hard plate 31, and ring clamps 37 are provided on four right angles of the transparent hard plate 31.

The upper sectional plane 3 is inserted into the four vertical rods 11 on the bracket 1 one by one through the four ring clamps 37 and is located at the upper ends of the four vertical rods 11 .

As shown in FIGS. 1 and 5 , the generating complex plane 4 includes a square flat plate 41 , a longitudinal slideway 42 , a longitudinal upper slideway 44 , a transverse left slideway 46 and a transverse right slideway 48 .

The vertical slideway 42 and the vertical upper slideway 44 are respectively fixed on the front and rear edges of the square flat plate 41, and the horizontal left slideway 46 and the horizontal right slideway 48 are respectively fixed on the left and right edges of the square flat plate 41.

On the vertical slideway 42 and the vertical upper slideway 44, the vertical lower slider 43 and the vertical upper slider 45 are respectively provided with one-to-one correspondence; The left slider 47 and the horizontal right slider 49 are provided with a plurality of jammers 410 on the square plate 41 .

Generate the complex plane 4 through the vertical lower slider 43, the vertical upper slider 45, the horizontal left slider 47 and the horizontal right slider 49 respectively connect the longitudinal front end pulley 813, the longitudinal rear end pulley 814, and the horizontal left end pulley 811 in the mobile support 8 And horizontal right end pulley 812.

As shown in FIGS. 1 and 6 , the real part curved surface 5 includes a lower kerf ridge line 51 , a curve L31 slide rail 52 , a curve L32 slide rail 53 , a red wire mesh 54 and a first belt card slider 55 .

The lower kerf line 51 is a closed coil made of hard wire, and the two ends of the curve L31 slide rail 52 and the curve L32 slide rail 53 are respectively fixed on the lower kerf line 51, and the curve L31 slide rail 52 and the curve L32 slide rail 53 and the lower kerf line 51 are connected with each other with a red line net 54, the curve L31 slide rail 52 intersects with the curve L32 slide rail 53, and the first tape slide block is arranged on the curve L31 slide rail 52 or the curve L32 slide rail 53 55, the first card slide block 55 is provided with a connecting ring 56, and the lower ridge line 51 is provided with a plurality of square fixing cards 57, and each square fixing card 57 is provided with a screw hole 58.

The opening of the real part curved surface 5 is set downward, and the real part curved surface 5 is fixed on the upwardly set surface of the projection plane 2 through a plurality of square fixing clips 57 provided.

As shown in FIGS. 1 and 7 , the imaginary part curved surface 6 includes an upper kerf ridge line 61 , a curve L41 slide rail 62 , a curve L42 slide rail 63 , a white wire mesh 64 and a second belt card slider 65 .

The upper kerf line 61 is a closed coil made of hard metal wire. The two ends of the curve L41 slide rail 62 and the curve L42 slide rail 63 are respectively fixed on the upper kerf line 61. The curve L41 slide rail 62 curve L42 slide rail 63 and the upper kerf line 61 are connected with each other with a white line net 64, and the curve L41 slide rail 62 intersects with the curve L42 slide rail 63, and the second belt card slide block is arranged on the curve L41 slide rail 62 or the curve L42 slide rail 63 65, the second belt clip slider 65 is provided with a connecting ring clip 66, and a plurality of ring-shaped fixing clips 67 are arranged on the upper kerf line 61, and each ring-shaped fixing clip 67 is provided with a pin hole 68.

The opening of the imaginary part curved surface 6 is set upward, and the imaginary part curved surface 6 is fixed on the lower bottom surface of the upper section plane 3 by a plurality of annular fixing clips 67 provided.

As shown in FIGS. 1 and 8 , the sliding round rod 7 includes a shaft tube 71 , a lower plunger shaft 72 , a lower sliding collar 73 , an upper sliding collar 75 and a push-and-turn handle 712 .

The lower plunger shaft 72 is vertically fixed on the lower end plane of the shaft tube 71, and the lower sliding collar 73 and the upper sliding collar 75 are respectively sleeved on the shaft tube 71 and can rotate and move up and down. The ring 75 is respectively provided with a lower collar clip 74 and an upper collar clip 76 in one-to-one correspondence, and the lower collar clip 74 and the upper collar clip 76 are respectively provided with a yellow indicator light 711 and a green indicator light 710. The lower part is provided with a lower left pulley 77 and a lower right pulley 78, and the upper part of the shaft tube 71 is respectively provided with a push and turn handle 712 and a first pin hole 79.

One end of the lower rod shaft 72 on the sliding rod 7 passes through the gap of the curved slide rail on the real part curved surface 5, and is inserted into the cylinder socket 25 on the ball slider 24 on the projection plane 2, and the lower sliding collar 73 The upper lower collar clip 74 is in contact with the connecting ring 56 on the first clip slider 55 in the real part curved surface 5 .

As shown in Figures 1 and 9, the mobile support 8 includes a support shaft tube 81, a transverse left strut 82, a transverse right strut 83, a longitudinal front strut 86, a longitudinal rear strut 88 and an inserting rod 810. The left and right sides of the upper end of 81 are respectively provided with horizontal left struts 82 and horizontal right struts 83, and the front and rear sides are respectively provided with longitudinal front struts 86 and longitudinal rear struts 88. There is a horizontal shaft tube pulley 85, a horizontal left end pulley 811, a horizontal lower pulley 84, a horizontal right end pulley 812, respectively, at the inner and outer ends of the horizontal right strut 83, and a longitudinal sliding pulley, respectively at the inner and outer ends of the longitudinal front strut 86. Wheel 87 longitudinal front end pulley 813 is respectively provided with longitudinal shaft tube pulley 89 longitudinal rear end pulley 814 at the inside and outside two ends of vertical back strut 88, and the lower segment of support shaft tube 81 is provided with inner inserting rod 810 and pin hole 815.

As shown in FIGS. 1 and 10 , the drawing mechanism 9 includes a chute longitudinal bar 91 , a chute cross bar 92 and a paintbrush 96 . A horizontal slider 93 is arranged in the chute of the chute cross bar 92, a longitudinal slider 94 is arranged in the chute of the chute longitudinal bar 91, and a vertical pin shaft is arranged between the longitudinal slider 94 and the horizontal slider 93. 95 is connected, the lower end of pin shaft 95 is provided with paintbrush 96, is provided with spring 916 between paintbrush 96 and pin shaft 95, is provided with indicator light 915 at the upper end of pin shaft 95, is provided with at the front and rear ends of chute longitudinal bar 91 respectively. Jack 98 is provided with lower jack 97, middle part both sides are respectively provided with left wire ring 911 right wire ring 912, are respectively provided with left jack 99 right jack 910 at the left and right ends of chute cross bar 92, middle part two The sides are respectively provided with a lower thread ring 913 and an upper thread ring 914.

As shown in Figures 1 and 11, the connection system 10 includes a real axis left pull wire 101, a real axis right pull wire 102, an imaginary axis pull wire 103 and an imaginary upper pull wire 104, and the lower end of the real axis left pull wire 101 is connected to the lower collar clip 74, The upper end successively passes through the lower right pulley 78, the transverse shaft tube pulley 85, and the left end pulley 811 of the transverse direction is connected with the left wire ring 911 on the longitudinal rod 91 of the chute; Lower pulley 84 transverse right end pulley 812 links to each other with the right line ring 912 on the chute longitudinal bar 91; The lower line ring 913 on the chute cross bar 92 is connected; the lower end of the upper backstay 104 on the virtual axis is connected on the upper collar clip 76, and the upper end passes through the lower left pulley 77, the longitudinal axis tube pulley 89, the longitudinal rear end pulley 814 and the chute in turn. The upper wire ring 914 on the cross bar 92 is connected. .

The working principle of the compound function four-dimensional space demonstration and image plotter of the present invention is that, according to the principle of space projection and orthogonal synthesis, the moving points that change along the track on the two real curved surfaces are transformed into vertical points on another complex plane through projection points. Axis movement, so as to achieve demonstration and drawing functions. Main advantages: simple operation, all demonstrations and drawings can be completed by simply pushing and turning the handle after assembly; complete functions: it can demonstrate space analytic geometry and composite functions of university mathematics; strong applicability: choosing different shapes of surfaces can complete multiple Demonstration and image drawing of various functions can be demonstrated or experimented in classrooms, laboratories, families and other occasions.

The compound function four-dimensional space demonstration and image drawing instrument of the present invention has a demonstration function, that is, a demonstration of the change of a real-valued function in a complex variable function, and the operation steps are:

1. Function settings of the model:

The complex variable function is w=f(z)=u(x,y)+iv(x,y), where, is the imaginary unit, H ₁ =u(x,y) is the real part, H ₂ =v(x,y) is the imaginary part, z=x+iy is the complex variable, and the complex plane where the complex variables z and w are located refers to The projection plane 2 and generating complex plane 4 in the claims, and the images of the binary real functions H ₁ =u(x,y), H ₂ =v(x,y) in the three-dimensional real space are respectively in the claims The real part surface 5 and the imaginary part surface 6.

2. Assemble the demonstration device, place the conical feet of the bracket on a horizontal surface, turn the adjusting nut to make it stable, and fix the side of the projection plane with the slide rail upwards above the baffle in the bracket; open the real part of the curved surface It is fixed downward on the projection plane through the square fixed card; the push-turn handle on the sliding round rod is removed, and one end of the lower insertion rod shaft passes through the gap of the curved slide rail on the real part surface, and is inserted into the projection plane. In the cylindrical socket on the slider, connect the lower collar clip on the lower sliding collar with the connecting ring on the slider with clip in the real part surface; fix the opening of the imaginary part curved surface upward through the square fixing clip on the upper On the lower bottom of the sectional plane, let the gap of the curved slide rail on the imaginary part surface and the pipe shaft of the upper sectional plane be sleeved on the other end of the sliding round rod, fix the four right angles of the upper sectional plane on the vertical rod of the bracket, and put the upper The upper collar clip on the sliding collar is locked in the connecting ring clip on the belt clip slider in the imaginary part curved surface, and the pushing and turning handle is fixed on the upper end of the sliding round bar.

3. Adjustment of the initial state, adjust the positions of the projection plane, the upper sectional plane, the real part surface, and the imaginary part surface, so that the upper and lower projection curves of the curve families L11, L21, L31, and L41 coincide, and the curve families L12, L22, L32, L42 The upper and lower projection curves coincide, and the lower end of the sliding rod is moved to the point P0 of the projection plane, and it is perpendicular to the sectional plane on the projection plane. 4. Demonstration of function relationship, turn on the red and yellow indicator lights on the upper and lower sliding collars, push the push-turn handle with your hands to let the lower end of the sliding round rod move along the curve L11 or L12 slide rail, and the upper and lower sliding collars follow the belt card sliders respectively The movement on the imaginary part surface and the real part surface moves up and down, that is, the change of the two real function values is the result of the change of the complex variable z along the curve L11 or L12 on the complex plane. 5. When the demonstration is over, push the sliding rod to the predetermined position to stop, and turn off the indicator light.

The composite function four-dimensional space demonstration and image drawing instrument of the present invention has a drawing function, that is, it can draw a curve of a complex variable function, and the operation steps are:

1. The setting of the drawing function is the same as that of the demonstration.

2. Assemble the drawing device, and continue to add parts on the basis of completing the demonstration device: Insert the lower end of the shaft tube of the mobile bracket into the socket at the upper end of the sliding round rod, and use a pin to connect the two through the pin hole to generate a complex plane Fixed on the four support rods on the mobile bracket, connect the two ends of the longitudinal rod and the horizontal rod on the drawing mechanism to the four sliders on the generated complex plane; connect the lower end of the real axis left pull wire in the connection system to the lower sleeve On the ring card, the upper end passes through the lower right pulley, the horizontal shaft tube pulley, and the horizontal left end pulley in turn to connect with the left line ring on the longitudinal rod of the chute, and the lower end of the real shaft right cable is connected to the lower ring card, and the upper end passes through the horizontal The pulley at the horizontal right end of the lower pulley is connected with the right wire ring on the longitudinal bar of the chute, and the lower end of the virtual axis pull-down line is connected to the upper collar clip, and the upper end passes through the longitudinal front end pulley of the lower pulley and the lower end of the cross bar of the chute in turn. The wire ring links to each other, the lower end of the backguy on the virtual shaft is connected on the upper collar clip, and the upper end passes through the lower left pulley longitudinal shaft tube pulley longitudinal rear end pulley successively and links to each other with the upper wire ring on the chute cross bar.

3. Adjust the initial state. Fix a piece of rectangular paper with a rectangular coordinate system Ouv on the generated complex plane with a paper jammer, and make the real axis and imaginary axis parallel to the horizontal bar and vertical bar on the drawing mechanism respectively. , adjust the positions of the projection plane, the upper sectional plane, the real part surface, and the imaginary part surface, so that the upper and lower projection curves of the curve families L11, L21, L31, and L41 coincide, and the upper and lower projection curves of the curve families L12, L22, L32, and L42 coincide , move the lower end of the sliding rod to point P0 of the projection plane, and make it perpendicular to the sectional plane on the projection plane, move the brush to point P1 (corresponding point of P0) in the coordinate system Ouv, and adjust the drawstring to make it in tension.

4. Demonstration and drawing, turn on the red and yellow indicator lights on the up and down sliding collar and the red indicator light on the brush, push the push-turn handle with your hands to let the lower end of the sliding round rod move along the curve L11 or L12 slide rail, and slide the collar up and down with The movement of the slider on the imaginary part surface and the real part surface respectively moves up and down, that is, the change of the two real function values is the result of the change of the complex variable z along the curve L11 or L12 on the complex plane. Draw the curves of the two surfaces on the paper.

5. When finished, push the sliding round rod to the predetermined position to stop, turn off the indicator light, if you are not drawing, you can form a complex plane generated by the mobile bracket and the drawing mechanism into one, which is called a drawing device, untie the connecting line and the pin at the lower end of the mobile bracket, Place the plotter on the bezel of the stand.

The economic value and application prospect of the compound function four-dimensional space demonstration and image plotter of the present invention: with technological progress and economic development, higher education needs more and more advanced equipment to improve teaching effect and practical training, complex variable function, mapping, space analysis Geometry and other knowledge is an important content of learning at the university level in my country. Due to the influence of real variable functions and geometric meanings, it is extremely difficult to express multiple functions in one system at the same time. The teaching mainly relies on description or two simple plane graphics , which is not easy for junior college students who are limited to two-dimensional or three-dimensional real space to understand deeply, and some physical devices are urgently needed in teaching to truly represent what they have learned.

From the perspective of the domestic market, according to the tenth item "Education, Science and Technology and Culture Data" in the statistical information released by the National Bureau of Statistics in 2015, there are more than 6 million students in general higher education, a considerable number, and its market prospects are very broad. Good economic benefits.

The parts not involved in the present invention are the same as the prior art or can be realized by adopting the prior art.

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

Claims (10)

1. a kind of compound function space-time demonstration and Image Rendering instrument, which is characterized in that including stent (1), projection plane (2), upper cutting plane (3), generation complex plane (4), real part curved surface (5), imaginary part curved surface (6), slip round bar (7), mobile stent (8), picture mechanism (9), connection system (10),

Stent (1) includes baffle (15) and four upright bars (11), and each upright bar (11) is hard straight cylindrical bar, and baffle (15) is Rectangle hardboard, four upright bars (11) are respectively and vertically fixed on four right angles of baffle (15), and the lower end of every upright bar (11) is set There is conical surface stabilizer blade (12), sucker (13) is internally provided in conical surface stabilizer blade (12), in every upright bar (11) and conical surface stabilizer blade (12) Between be equipped with adjusting nut (14)；

Upper cutting plane (3) is fixed on the upper end of upright bar (11)；

Projection plane (2) is fixed on upright bar (11) middle and lower part and between upper cutting plane (3) and baffle (15)；

Real part curved surface (5) is fixed in the upper plane of projection plane (2)；

Imaginary part curved surface (6) is fixed on the bottom surface of cutting plane (3)；

Round bar (7) is slided across real part curved surface (5) and imaginary part curved surface (6), lower upper both ends respectively with projection plane (2) and upper truncated Face (3) is connected；

Mobile stent (8) is fixed on the upper end for sliding round bar (7)；

Generation complex plane (4) is fixed on mobile stent (8), and picture mechanism (9) is connected to above generation complex plane (4)；

Between picture mechanism (9), real part curved surface (5), imaginary part curved surface (6), slip round bar (7) fortune is formed by connecting system (10) Dynamic entity.

2. compound function space-time demonstration as described in claim 1 and Image Rendering instrument, which is characterized in that upper cutting plane (3) including transparent hardboard (31), groove sliding block (34) and pipe axis (35),

Curve L21 grooves (32) and curve L22 grooves (33), curve L21 grooves (32) and song are provided on transparent hardboard (31) Line L22 grooves (33) are intersecting, and groove sliding block (34) is embedded in curve L21 grooves (32) or curve L22 grooves (33), in groove Sliding block (34) is internally provided with pipe axis (35)；Multiple square holes (36) are provided on transparent hardboard (31), in transparent hardboard (31) Annular holder (37) is both provided on four right angles；

Upper cutting plane (3) is inserted into four upright bars (11) on stent (1) by four annular holders (37) one-to-one correspondence and position In the upper end of four upright bars (11).

3. compound function space-time demonstration as claimed in claim 2 and Image Rendering instrument, which is characterized in that imaginary part curved surface (6) including upper section crest line (61), curve L41 sliding rails (62), curve L42 sliding rails (63), white gauze (64) and the second band card Sliding block (65),

The closing coil that upper section crest line (61) is made by hard metal wire, curve L41 sliding rails (62) and curve L42 sliding rails (63) Both ends are separately fixed on section crest line (61), curve L41 sliding rails (62) curve L42 sliding rails (63) and upper section crest line (61) Between be connected with white gauze (64), curve L41 sliding rails (62) and curve L42 sliding rails (63) intersect, in curve L41 sliding rails (62) or Curve L42 sliding rails (63) are equipped with the second band card sliding block (65), and the second band card sliding block (65) is equipped with connection ring card (66), upper to cut Mouth crest line (61) is equipped with multiple annular fixing cards (67), and pin hole (68) is equipped on each annular fixing card (67)；

The opening upwards setting of imaginary part curved surface (6), imaginary part curved surface (6) are fixed on by multiple annular fixing cards (67) of setting On the bottom surface of cutting plane (3).

4. compound function space-time demonstration as claimed in claim 2 and Image Rendering instrument, which is characterized in that

Projection plane (2) includes rectangle hardboard (21), curve L11 sliding rails (22), curve L12 sliding rails (23), ball slider (24) With cylindricality fixture (28),

Curve L11 sliding rails (22) and curve L12 sliding rails (23) are separately fixed above rectangle hardboard (21), curve L11 sliding rails (22) and curve L12 sliding rails (23) are intersecting, and ball slider (24) is embedded in curve L11 sliding rails (22) or curve L12 sliding rails (23) It is interior, cylinder jack (25) is equipped on ball slider (24)；Space coordinate is equipped at the right angle end of rectangle hardboard (21) It is (26), multiple circular holes (27) is provided on rectangle hardboard (21), cylindricality is equipped on four right angles of rectangle hardboard (21) Fixture (28)；

The face-up setting of curve L11 sliding rails (22) and curve L12 sliding rails (23), projection plane (2) are set on projection plane (2) It is corresponded and is inserted into four upright bars (11) on stents (1) and positioned at four upright bars (11) by four cylindricality fixtures (28) At the position of middle and lower part, projection plane (2) is between stent (1) Internal baffle (15) and upper cutting plane (3).

5. compound function space-time demonstration as claimed in claim 3 and Image Rendering instrument, which is characterized in that

Real part curved surface (5) includes lower section crest line (51), curve L31 sliding rails (52), curve L32 sliding rails (53), red gauze (54) and first band card sliding block (55),

The closing coil that lower section crest line (51) is made by hard metal wire, curve L31 sliding rails (52) and curve L32 sliding rails (53) Both ends are separately fixed on lower section crest line (51), curve L31 sliding rails (52), curve L32 sliding rails (53) and lower section crest line (51) it is connected between with red gauze (54), curve L31 sliding rails (52) and curve L32 sliding rails (53) are intersecting, in curve L31 sliding rails (52) or curve L32 sliding rails (53) are equipped with first band card sliding block (55), and first band card sliding block (55) is equipped with connection annulus (56), lower section crest line (51) is equipped with multiple rectangular fixing cards (57), and screw hole is equipped on each rectangular fixing card (57) (58)；

Real part curved surface (5) Open Side Down setting, real part curved surface (5) is fixed on throwing by multiple rectangular fixing cards (57) of setting On the surface set upward of shadow plane (2).

6. compound function space-time demonstration as claimed in claim 5 and Image Rendering instrument, which is characterized in that slide round bar (7) including central siphon (71), lower plunger axis (72), lower slider lantern ring (73), upper slip collar (75) and push-jump handle (712),

Lower plunger axis (72) is vertically fixed on the lower end plane of central siphon (71), lower slider lantern ring (73) and upper slip collar (75) It is respectively fitted on central siphon (71) and can rotate and move up and down, one is distinguished on lower slider lantern ring (73) and upper slip collar (75) One is correspondingly provided with lower collar card (74) and upper lantern ring card (76), and yellow instruction is respectively equipped on lantern ring card (76) on lower collar card (74) Lamp (711) and green indicator light (710) are equipped with lower left chain wheel (77) and lower right pulley (78), in central siphon in the lower part of central siphon (71) (71) top is respectively equipped with push-jump handle (712) and the first pin hole (79)；

It slides round bar (7) and is equipped with one end of lower plunger axis (72) across the gap of real part curved surface (5) upper curve sliding rail, be inserted into In cylinder jack (25) on projection plane (2) on ball slider (24), lower collar card (74) on lower slider lantern ring (73) with Connection annulus (56) in real part curved surface (5) on first band card sliding block (55) connects.

7. compound function space-time demonstration as claimed in claim 6 and Image Rendering instrument, which is characterized in that

Mobile stent (8) including stent central siphon (81), laterally left strut (82), laterally right strut (83), longitudinal front strut (86), Longitudinal rear pole (88) and interpolation pole (810),

Laterally left strut (82), laterally right strut (83), the preceding support in longitudinal direction are uniformly arranged in the outer surface of upper of stent central siphon (81) Bar (86) and longitudinal rear pole (88), correspond respectively at the inside and outside both ends of laterally left strut (82) equipped with lateral central siphon pulley (85) and lateral left end pulley (811) it, is corresponded respectively equipped with lateral lower sheave at the inside and outside both ends of laterally right strut (83) (84) and lateral right end pulley (812) it, is corresponded respectively at the inside and outside both ends of longitudinal front strut (86) equipped with longitudinal lower sheave (87) and before longitudinal direction head sheave (813), correspond at the inside and outside both ends of longitudinal rear pole (88) and slided equipped with longitudinal central siphon respectively (89) and longitudinally aft end pulley (814) are taken turns, interpolation pole (810) and the second pin hole are equipped in the hypomere of stent central siphon (81) (815)；

Mobile stent (8) is equipped with interpolation pole (810) by the hypomere of stent central siphon (81) and the second pin hole (815) connection is slided The first pin hole (79) in round bar (7).

8. compound function space-time demonstration as claimed in claim 7 and Image Rendering instrument, which is characterized in that

It generates complex plane (4) and includes square plate (41), longitudinal glide path (42), laterally longitudinal sliding way (44), left slideway (46) and laterally right slideway (48),

Longitudinal glide path (42) and longitudinal sliding way (44) are separately fixed at the front and rear side edge of square plate (41) above, laterally left Slideway (46) and lateral right slideway (48) are separately fixed at the left and right side edge of square plate (41) above,

It corresponds and is equipped on longitudinal sliding block (43) and longitudinal direction respectively on longitudinal glide path (42) and longitudinal sliding way (44) Sliding block (45) on lateral left slideway (46) and laterally right slideway (48) corresponds and is equipped with lateral left slider (47) and horizontal stroke respectively Sliding block (49) to the right are equipped with multiple paperboard devices (410) above square plate (41)；

It generates complex plane (4) and passes through longitudinal sliding block (43), longitudinal top shoe (45), lateral left slider (47) and lateral right sliding block (49) head sheave (813), longitudinally aft end pulley (814), lateral left end pulley before the longitudinal direction in mobile stent (8) are connected respectively (811) and lateral right end pulley (812).

9. compound function space-time demonstration as claimed in claim 8 and Image Rendering instrument, which is characterized in that picture mechanism (9) including sliding slot vertical pole (91), sliding slot cross bar (92) and paintbrush (96),

Transverse slider (93) is equipped in the sliding slot of sliding slot cross bar (92), longitudinal sliding block is equipped in the sliding slot of sliding slot vertical pole (91) (94), sliding slot cross bar (92) is connected by transverse slider (93) with sliding slot vertical pole (91) with longitudinal sliding block (94) in right-angled intersection；

It is connected between longitudinal sliding block (94) and transverse slider (93) by vertically disposed pin axis (95), in pin axis (95) Lower end be equipped with paintbrush (96), equipped with spring (916) between paintbrush (96) and pin axis (95), set in the upper end of pin axis (95) There is red indicator light (915)；It is corresponded respectively equipped with lower jack (97) in the end of two broadsides of sliding slot vertical pole (91) With upper jack (98), the both sides in the middle part of sliding slot vertical pole (91) long side are corresponded respectively equipped with left wire loop (911) and right wire loop (912)；It is corresponded respectively in the end of two broadsides of sliding slot cross bar (92) equipped with left jack (99) and right jack (910), Both sides in the middle part of sliding slot cross bar (92) long side are corresponded respectively equipped with lower wire loop (913) and upper wire loop (914).

10. compound function space-time demonstration as claimed in claim 9 and Image Rendering instrument, which is characterized in that connection system (10) including bracing wire (104) in real axis Zola line (101), the right bracing wire of real axis (102), imaginary axis pull-down line (103) and the imaginary axis,

It is terminated under real axis Zola line (101) on lower collar card (74), upper end sequentially passes through lower right pulley (78), lateral central siphon is slided Wheel (85), lateral left end pulley (811) are connected with the left wire loop (911) on sliding slot vertical pole (91)；The right bracing wire of real axis (102) lower end It is connected on lower collar card (74), upper end sequentially passes through lateral lower sheave (84), lateral right end pulley (812) and sliding slot vertical pole (91) On right wire loop (912) be connected；It is terminated under imaginary axis pull-down line (103) on lantern ring card (76), upper end sequentially passes through longitudinal direction Head sheave (813) is connected with the lower wire loop (913) on sliding slot cross bar (92) before lower sheave (87), longitudinal direction；Bracing wire (104) in the imaginary axis Under terminate on lantern ring card (76), upper end sequentially passes through lower left chain wheel (77), longitudinal central siphon pulley (89), longitudinally aft end and slides Wheel (814) is connected with the upper wire loop (914) on sliding slot cross bar (92).