CN100392685C - Lissajous figure demonstrating and automatically tracing instrument - Google Patents

Abstract

The present invention relates to a Lissajous figure demonstrating and automatically tracing instrument which can make mechanical and mutually perpendicular simple harmonic vibration, and can automatically trace figures on paper. The speed of the instrument is controllable. The instrument is composed of gears (2), (8) and (10), a supporting column (3), a column (9), vibrating beams (1) and (7), a four layer grooved rail intersection tracing mechanism, an animation pen (12) at the intersection, tracing pens (27) and (31), cosine and sine image tracing recording plates (25) and (29) and toothed racks (26) and (30), wherein the supporting column (3) and the column (9) are arranged on the gears, and the toothed racks (26) and (30) are installed on the cosine and sine image tracing recording plates (25) and (29). Drive and slide are matched to work. The animation pen can automatically trace Lissajous figures on paper, the tracing pen (27) automatically traces cosine images on paper, and the tracing pen (31) automatically traces sine images on paper.

Description

The Lissajous figure demonstrating and automatically tracing instrument

The present invention mainly belongs to the physics teaching demonstrator, particularly can the ocular demonstration lissajous figures, can be depicted in lissajous figures (style figure) on the blank sheet of paper automatically again, and can also be two branches vibrations of lissajous figures: $x=A_1\mathrm{COS}(\frac{2\mathrm{\&pi;}}{T_1}t+{\mathrm{\&Phi;}}_1)$ The image and $y={\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="C0110645100202.png,C0110645100211.png"\; state="\{\{state\}\}">A</figure-callout>}}_2\mathrm{Sin}(\frac{2\mathrm{\&pi;}}{{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="C0110645100202.png,C0110645100211.png"\; state="\{\{state\}\}">T</figure-callout>}}_2}+{\mathrm{\&Phi;}}_2)$ Image also can be depicted in the demonstration instrument for teaching on the blank sheet of paper simultaneously automatically.Make it have more novelty at home, outward, have more creativeness, have more practicality.

In type of the present invention before the applying date, utility model (ZL patent No. 97209296X) " lissajous figures demonstration instrument for teaching " is arranged, it is that law of cognition according to the people is always from the perception to the rational faculty, the synthetic lissajous figures of the mutually vertical simple harmonic oscillation of do with machinery, the speed of doing orthogonal simple harmonic oscillation is slowed down greatly, even its speed, manually can control, make naked eyes can observe directly particle and do the physical process of mutually vertical simple harmonic oscillation and the physical process of synthetic lissajous figures (style figure).

" the animation pen " that naked eyes can also intuitively be observed " four layers grooved rail intersect describe mechanism " follows the track regular movement of lissajous figures (style figure), and be smooth, fluently, automatically and style figure be depicted on the blank sheet of paper.

Utility model " lissajous figures demonstrator " this genus inventing type, but its main designer Chen Chunan does not apply for patent of invention.So its novelty of utility model " lissajous figures demonstration instrument for teaching "; creative, practicality; that science and technology is worth is also really not objective, embody comprehensively; the patent right law protection time limit; the developing of produce market; the society material wealth increasing degree, show state-nation's spiritual wealth value etc. objectively, certain limit is all arranged.Therefore, the main inventor Chen Chunan of utility model patent " lissajous figures demonstration instrument for teaching " is keeping utility model " lissajous figures demonstration instrument for teaching ", originally can demonstrate lissajous figures, can be depicted in " lissajous figures " (style figure) automatically outside the dual-use function structure on the paper again, through further innovative design, increased newly and can be two branches vibrations of the mutually vertical simple harmonic oscillation of making machinery: $x=A_1\mathrm{COS}(\frac{2\mathrm{\&pi;}}{T_1}t+{\mathrm{\&Phi;}}_1)$ (cosine image) and $y={\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="C0110645100202.png,C0110645100211.png"\; state="\{\{state\}\}">A</figure-callout>}}_2\mathrm{Sin}(\frac{2\mathrm{\&pi;}}{T_2}t+{\mathrm{\&Phi;}}_2)$ Two images of image (sinusoidal image), also can automatically be depicted on the blank sheet of paper, and sine is visual, cosine is visual, lissajous figures (style figure) three can be depicted on the blank sheet of paper simultaneously automatically, also can be only automatically be depicted on the blank sheet of paper some figures (image) wherein, also can automatically be depicted in wherein any two figures (image) in three figures (image) on the blank sheet of paper simultaneously, make inventing type Lissajous figure demonstrating and automatically tracing instrument " have more novelty at home, outward, have more creativeness, have more practicality.The science and technology that more can embody it is worth; make junior middle school both domestic and external " mathematics " senior middle school, special secondary school " mathematics ", " physics "; the classroom instruction demonstration of junior college, university's " general physics ", " mathematical physics "; can both use it; the legal protection time limit of this patent of invention achievement is increased; further open up produce market, further increase the increasing degree of social material values, really show the value of state-nation's spiritual wealth etc. objectively.

The object of the present invention is achieved like this, describes mechanism by framework, walking beam, gear set and four layers of grooved rail that hollow circular cylinder penholder seat is housed, and cosine, sinusoidal image are described mechanism and formed.Framework is a sphere of movements for the elephants shape, and the four edges beam inboard of crossbeam 5, sill 6, left crossbeam 16, right vertical beam 17 thereon, has all milled same even depth with milling machine, same widths, equal length, symmetrical straight groove rail, 20,21,22,23;

Described walking beam, formed by vertical vibrating beam 1 that is crossed as " ten " word shape mutually and horizontal vibration beam 7, be provided with one and its tool beam 13 of adding at regular intervals on the upper strata of vertical vibrating beam, along vertical vibrating beam and it add beam directly to, respectively opened an equal in length, width equates, direction is identical, at conplane straight groove rail 4, the slide block of vertical vibrating beam 1 by being provided with on its two ends, be installed in the entablature 5 of sphere of movements for the elephants shape framework respectively, the inboard straight groove 20 that is provided with of 6 two side bars of sill, within 21, make itself and entablature, sill, realization is slidingly matched, be provided with one and its tool beam of adding at regular intervals on the upper strata of horizontal vibration beam, along horizontal vibration beam and it add beam directly to, respectively opened an equal in length, width equates, direction is identical, at isoplanar straight groove rail, the slide block of horizontal vibration beam 7 by being provided with on its two ends, be installed in the left vertical beam 16 of sphere of movements for the elephants shape framework respectively, the inboard straight groove rail 22 that is provided with of 17 two side bars of right vertical beam, in 23, make itself and left vertical beam, right vertical beam is realized being slidingly matched, vertical vibrating beam 1 is level the adding between the beam 14 of beam 7 and it of shaking, be slidingly matched, horizontal vibration beam 7 add beam 14 the adding between the beam 13 of vertical vibrating beam 1 and it, be slidingly matched.

Described gear set, by rotating shaft be fixed on gear 2, rotating shaft on the middle cross beam 15 be fixed in gear 8, rotating shaft on the vertical beam 18 be fixed on mesomerism gear 10 on middle cross beam and the middle vertical beam junction and carry out transmission and cooperate institute to form; The gear 2 that rotating shaft is fixed on the middle cross beam 15 installs within the straight groove rail 4 of vertical vibrating beam by a cylindrical columns 3 that is provided with on its edge, realization is slidingly matched, gear 8 during rotating shaft is fixed on the vertical beam 18, have within the straight groove rail of horizontal vibration beam by cylindrical columns 9 devices that are provided with on its edge, realize being slidingly matched;

The described mechanism of describing, the animation penholder is inserted within the hollow of hollow circular cylinder penholder seat 12, hollow circular cylinder penholder seat is installed in vertical vibrating beam 1 and its straight groove rail of adding beam 13, horizontal vibration beam 7 and its straight groove rail infall of adding beam 14, within four layers of square hole that grooved rail constituted 11, hollow circular cylinder penholder seat 12 and four layers of square hole that grooved rail constituted 11 are carried out and are slidingly matched.

Hollow circular cylinder penholder seat 12 is with the motion campaign of the infall of vertical vibrating beam 1 and horizontal vibration beam 7, therefore the animation pen is demonstrated the track lissajous figures of infall, be depicted on a blank sheet of paper, reaches the purpose of its figure of type demonstrator development Lissajous figure demonstrating and automatically tracing of the present invention.

Described, cosine, sinusoidal image is described mechanism, the cosine image is described mechanism, and device has two slide rails 24 of " Jiong " shape, and device is below gear 2, each bar slide rail is impartial to the distance of the rotating shaft of gear 2, symmetry, Open Side Down, " the cosine image is described data board " 25, and it places between two slide rails 24 of two cunnings, it and two slide rails 24, be slidingly matched, the tooth bar 26 of device on the long limit of " the cosine image is described data board " 25, it cooperates with gear 2 transmissions, " the cosine image is described data board " 25, open along center line one port, an end is opening not, and the central channel of certain width is arranged, rotating shaft below this groove and the gear 2 can be slided relatively.Describe " describing pen " 27 of cosine image, device is at 27 places, lower end of horizontal vibration beam 1.

Described " sinusoidal image is described data board " 29 two " Jiong " slide rails 28, " sinusoidal image is described data board ", tooth bar 30 members such as grade, with " it is identical that the cosine image is described the structure of members such as mechanism; different is; sinusoidal image is described mechanism arrangement below gear 8; gear 8 both cooperated with mesomerism gear 10 transmissions; cooperate with the tooth bar transmission again; make " sinusoidal image is described data board " 29, outwards show sinusoidal image along X-direction, reach further demonstration letter and wipe vibrational diagram, and describe the development purpose of the sinusoidal image of cosine image automatically at blank sheet of paper.

Below in conjunction with drawings and Examples type of the present invention is further specified.

Fig. 1 utilizes " circle of reference " to push away particle of card and is the figure that vibration is wiped in letter.

Fig. 2 utilizes " circle of reference " to push away line of card and is the figure that vibration is wiped in letter.

Fig. 3, vertical vibrating beam 1 and add the location diagram of beam 13.

Fig. 4, for vertical vibrating beam 1 and add beam 13, horizontal vibration beam 7 and add beam 14 and the location diagram of hollow circular cylinder penholder seat 12.

Accompanying drawing 5 is type one-piece construction principle sketch of the present invention.It should be certain width of cloth figure in the Figure of description for a Figure of abstract, so Figure of description 5 also is a Figure of abstract

Accompanying drawing 6, the cosine image is described the mechanism principle sketch.

Accompanying drawing 7, sinusoidal image is described the mechanism principle sketch.

The ultimate principle of type of the present invention is: according to the physics teaching material content, utilize the method for " circle of reference " research spring oscillator vibration regularity, radius is R _AParticle M, when making uniform circular motion, the displacement of the projection P of particle M on X-axis is X _oFig. 1

x＝R _ACOSa

$\underset{\&CenterDot;}{\&CenterDot;\&CenterDot;}a=\frac{2\mathrm{\&pi;<figure-callout\; id="1"\; label="t\; T"\; filenames="C0110645100193.png,C0110645100194.png"\; state="\{\{state\}\}">t</figure-callout>}}{T_{}}+{\mathrm{\&Phi;}}_1$

$\stackrel{\&CenterDot;}{\&CenterDot;\&CenterDot;}x=R_A\mathrm{COS}(\frac{2\mathrm{\&pi;}}{T_1}t+{\mathrm{\&Phi;}}_1)$

This equation is the equation of simple harmonic oscillation, i.e. M motion of projection P point on X-axis is simple harmonic oscillation, and the equilibrium position is at the initial point of X-axis, i.e. center of circle O _AThe place, R _ABe that the P point is made the simple amplitude of vibration of wiping.T ₁Being the cycle that particle M does uniform circular motion, also is that the P point is done letter and wiped the vibration period.

Φ ₁Be particle M when time t=0, R _AAnd the angle between the X-axis, when also being t=0, the P point is made the first phase that vibration is wiped in letter.+

If projection straight line MP is prolonged, Fig. 2, the projection straight line after the prolongation is represented with S, gets 1 P ' on S arbitrarily, then P ' is being parallel to O _AVibration back and forth on the O ' P ' straight line on the straight line of P, equilibrium position are promptly crossed O 0 ' _AThe straight line of y axle on.According to:

PP′//O _AO′，x′//x

∵O′P′＝O _AP＝X

The displacement equation of P ' also is

$x^{\&prime;}=R_A\mathrm{COS}(\frac{2\mathrm{\&pi;}}{T_1}t+{\mathrm{\&Phi;}}_1)$

Be that P ' is selected arbitrarily, thus the last each point of projection straight line S, all do equal simple harmonic oscillation, vibration equation all is $x^{\&prime;}=R_A\mathrm{COS}(\frac{2\mathrm{\&pi;}}{T_1}t+{\mathrm{\&Phi;}}_1),$ If in Fig. 3, overlaps with vibration projection straight line S all the time with the beam 1 that vertically shakes, the then simple harmonic oscillation that equates fully of the work of any point on the vertical vibrating beam 1 and P point, like this, from theory to practice.

Fig. 5 also is a Figure of abstract for this Lissajous figure demonstrating and automatically tracing instrument one-piece construction principle sketch.

It is described mechanism by framework, walking beam, gear set and four layers of grooved rail that hollow circular cylinder penholder seat is housed and is formed.Framework is a sphere of movements for the elephants shape, is made up of entablature 5, sill 6, left vertical beam 16, right vertical beam 17, middle cross beam 15, middle vertical beam 18.And same even depth has all been milled with milling machine in the four edges beam inboard of crossbeam 5, sill 6, left vertical beam 16, right vertical beam 17 thereon, same widths, and equal length, symmetrical directly to traverse rod, 20,21,22,23;

Described walking beam, formed by vertical vibrating beam 1 that is crossed as " ten " word shape mutually and horizontal vibration beam 7, be provided with one and its tool beam 13 of adding at regular intervals on the upper strata of vertical vibrating beam, Fig. 3 along vertical vibrating beam and it add beam directly to, having opened respectively that an equal in length, width equate, direction is identical, at conplane straight groove rail 4, is to use the synchronous processing method, mill out the accurate rough bamboo mat that comes with milling machine and close smoother; See Fig. 5, the slide block of vertical vibrating beam 1 by being provided with on its two ends, be installed in the entablature 5 of sphere of movements for the elephants shape framework respectively, the inboard straight groove rail 20 that is provided with of 6 two side bars of sill, within 21, make itself and entablature, sill, realization is slidingly matched, vertical vibrating beam 1 is overlapped with S among Fig. 2 in vibration processes all the time, make each particle on the vertical vibrating beam 1 all do the simple harmonic oscillation that equates along X-direction, be provided with one and its tool beam of adding at regular intervals on the upper strata of horizontal vibration beam 7, along horizontal vibration beam and it add beam directly to, respectively opened an equal in length, width equates that direction is identical, at isoplanar straight groove rail, the slide block of horizontal vibration beam 7 by being provided with on its two ends, be installed in the left vertical beam 16 of sphere of movements for the elephants shape framework respectively, the inboard straight groove rail 22 that is provided with of 17 two side bars of right vertical beam, in 23, make itself and left vertical beam, right vertical beam is realized being slidingly matched, and its job operation and effect are with vertical vibrating beam 1 together.

Described gear set, by rotating shaft be fixed on gear 2, rotating shaft on the middle cross beam 15 be fixed in gear 8, rotating shaft on the vertical beam 18 be fixed on mesomerism gear 10 on middle cross beam and the middle vertical beam junction and carry out transmission and cooperate institute to form; Rotating shaft is fixed on gear 2 on the middle cross beam 15 and a cylindrical columns 3 is set by gear drive, the effect that makes cylinder pillar 3 do uniform circular motion, make gear 2 and cylindrical columns 3 have " circle of reference " function on its edge, cylindrical columns 3 devices are within the straight groove rail 4 of vertical vibrating beam, realization is slidingly matched, each particle is all wiped vibration along the letter that X-direction is done to equate on the transmission vertical vibrating beam 1, and vibration equation is:

$X=R_3\mathrm{COS}(\frac{2\mathrm{\&pi;}}{T_1}t+{\mathrm{\&Phi;}}_1)$

R ₃It is the radius of gyration of cylindrical columns 3.

Gear 8 during rotating shaft is fixed on the vertical beam 18, install within the straight groove rail of horizontal vibration beam by a cylindrical columns 9 that is provided with on its edge, realization is slidingly matched, and each point is also all made equal simple harmonic oscillation, Fig. 5 along Y direction on the transmission horizontal vibration beam 7.

Vibration equation: y=R ₉COS (2 π t/T ₂+ Φ ₂), R ₉Be the radius of gyration of the cylindrical columns 9 at gear 8 edges on the vertical beam 18 during Fig. 5 shaft is fixed on to gear 8 rotating shafts, each point is done the equilibrium position of simple harmonic oscillation on the walking beam 7, on the horizontal linear of crossing gear 8 centers of circle, and the radius of gyration of the cylindrical columns 9 above the gear 8, also be amplitude, T ₂Be the cycle, Φ ₂It is first phase.The transmission of gear 2 and gear 8 is by mesomerism gear 10 transmissions.

Particle on the particle in gear 2, gear 8,10 3 gear uniform rotation of the mesomerism gear process on the vertical walking beam 1 and the walking beam 7 of level is done orthogonal simple harmonic oscillation, and the track of intersection point 11 is exactly a lissajous figures.

The assembly structure that described four layers of grooved rails intersection that hollow circuit cylinder penholder seat is housed are described mechanism is: vertical vibrating beam 1 is slidingly matched between horizontal vibration beam 7 and its two straight beams adding beam 14, sees Fig. 4; Horizontal vibration beam 7 add beam 14 between vertical vibrating beam 1 and its after frame beam 13, be slidingly matched.(drafting of Fig. 4 horizontal vibration beam 7 half-twists among Fig. 5, refills and joins a left side of painting behind the hollow circular cylinder penholder seat 12 and look cut-open view).Therefore, in Fig. 5, there are four layers of beam that grooved rail is all arranged at 11 places that vertical vibrating beam 1 and horizontal vibration beam 7 intersect, and constitute a foursquare square hole that certain depth is arranged, i.e. the position of intersection point 11 among Fig. 5.Hollow circular cylinder penholder seat 12 is installed within the square hole at intersection 11 places, sees Fig. 4.This structure is equipped with hollow circular cylinder penholder seat, and four layers of grooved rail intersect describes mechanism.Hollow circular cylinder penholder seat, no matter askew to where all have two beam supports that play point actions partially, make it can not be askew partially.Therefore, being inserted in animation pen in the hollow circular cylinder penholder seat 12 can be accurately, be drawn on a blank sheet of paper intersecting the track of the synthetic lissajous figures in 11 places among Fig. 5 glibly.

In operating process, can gear 2, gear 8, mesomerism gear 10 wherein any one gear be used as driving wheel, the artificial arbitrarily control of transmission speed.Therefore, in Fig. 5, vertical vibrating beam 1 and horizontal vibration beam 7 each particle are made the physical process that the intersection point 11 of the physical process of vibration and synthetic lissajous figures track is wiped in vertical letter mutually respectively, and naked eyes can be observed very clearly.According to $\frac{T_1}{{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="C0110645100202.png,C0110645100211.png"\; state="\{\{state\}\}">T</figure-callout>}}_2}=\frac{R_1}{{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="C0110645100202.png,C0110645100211.png"\; state="\{\{state\}\}">R</figure-callout>}}_2}$

With the standby tooth group of different radii, alternative commentaries on classics is fixed on the gear 8 on the middle vertical beam, then can change the ratio of orthogonal simple harmonic motion cycle.

Change the size of the radius of gyration of cylinder pillar 3 or cylindrical columns 9, then can change the amplitude of doing simple harmonic oscillation.Time t=0, change cylinder pillar 3 or cylindrical columns 9 radially with the horizontal direction angle, then change the first phase of doing simple harmonic oscillation.

Type demonstration instrument for teaching of the present invention, no matter whether mesomerism gear 10 makes uniform circular motion, and lissajous figures is constant.This is the another feature of this demonstrator.

Described, cosine, sinusoidal image are described mechanism, are two branch vibrations of the mutually vertical simple harmonic oscillation of demonstration machinery $X=A_1\mathrm{COS}(\frac{2\mathrm{\&pi;}}{T_1}t+{\mathrm{\&Phi;}}_1)$ Image---cosine image and $y=A_{21}\sin (\frac{2\mathrm{\&pi;}}{T_2}t+{\mathrm{\&Phi;}}_2)$ Image-sinogram as if such realization.The following Fig. 6 of meeting personally device at the gear (2) of accompanying drawing 5 has two Shape, the parallel sliding track (24) of certain width is arranged, between both slide rails of parallel sliding track (24), there be the rectangular of a lightweight can record $X=A_1\mathrm{COS}(\frac{2\mathrm{\&pi;}}{T_1}t+{\mathrm{\&Phi;}}_1),$ Image " the cosine image is described data board " (25) " cosine is described visual data board " (25) have processed one along its centerline direction with milling machine (or machine for sawing), one end opening, one end is opening not, the central channel that certain-length is arranged, the effect of this central channel has two: the one, when " the cosine image is described data board " (25) below gear (2) during translation, the rotation axis of gear (2) can unhinderedly slide relatively along the centre of this central channel; The 2nd, this central channel can be represented $X=A_1\mathrm{COS}(\frac{2\mathrm{\&pi;}}{T_1}t+{\mathrm{\&Phi;}}_1),$ The balance prosposition of image one cosine image, also can represent time (seven seconds) axle, " left side of cosine picture record plate (25); be equipped with a tooth bar (26); Fig. 7 when gear (2) uniform rotation counterclockwise the time along its rectangular long limit, this rack and pinion drive mechanism gearing has " the cosine image is described data board " (25) of tooth bar (26), two " Jiong " shapes; between the parallel slide rail (24), do at the uniform velocity straight line translation." the cosine image is described data board " (25) are in making at the uniform velocity straight line translation process, " the cosine image is described data board " (25), central channel, unhinderedly slip over the following rotation axis of gear (2), the translation direction is along the y direction of principal axis, from top to bottom, along doing at the uniform velocity straight line translation from inside to outside, " describing pen " (27) are handle automatically $X=A_1\mathrm{COS}(\frac{2\mathrm{\&pi;}}{T_1}t+{\mathrm{\&Phi;}}_1)$ Image---the cosine image is depicted on the blank sheet of paper of " the cosine image is described data board " (25) automatically, intuitively shows to the student $X=A_1\mathrm{COS}(\frac{2\mathrm{\&pi;}}{T_1}t+{\mathrm{\&Phi;}}_1)$ Image---the shape of cosine image, amplitude A ₁Size, first phase φ ₁Size, and the frequency of horizontal vibration (1) vibration $f=\frac{1}{T}$ In time t internal vibration how many times.

" describe pen " (2T) its lower end (27) of being mounted in horizontal vibration beam (1) shown in Figure 5 located, it is the same with all particles on the horizontal vibration beam (1), all is that the phase place of work machinery is identical, and amplitude A is identical, the simple harmonic oscillation that cycle is identical, vibration equation all is $X=A_1\mathrm{COS}(\frac{2\mathrm{\&pi;}}{T_1}t+{\mathrm{\&Phi;}}_1)$ Therefore, the cosine image of describing to write down on " the cosine image is described data board " (25) blank sheet of paper.Essence is the string image that horizontal vibration beam 1 is done the simple harmonic oscillation of machinery, its vibration equation intuitively confirmed be exactly $X=A_1\mathrm{COS}(\frac{2\mathrm{\&pi;}}{T_1}t+{\mathrm{\&Phi;}}_1),$ This visual figure to the student is directly perceived show after, and can also make the student intuitively observe the simple harmonic oscillation equation $X=A_1\mathrm{COS}(\frac{2\mathrm{\&pi;}}{T_1}t+{\mathrm{\&Phi;}}_1)$ Middle amplitude A ₁Size, first phase Φ ₁Size, at time t in second, vibration frequency $f=\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="C0110645100193.png,C0110645100194.png"\; state="\{\{state\}\}">T</figure-callout>}}_1}$ Finish the how many times vibration, therefore, it can make the student believe horizontal vibration beam I (comprising vertical vibrating beam 7) really, all is the simple harmonic oscillation of making machinery.Automatically describe the cosine image noted on " the cosine image is described data board " blank sheet of paper, when theory pushes away card, be to make " at the uniform velocity garden Zhou Yundong " from gear, harmonic motion and transmission " the cosine image is described data board " were done at the uniform velocity straight line translation and are pushed away that card comes out between transmission horizontal vibration beam was done, it is the figure of cosine image, but because gear 2, horizontal vibration beam 1, tooth bar 26, all be to belong to mechanical drive, interconnect, therefore, when practical operation is demonstrated, no matter whether the rotating speed of gear is even, and speed how, and the cosine image is irrelevant with the speed of rotating speed and translation all the time.Image is extremely stable, lecture experiment success ratio 100%, and this is an outstanding advantage of doing the mechanical type simple harmonic oscillation.Demonstration $y={\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="C0110645100202.png,C0110645100211.png"\; state="\{\{state\}\}">A</figure-callout>}}_2\mathrm{Sin}(\frac{2\mathrm{\&pi;}}{T_2}t+{\mathrm{\&Phi;}}_2)$ The method of two " parallel sliding track " (28) " sinusoidal image is described data board " (29) tooth bars (30) of image---sinusoidal image " are described pen " (31) their structure and assembling transmission is followed $X=A_1\mathrm{COS}(\frac{2\mathrm{\&pi;}}{T_1}t+{\mathrm{\&Phi;}}_1),$ (27) their structure that image---cosine image two " parallel sliding track " (24) " the cosine image is described data board " (25) tooth bars (26) " are described pen ", and the assembling drive method identical.But the installation site difference is described sinusoidal visual two " parallel sliding track " (28) " sinusoidal image is described data board " (29) tooth bars (30), device below gear (8).When intermediary's gear (10) clockwise direction is rotated, transmission gear also is counterclockwise to rotate, tooth bar translation below the tooth transmission below the gear, direction along the X-axis positive dirction from left to right, from inside to outside do the straight line translation, " describing pen " (31) that are installed in vertical vibrating beam right-hand member are depicted in the figure of sinusoidal image automatically on the blank sheet of paper of " sinusoidal image is described data board " (29), intuitively show to the student.Gear 8 is thicker than the thickness of mesomerism gear, tooth below the gear (8) both constituted gear---gear drive with mesomerism gear (10), transmission mutually, and gear (8) constitutes gear---rack gear with tooth bar (30) again, transmission mutually, gear (8) driving rack is done at the uniform velocity straight line translation.The central channel of " just surplus image is described data board " (29) slips over the following rotating shaft of gear (8) unimpededly between the central channel

Inventing type, the Lissajous figure demonstrating and automatically tracing instrument " than the further innovative design of utility model " lissajous figures demonstration instrument for teaching " warp; increased cosine image demonstration device and sinusoidal image demonstration device newly; but general structure is still the same with utility model " lissajous figures demonstration instrument for teaching ": structure letter U.S.; lines are lucid and lively; in light weight, and teacher's 1 staff is guided and supported and taken to conveniently, and is easy and simple to handle; image stability, no matter the rotating speed speed how or not evenly, image all remains unchanged, lecture experiment, success ratio 100%, during the demonstration operation, lissajous figures, cosine image, sinusoidal image, the three can be depicted on the paper simultaneously, also can only describe wherein any two figure pictographs (image), also can only describe wherein any figure (image) naked eyes and can also intuitively observe $X=A_1\mathrm{COS}(\frac{2\mathrm{\&pi;}}{T_1}t+{\mathrm{\&Phi;}}_1)$ $y={\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="C0110645100202.png,C0110645100211.png"\; state="\{\{state\}\}">A</figure-callout>}}_2\mathrm{Sin}(\frac{2\mathrm{\&pi;}}{T_2}t+{\mathrm{\&Phi;}}_2)$ Amplitude A in two images ₁, A ₂, therefore, have more novelty, have more creativeness, have more practicality, be optimal demonstrator.Produce market will further enlarge, junior middle school " mathematics " senior middle school, special secondary school " mathematics " " physics " junior college, university's " general physics ", " mathematical physics " all will be used it, and wealth of society increasing degree increases greatly, can objectively and impartially embody the value of state-nation's spiritual wealth." oscillograph " " computer " also can show lissajous figures and sinusoidal image, the cosine image, but because the electric current vibration frequency is very high, the physics that the electric current that naked eyes be can't see both is at all done simple harmonic oscillation cross and synthesize lissajous figures physical process, both more can not be intuitively, controllably, figure (image) is depicted on the blank sheet of paper automatically, about $X=A_1\mathrm{COS}(\frac{2\mathrm{\&pi;}}{T_1}t+{\mathrm{\&Phi;}}_1),$ $y={\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="C0110645100202.png,C0110645100211.png"\; state="\{\{state\}\}">A</figure-callout>}}_2\mathrm{Sin}(\frac{2\mathrm{\&pi;}}{{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="C0110645100193.png,C0110645100194.png"\; state="\{\{state\}\}">T</figure-callout>}}_1}+{\mathrm{\&Phi;}}_2)$ But both can not expire amplitude A ₁≠ A ₂, the cycle Be just whole ratio, first phase Φ ₁≠ Φ ₂All conditions, the both is very heavy, when both demonstrate, annex is all a lot, portable the carrying of both teacher 1 people inconvenience in the presentation process, and " computer " demonstration lissajous figures, cosine image, sinusoidal image also will take a lot of times volumes " demonstration program ", general teacher does not possess the ability of volume " demonstration program ", the student is to compiling the sense that " demonstration program " more has a kind of reality to think, and both demonstrate image and can image be flashed because of the fluctuation of electric current, instability, and both cannot say for sure to demonstrate,prove success ratio 100% lecture experiment.

Therefore, inventing type, the Lissajous figure demonstrating and automatically tracing instrument is alternative " oscillograph ", " computer " ocular demonstration Lee's Sa such as image, cosine image, the optimal religion directly perceived of sinusoidal image Learn demonstrator.

Effect also has:

The first, have more novelty. To the applying date, not yet openly used at home this The demonstration instrument of type.

The second, have more creativeness. Type demonstrator of the present invention, than utility model: Li Sa as figure The mechanism that shape increased ocular demonstration newly, describe cosine image, sinusoidal image automatically intuitively drills Showing the true rule of physics, is not analog demenstration, neither indirectly reflect demonstration, scientific strong. " oscillograph " " computer " profit has shaking of the electric current of mutually vertically doing simple harmonic oscillation before the applying date Moving, be analog demenstration, indirectly reflection demonstration, simultaneously, in scientific research, research is mutually appoints During the meaning angle, different cycles, different first phases, the synthesising pattern of various amplitude simple harmonic oscillation is carried Supplied method and the approach of dealing with problems.

Four layers of grooved rail intersect describes mechanism, is a kind of have novelty, creativeness and practicality New transmission mechanism in Lee's Sa duty graphic teaching demonstrator, has and automatically describes function. For its Its aspect design class like automatically describe mechanism or processing equipment provide a kind of new mentality of designing and Way to solve the problem. Inventing type, the Lissajous figure demonstrating of initiative are retouched automatically both at home and abroad Paint instrument " " model machine " trial-produceed successfully, its duty meets the invention designing requirement fully Ideal. More than be exactly inventing type Lissajous figure demonstrating and automatically tracing instrument ", be Have most novelty the present age both at home and abroad, the most creative, the explanation that has practicality most.

Claims (2)

1. Lissajous figure demonstrating and automatically tracing instrument, by framework, walking beam, gear set and lissajous figures describe mechanism, cosine image displaying mechanism, sinusoidal image displaying mechanism sequentially mechanical realization be connected, it is characterized in that: described framework is sphere of movements for the elephants shape, and thereon crossbeam (5), sill (6), left crossbeam (16), right crossbeam (17) along the inboard of each bar beam directly to, all opened a same even depth, equal length, same widths, symmetrical straight groove rail (20), (21), (22), (23);

Described walking beam is made up of the total beam of vertical vibrating of article one vertical direction installation that is crossed as "+" word shape mutually and the total beam of horizontal vibration that the second horizontal direction is installed, article one, the total beam of vertical vibrating is on the upper strata of its vertical vibrating beam (1), directly has a determining deviation with it along it to installing one, Dui Cheng article one is added beam (13) in opposite directions, along vertical vibrating beam (1) and it add beam (13) directly to respectively having opened an equal in length, width equates, direction is identical, at conplane straight groove rail (4), a slide block of symmetry is in opposite directions installed at the two ends of vertical vibrating beam (1) respectively, constitute the total beam of article one vertical vibrating, the slide block at vertical vibrating beam (1) two ends is installed in the entablature (5) of sphere of movements for the elephants shape framework respectively, the straight groove rail (20) of (6) two side bar inboards of sill, (21) be slidingly matched within, each particle of the total beam of realization article one vertical vibrating is all done the simple harmonic oscillation of identical rule, the total beam of second horizontal vibration is on the upper strata of its horizontal vibration beam (7), directly has a determining deviation with it along it to installing one, Dui Cheng second is added beam (14) in opposite directions, along horizontal vibration beam (7) and it add beam (14) directly to respectively having opened an equal in length, width equates, direction is identical, at conplane straight groove rail, a slide block of symmetry is in opposite directions installed at the two ends of horizontal vibration beam (7) respectively, constitute the total beam of second horizontal vibration, the slide block at horizontal vibration beam (7) two ends is installed in the left vertical beam (16) of sphere of movements for the elephants shape framework respectively, the straight groove rail (22) of (17) two side bar inboards of right vertical beam, (23) be slidingly matched within, each particle of realization second horizontal vibration beam is all done the simple harmonic oscillation of identical rule, vertical vibrating beam (1) is added between the beam (14) at the second of horizontal vibration beam (7) and horizontal vibration beam (7) and is slidingly matched, and the second of horizontal vibration beam (7) is added beam (14) and added between the beam (13) in article one of vertical vibrating beam (1) and vertical vibrating beam (1) and be slidingly matched;

Described gear set is fixed on first gear (2) on the middle cross beam (15) by rotating shaft, rotating shaft is fixed on second gear (8) on the middle vertical beam (18), rotating shaft be fixed on the 3rd mesomerism gear (10) on middle cross beam (15) and middle vertical beam (18) junction carry out transmission cooperate form, rotating shaft is fixed on first gear (2) on the middle cross beam (15) and is installed in by first circular pillar (3) of installing on its edge within the straight groove rail (4) of vertical vibrating beam (1) and realizes being slidingly matched, rotating shaft is fixed on second gear (8) on the middle vertical beam (18), is installed in by second cylindrical columns (9) of installing on its edge within the straight groove rail of horizontal vibration beam (7) to realize being slidingly matched;

Described lissajous figures is described mechanism, the animation penholder is inserted within the hollow of hollow circular cylinder penholder seat (12), hollow circular cylinder penholder seat is installed in to be added beam (13) and horizontal vibration beam (7) and its second by first of vertical vibrating beam (1) and it and adds within the square hole (11) of four layers of grooved rail infall that beam (14) constituted, hollow circular cylinder penholder seat (12) is carried out with four layers of square hole that grooved rail constituted (11) and is slidingly matched, and transmission " animation pen " is described lissajous figures automatically on blank sheet of paper;

2. according to the Lissajous figure demonstrating and automatically tracing instrument of claim 1, described cosine image displaying mechanism is made up of two slide rails (24) and cosine image displaying data board (25) that " ∩ " shape structure shape is installed, two slide rails (24) of " ∩ " shape structure shape along the inboard of each bar slide rail directly to, all opened a same even depth, equal length, parallel in opposite directions, symmetrically, at grade directly to slide rail be installed in first gear (2) below, article two, slide rail (24) is installed with the rotating shaft symmetry of first gear (2) and the also vertical sill (6) of vertical X-axis, cosine image displaying data board (25) is the uniformly positive rectangular slab of a thickness, processed an end opening along its longitudinal centre line, one end is opening not, the center grooved rail that certain width is arranged, article one, tooth bar (26) is installed on the long limit of positive rectangular slab and is parallel with the center grooved rail, constitute cosine image displaying data board (25), two long limits of cosine image displaying data board (25) are installed in respectively between two slide rails (24) of " ∩ " shape structure shape and are slidingly matched, article one tooth bar (26) that is installed on the long limit of cosine image displaying record plate (25) cooperates with first gear (2) transmission, describe the interior close sill (6) of circular hole that penholder (27) is inserted in article one vertical vibrating Zong Liang lower end for first, realize describing the cosine image automatically on the blank sheet of paper of cosine image displaying data board (25), described sinusoidal image is described mechanism and is made up of two slide rails (24) and sinusoidal image displaying data board (29) that " ∩ " shape structure shape is installed, two slide rails (24) of " ∩ " shape structure shape along the inboard of each bar slide rail directly to all having opened a same even depth, equal length, parallel in opposite directions, symmetrically, at grade directly to slide rail be installed in second gear (8) below, article two, slide rail (24) is installed with the rotating shaft of second gear (8) symmetry and also vertical right vertical beam (17) of vertical Y axle, it is the uniformly positive rectangular slab of a thickness that sinusoidal image is described data board (29), processed an end opening along its longitudinal centre line, one end is opening not, the center grooved rail that certain width is arranged, second tooth bar (30) is installed on the long limit of positive rectangular slab and is parallel with the center grooved rail, constitute sinusoidal image displaying data board (29), two long limits of sinusoidal image displaying data board (29) are installed in respectively between two slide rails (24) of " ∩ " shape structure shape and are slidingly matched, the second gear bar (30) that is installed on the long limit of sinusoidal visual data board (29) cooperates with second gear (8) transmission, describe the interior close right vertical beam (17) of circular hole that penholder (31) is inserted in the total beam right-hand member of second horizontal vibration, realize describing automatically sinusoidal image and describe on the blank sheet of paper of data board (29) for second in sinusoidal image.

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