CN2313258Y - Lisaru figure-teaching demonstration instrument - Google Patents

Abstract

The utility model relates to a lisaru figure-teaching demonstration instrument which can control rotational speed, make mechanically mutually vertical simple harmonic vibration and automatically describe figurers on paper. A stanchion (3) on a gear (2) of the utility model can drive a vertical vibrating beam (1) to make the simple harmonic vibration along a horizontal direction, and a stanchion (9) on a gear (8) can drive a horizontal vibrating beam (7) to make the simple harmonic vibration along a vertical direction; a lisaru figure can be formed on the crossing point (11) of the vertical vibrating beam and the horizontal vibrating beam. The vibrating beam (1) and a frame complementing beam on the upper layer of the vibrating beam (1) as well as the vibrating beam (7) and a frame complementing beam on the upper layer of the vibrating beam (7) are all provided with grooved rails which are installed by crossing, and the intersection point (11) of the four grooved rails is provided with a hollow circular cylinder penholder seat to form a four-layer grooved rails crossed drawing mechanism with a pen automatically draw the figures on the paper.

Description

The lissajous figures demonstration instrument for teaching

The utility model belongs to the physics teaching demonstrator, particularly can ocular demonstration describes the demonstration instrument for teaching of lissajous figures.

The applying date had " oscillograph " can drill lissajous figures in the past.

But oscillograph has weak point, and it is exactly that particle is made the process of orthogonal simple harmonic oscillation and the synthetic process of lissajous figures, is that the vibration by electric current realizes.Because the frequency of electric current vibration is very high, therefore, naked eyes can't be observed the physical process of orthogonal simple harmonic oscillation and the physical process of synthetic lissajous figures at all, and intuitive is poor, and the student understands still difficult.The purpose of this utility model is at above-mentioned situation, and always from the perception to the rational faculty, therefore development is with the synthetic lissajous figures of the orthogonal simple harmonic oscillation of machinery according to people's law of cognition.The speed of mutually vertical simple harmonic oscillation and the speed of synthetic lissajous figures are slowed down greatly, even its speed manually can be controlled, make the student can observe directly particle and make the physical process of mutually vertical simple harmonic oscillation and the physical process of synthetic lissajous figures, can also observe the lissajous figures demonstration instrument for teaching, it automatically is depicted in lissajous figures on a blank sheet of paper, solve the intuitive problem, the reform teaching means is improved the quality of teaching.

The purpose of this utility model is achieved in that describing mechanism by framework, walking beam, gear set and four layers of grooved rail that hollow circular cylinder penholder seat is housed is formed.Framework is a sphere of movements for the elephants shape, and the four edges beam inboard of crossbeam 5, sill 6, left vertical beam 16, right vertical beam 17 thereon, has all milled same even depth with milling machine, 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, 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 rail 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, install within the straight groove rail of horizontal vibration beam by a cylindrical columns 9 that is 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, thus the animation pen the demonstration of the track lissajous figures of infall, be depicted on a blank sheet of paper, reach the purpose of the utility model demonstrator development.

Below in conjunction with drawings and Examples the utility model is further specified.

Fig. 1 utilizes " circle of reference " to push away the figure that particle of card is done simple harmonic oscillation.

Fig. 2 utilizes " circle of reference " to push away the figure that line of card is done simple harmonic oscillation.

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 cylinder penholder seat 12.

Accompanying drawing 5 is the utility model one-piece construction principle sketch.

Basic reason of the present utility model is former to be: 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 doing at the uniform velocity fast circular motion, the displacement of the projection P of particle M on X-axis is x.Fig. 1 x=R _ACOSa

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 _AIt is the amplitude that the P point is done simple harmonic oscillation.T ₁Being the cycle that particle M does uniform circular motion, also is that the P point is done simple harmonic motion cycle.

φ 1 be 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 of simple harmonic oscillation.

If projection straight line MP is prolonged, Fig. 2, the projection straight line after the prolongation is represented with S, gets any 1 P ' on S, then P ' is being parallel to O _AVibration back and forth on the O ' P ' straight line on the straight line of P, balance is drawn and is put at O ', promptly crosses O _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

$x\′=R_A\mathrm{COS}(\frac{2\mathrm{\π}}{\mathrm{\π}}t+{\mathrm{\Φ}}_1)$

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=R _ACOS (2 π t/ _T1+ φ ₁), if in Fig. 3, overlaps with vibration projection straight line S all the time with a vertical vibrating beam 1, 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 is the one-piece construction principle sketch of the utility model lissajous figures demonstration instrument for teaching.

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, opened respectively that an equal in length, width equate, direction is identical, at conplane straight groove rail 4, be 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, direction is identical, at isoplanar straight groove rail, the slide block of horizontal vibration beam 7 by being provided with on its two ends is 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, its job operation and effect with vertical vibrating beam 1 with.

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 is provided with a cylindrical columns 3 on its edge, by gear drive, make cylindrical columns 3 do uniform circular motion, the effect that makes gear 2 and cylindrical columns 3 have " circle of reference " function, cylindrical columns 3 devices are within the straight groove rail 4 of vertical vibrating beam, realization is slidingly matched, and each particle is all done equal simple harmonic oscillation along X-direction on the transmission vertical vibrating beam 1, and vibration equation is: $x={\mathrm{<figure-callout\; id="3"\; label="R"\; filenames="Y9720929600111.png"\; state="\{\{state\}\}">R</figure-callout>}}_3\mathrm{COS}(\frac{2\mathrm{\&pi;}}{\mathrm{\&pi;}}t+{\mathrm{\&phi;}}_1)$

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, the radius of gyration of the cylindrical columns 9 above the gear 8, it also is amplitude, T2 is 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 circular 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 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 matter are made the physical process of the intersection point 11 of the physical process of vertical simple harmonic oscillation mutually and synthetic lissajous figures track respectively, and naked eyes can be observed very clearly

With the equipment gear group of different radii, alternative rotating shaft 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.

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

Effect:

The first, have novelty.To the applying date, the still unexposed at home demonstration instrument that used the type.

The second, creative." oscillograph " utilizes the vibration of vertically making the electric current of simple harmonic oscillation mutually before the applying date, can demonstrate lissajous figures, but because the frequency of oscillating current is too high, the building-up process of mutually vertical simple harmonic oscillation process and synthetic lissajous figures, naked eyes can't be observed clear at all, and intuitive is poor, the lissajous figures demonstration instrument for teaching, with the synthetic lissajous figures of the orthogonal simple harmonic oscillation of machinery, manually can control the speed of vibration frequency.Therefore, naked eyes are can Direct observation clear, and the physical process and the synthetic physical process of lissajous figures of vibration wiped in mutually vertical letter, and be very directly perceived, and this is one of creative.

This demonstrator intersects by four layers of special grooved rail describes mechanism, can make the animation pen that the lissajous figures building-up process is drawn in one on paper, and this is two of a creativeness.

The 3rd, have practicality.As the demonstrator in school's physics teachings such as university, junior college, technical secondary school, regular senior secondary school, can also drill instrument as university's (mathematics, physics) teaching.Reform the classroom instruction means, improve Classroom Teaching, school is many, and demand is also many, and this is one of practicality.Simultaneously, in scientific research, research is mutually when arbitrarily angled, different cycles, and different first phases, the synthesising pattern of various amplitude simple harmonic oscillation provides the method and the approach of dealing with problems, and this is two of a practicality.

Four layers of grooved rail intersect describes mechanism, is a kind of new gear train with novelty, creativeness and practicality, in Lee's Sa duty graphic teaching demonstrator, has and describes function automatically.For the others design class provides a kind of new mentality of designing and the approach of dealing with problems like describing mechanism automatically.

It more than is exactly the effect of " each graphic teaching demonstrator of Lee's Sa ".

Claims (1)

1. lissajous figures demonstration instrument for teaching, by framework, walking beam, gear set and describe mechanism sequentially mechanical realization be connected, it is characterized in that: described framework is sphere of movements for the elephants shape, and crossbeam thereon ⁽⁵⁾, sill ⁽⁶⁾, left vertical beam ⁽¹⁶⁾, right vertical beam ⁽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 by the vertical vibrating beam that is crossed as " ten " word shape mutually ⁽¹⁾With the horizontal vibration beam ⁽⁷⁾Form, be provided with on the upper strata of vertical vibrating beam one with its tool beam of adding at regular intervals ⁽¹³⁾, along vertical vibrating beam and it add beam directly to, opened respectively that an equal in length, width equate, direction is identical, at conplane straight groove rail ⁽⁴⁾, the vertical vibrating beam ⁽¹⁾By the slide block that is provided with on its two ends, be installed in the entablature of sphere of movements for the elephants shape framework respectively ⁽⁵⁾, sill ⁽⁶⁾Article two, the inboard straight groove rail that is provided with of side bar ⁽²⁰⁾, ⁽²¹⁾In, make itself and entablature, sill is realized being slidingly matched, and is 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 that direction is identical, at isoplanar straight groove rail, horizontal vibration beam ⁽⁷⁾By the slide block that is provided with on its two ends, be installed in the left vertical beam of sphere of movements for the elephants shape framework respectively ⁽¹⁶⁾, right vertical beam ⁽¹⁷⁾Article two, the inboard straight groove rail that is provided with of side bar ⁽²²⁾, ⁽²³⁾In, making itself and left vertical beam, right vertical beam is realized being slidingly matched the vertical vibrating beam ⁽¹⁾At the level beam that shakes ⁽⁷⁾With its beam of adding ⁽¹⁴⁾Between, be slidingly matched the horizontal vibration beam ⁽⁷⁾Add beam ⁽¹⁴⁾At the vertical vibrating beam ⁽¹⁾With its beam of adding ⁽¹³⁾Between, be slidingly matched;

Described gear set is fixed on middle cross beam by rotating shaft ⁽¹⁵⁾On gear ⁽²⁾, rotating shaft is fixed on middle vertical beam ⁽¹⁸⁾On gear ⁽⁸⁾, rotating shaft is fixed on the mesomerism gear on middle cross beam and the middle vertical beam junction ⁽¹⁰⁾Carrying out the transmission cooperation forms; Rotating shaft is fixed on middle cross beam ⁽¹⁵⁾On gear ⁽²⁾By a cylindrical columns that is provided with on its edge ⁽³⁾Device is at the straight groove rail of vertical vibrating beam ⁽⁴⁾Within, realizing being slidingly matched, rotating shaft is fixed on middle vertical beam ⁽¹⁸⁾On gear ⁽⁸⁾, by a cylindrical columns that is provided with on its edge ⁽⁹⁾Device is realized being slidingly matched within the straight groove rail of horizontal vibration beam;

The described mechanism of describing, the animation penholder is inserted in hollow circular cylinder penholder seat ⁽¹²⁾Hollow within, hollow circular cylinder penholder seat is installed in the vertical vibrating beam ⁽¹⁾With its beam of adding ⁽¹³⁾Straight groove rail, horizontal vibration beam ⁽⁷⁾With its beam of adding ⁽¹⁴⁾Straight groove rail infall, by four layers of square hole that grooved rail constituted ⁽¹¹⁾Within, hollow circular cylinder penholder seat ⁽¹²⁾With four layers of square hole that grooved rail constituted ⁽¹¹⁾Implementation is slidingly matched.

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