CN104309371B - A kind of conic section drawing apparatus - Google Patents
A kind of conic section drawing apparatus Download PDFInfo
- Publication number
- CN104309371B CN104309371B CN201410586846.8A CN201410586846A CN104309371B CN 104309371 B CN104309371 B CN 104309371B CN 201410586846 A CN201410586846 A CN 201410586846A CN 104309371 B CN104309371 B CN 104309371B
- Authority
- CN
- China
- Prior art keywords
- guide rail
- slide block
- conic section
- tooth bar
- gear
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
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Classifications
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B43—WRITING OR DRAWING IMPLEMENTS; BUREAU ACCESSORIES
- B43L—ARTICLES FOR WRITING OR DRAWING UPON; WRITING OR DRAWING AIDS; ACCESSORIES FOR WRITING OR DRAWING
- B43L11/00—Non-circular-curve-drawing instruments
- B43L11/02—Non-circular-curve-drawing instruments for drawing conic sections
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B43—WRITING OR DRAWING IMPLEMENTS; BUREAU ACCESSORIES
- B43L—ARTICLES FOR WRITING OR DRAWING UPON; WRITING OR DRAWING AIDS; ACCESSORIES FOR WRITING OR DRAWING
- B43L11/00—Non-circular-curve-drawing instruments
- B43L11/02—Non-circular-curve-drawing instruments for drawing conic sections
- B43L11/04—Non-circular-curve-drawing instruments for drawing conic sections for drawing ellipses
- B43L11/05—Non-circular-curve-drawing instruments for drawing conic sections for drawing ellipses with gears
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- Engineering & Computer Science (AREA)
- Mechanical Engineering (AREA)
Abstract
A kind of conic section drawing apparatus of this disclosure of the invention, can realize parabola, ellipse, hyp drafting.Need first to arrange the angle between L shape mechanism and base guide rail according to the eccentricity of conic section during picture conic section, the acute angle between setting base guide rail and x guide rail is θ, fixed base guide rail, then fixed-focus; Then L shape mechanism promoted along base guide rail, the tooth bar two fixed with x slide block moves up in y guide rail side the distance of △ y, and by gear, the distance of △ y is passed to tooth bar one, the distance between pencil to focus will increase the length of △ y; The straight-bar fixed with y slide block moves up in x guide rail side the distance of △ x, and namely pencil increases the distance of △ x to the directrix of drawn conic section; Because
for certain value, so pencil is also definite value to distance and the pencil of focus to the ratio of distances constant of drawn conic section directrix and equal with tan θ, meets the definition of conic section, thus realize parabola, ellipse, hyp drafting.
Description
Art
The present invention adopts pure frame for movement to realize the drafting of conic section (parabola, ellipse, hyperbola).
Background technology
Conic section comprises ellipse, parabola, hyperbola, is all one of important topic of Study on Geometry all the time, in our real life, also there is various conic sections.
We run by the earth of life all the time on the circumsolar elliptical orbit of ring, and other planets of the solar system are also like this, and the sun is then positioned in an oval focus.If these planet speeds of service increase to a certain degree, they will run along parabola or hyperbola.The mankind launch artificial earth satellite or artificial planet will in accordance with this principle.Relative to an object, the motion of another object attracted by it by the law of universal gravitation, can not have any other track.Thus, conic section is said in the sense that, it constitutes the citation form in our universe.Many important curved surfaces are also derived, such as the face of cylinder, ellipsoid, single leaf and hyperboloid of two sheets and various parabolas etc. by conic section.
In brief, conic section no matter in mathematics or other science and technology field, or all occupies an important position in our real life.Conic section is not only the basis of planet research in physics, mechanics, electricity and calorifics, or the important component part in geometry teaching.Although the study of conic section and application are through in senior middle school, university and engineering application, so far, market still not having can the conic section of the different equation of accurate Drawing.But conical section drawing instrument for study, to study or use the personnel of this knowledge theory be but an indispensable instrument, by drawing the conic section of different equation, principle and the formation of different conic section can be understood, the integral status of drawing can also be improved, to the study of different equation of conic section and research.
Therefore, we wish, can as drafting circle the same with straight line convenient, go to draw conic section simply, thus realization is not only theoretic study to conic section, is more will apply in practical application.
Summary of the invention
The present invention is directed to the technology that the deficiencies in the prior art solve and be to provide that a kind of cost is low, simple to operate draws parabola, ellipse, hyp plotting unit.
A kind of conic section drawing apparatus of the present invention defines according to conic section second: as 0 < e < 1, and track is oval; During e=1, track is parabola; During e > 1, track is hyperbola, and wherein e is the eccentricity of conic section.Fixed one end of x guide rail and y guide rail, form L shape mechanism, x guide rail is arranged x slide block, y guide rail is arranged y slide block, wherein y slide block fixes a straight-bar vertical with y guide rail, the straight-bar other end and tooth bar one chain connection, and chain connection point arranges pencil; X slide block and tooth bar two are fixed, and tooth bar two is perpendicular to x guide rail, and tooth bar one and tooth bar two are by gears meshing, and the focal point settings of conic section is in gear centre; The summit of L shape mechanism to be arranged on a slide block and can to regulate rotational angle around both tie points, and this slide block is arranged on base guide rail.Need first to arrange the angle between L shape mechanism and base guide rail according to the eccentricity of conic section during picture conic section, the acute angle between setting base guide rail and x guide rail is θ, fixed base guide rail, then fixed-focus; Then L shape mechanism promoted along base guide rail, the tooth bar two fixed with x slide block moves up in y guide rail side the distance of Δ y, and by gear, the distance of Δ y is passed to tooth bar one, the distance between pencil to focus will increase the length of Δ y; The straight-bar fixed with y slide block moves up in x guide rail side the distance of Δ x, and namely pencil increases the distance of Δ x to the directrix of drawn conic section; Because
for certain value, so pencil is also definite value to distance and the pencil of focus to the ratio of distances constant of drawn conic section directrix and equal with tan θ, meets the definition of conic section, thus realize goal of the invention.
Thus a kind of conic section drawing apparatus of the present invention comprises: foundation guide rail mechanism, L shape guide rail mechanism, transmission mechanism; It is characterized in that described foundation guide rail mechanism comprises: be fixed on the pedestal of workbench, the base guide rail be arranged on pedestal, base guide rail arrange slide block one; Described L shape guide rail mechanism comprises: x guide rail, y guide rail and correspondence are arranged at x slide block, y slide block on two guide rails, and wherein one end of two guide rails is fixedly connected to form L shape structure; The summit of L shape guide rail mechanism is arranged on slide block one, and can regulate the anglec of rotation of L shape guide rail around tie point; Described transmission mechanism comprises: straight-bar, tooth bar one, gear, tooth bar two, one end of straight-bar and tooth bar one chain connection, and this chain connection point is image output point, and tooth bar one and tooth bar two pass through gears meshing; In transmission mechanism, the other end of straight-bar is fixedly installed on y slide block, and vertical with y guide rail, and one end of tooth bar two is arranged on x slide block, and vertical with x guide rail; During drawing, gear is fixed on workbench, can only rotate, and fixing point is the focus of painted conic section.
Further, in described transmission mechanism, arrange gear one and engage with tooth bar one, and to be arranged in parallel one x ' guide rail with tooth bar one, x ' guide rail is arranged x ' slide block, gear one axle center is fixed on x ' slide block; Arrange gear two to engage with tooth bar two, and to be arranged in parallel one y ' guide rail with tooth bar two, y ' guide rail is arranged y ' slide block, the axle center of gear two is fixed on y ' slide block; Gear one is axially connected with gear two, and x ' slide block or y ' slide block arrange a focus pin, as the focus of drawn conic section.
Further angle dial is set on slide block one, facilitates the angle between fine adjustment L shape guide rail mechanism and slide block one.
A kind of conic section drawing apparatus of the present invention, comprising: foundation guide rail mechanism, L shape guide rail mechanism, transmission mechanism; In conic section drawing process, simple translation is exported conic section by this device, have that cost is low, simple to operate draws parabola, ellipse, hyp effect.
Accompanying drawing explanation
Fig. 1 is the schematic diagram of a kind of conic section drawing apparatus of the present invention;
Fig. 2 is a kind of conic section drawing apparatus of the present invention schematic diagram;
Fig. 3 is a kind of conic section drawing apparatus of the present invention middle rack one and tooth bar two mesh schematic representation.
In figure: 1.y guide rail, 2.y slide block, 3. slide block one, 4. pedestal, 5. base guide rail, 6.x guide rail, 7.x slide block, 8.y ' guide rail, 9.y ' slide block, 10.x ' guide rail, 11. focus pins, 12. pencils, 13. gear two, 14.x ' slide blocks, 15. gears one.
Detailed description of the invention
For accompanying drawing, specific embodiments of the invention are described below.The long 280mm of x guide rail of the present invention long 275mm, y guide rail, the long 300mm of base guide rail, and x guide rail, y guide rail, x ' guide rail, y ' guide rail are two guide rail structure, and each guide rail is cylinder rod, and its diameter is 6mm, is connected between guide rail and slide block by linear bearing; X guide rail and Y guide rail are integrated fixed structure, and XY rail sections and base rail sections are chain connection.Unclamp hinge, the adjustment of two parts angle can be realized.; Fastening hinge, simple operations can realize drawing function.Rack pinion part, wherein two gears are the precision gear of 0.5 mould 20 tooth diameter 11mm; Article two, tooth bar is the accurate tooth bar that 0.5 Mould Breadth 4mm thick 8mm precision is international seven grades.
Structure one
model, and this relationship model is obtained horizontal movement increment Delta x, vertical motion increment Delta y by the tiltedly straight motion of decomposing slide block, and by regulating fixing θ angle to make this two componental movements increment keep proportions constant always, so just, can eccentricity e be determined and ensure that it is constant in whole drawing course, namely reaching our the set goal.By above-mentioned design, we realize tiltedly straight motion by linear bearing slide block group at slide on rails, by the Kinematic Decomposition of orthogonal vertical bar and horizon bar with transmit the horizontal movement increment Delta x and the vertical motion increment Delta y that realize paintbrush respectively, between chute and horizon bar, the size of angle θ is adjustable, forms thus
model.Have according to conic section second definition, graphical pointv arrives the ratio of distance p of corresponding directrix to the distance l of corresponding focus with it
so graphical pointv meets
relational expression.We adopt the accurate rack and pinion of 0.5 mould, easily can find out that two toothed rack motions are equal along the displacement size in nodel line direction after getting up from figure.Pencil is Δ l to the distance increment of focus pin, and pencil is Δ p to the distance increment of corresponding directrix, the horizontal movement increment Delta x of the kinetic vertical bar of pencil, the vertical motion increment Delta y of horizon bar, and be easy to get relation:
then obtain e=k=tan θ, namely graphical pointv is met the transformation of e in order to the control to θ value.So, the determination of eccentricity can be realized by θ angular adjustment.In addition, by the clutch of adjusting gear tooth bar, the size of initial Δ m can be changed.
According to the second definition of conic section, just conic section can be drawn out easily by adjusting several parameter.The nib of pencil is exactly dynamic some P (x in plane, y), position the F (-c of focus pin, 0) be exactly focal position, only need to control braking point P (x, y) distance to fixed point F (-c, 0) is a constant e (e > 0) with the ratio of distances constant of the boning out l (corresponding directrix) do not fixed a point by this, then the track of dynamic point is exactly specific conic section.
For oval and hyperbola, as long as determine c, e two parameters, namely draw the position of front focus F (-c, 0) and summit (-a, 0), just can determine eccentricity e=c/a, just can draw out ellipse or hyperbola.
For parabola, only need to determine this parameter of p, namely draw front focus
with the position of summit (0,0), parabola (parabolical eccentricity e=1) just can be drawn out.
In sum, for conic section (ellipse, hyperbola, parabola), as long as determine focal position and be positioned at the vertex position on axis of abscissas, just eccentricity can be tried to achieve
then regulate horn craving scale make θ=arctane and remain unchanged, finally drag pencil, just can draw out the conic section of corresponding parameter.
Claims (3)
1. a conic section drawing apparatus, this device comprises: foundation guide rail mechanism, L shape guide rail mechanism, transmission mechanism; It is characterized in that described foundation guide rail mechanism comprises: be fixed on the pedestal of workbench, the base guide rail be arranged on pedestal, base guide rail arrange slide block one; Described L shape guide rail mechanism comprises: x guide rail, y guide rail and correspondence are arranged at x slide block, y slide block on two guide rails, and wherein one end of two guide rails is fixedly connected to form L shape structure; The summit of L shape guide rail mechanism is arranged on slide block one, and can regulate the anglec of rotation of L shape guide rail around tie point; Described transmission mechanism comprises: straight-bar, tooth bar one, gear, tooth bar two, one end of straight-bar and tooth bar one chain connection, and this chain connection point is image output point, and tooth bar one and tooth bar two pass through gears meshing; In transmission mechanism, the other end of straight-bar is fixedly installed on y slide block, and vertical with y guide rail, and one end of tooth bar two is arranged on x slide block, and vertical with x guide rail; During drawing, gear is fixed on workbench, can only rotate, and fixing point is the focus of painted conic section.
2. a kind of conic section drawing apparatus as claimed in claim 1, it is characterized in that in described transmission mechanism, gear one is set and engages with tooth bar one, and to be arranged in parallel one x ' guide rail with tooth bar one, x ' guide rail is arranged x ' slide block, gear one axle center is fixed on x ' slide block; Arrange gear two to engage with tooth bar two, and to be arranged in parallel one y ' guide rail with tooth bar two, y ' guide rail is arranged y ' slide block, the axle center of gear two is fixed on y ' slide block; Gear one is axially connected with gear two, and x ' slide block or y ' slide block arrange a focus pin, as the focus of drawn conic section.
3. a kind of conic section drawing apparatus as claimed in claim 1, is characterized in that arranging angle dial on slide block one, facilitates the angle between fine adjustment L shape guide rail mechanism and slide block one.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410586846.8A CN104309371B (en) | 2014-10-28 | 2014-10-28 | A kind of conic section drawing apparatus |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410586846.8A CN104309371B (en) | 2014-10-28 | 2014-10-28 | A kind of conic section drawing apparatus |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN104309371A CN104309371A (en) | 2015-01-28 |
| CN104309371B true CN104309371B (en) | 2016-03-30 |
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201410586846.8A Expired - Fee Related CN104309371B (en) | 2014-10-28 | 2014-10-28 | A kind of conic section drawing apparatus |
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| Country | Link |
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Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105751782B (en) * | 2016-04-14 | 2017-03-01 | 烟台南山学院 | Multifunctional drawing instrument |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US3331133A (en) * | 1965-06-17 | 1967-07-18 | Grimmer Archibald Albert | Drawing instruments |
| EP0080316A2 (en) * | 1981-11-19 | 1983-06-01 | Gerald R. Witt | Scribing device for forming arcuate figures |
| US4790222A (en) * | 1987-10-29 | 1988-12-13 | Morgan Carey C | Apparatus for cutting various forms out of a picture frame mat or the like |
| CN2077802U (en) * | 1990-05-16 | 1991-05-29 | 叶俊 | Curve drawing instrument |
| CN2111202U (en) * | 1991-11-13 | 1992-07-29 | 龚永喜 | Universal curve compasses |
| CN2310683Y (en) * | 1997-11-06 | 1999-03-17 | 杨振起 | Ellipse gauge |
-
2014
- 2014-10-28 CN CN201410586846.8A patent/CN104309371B/en not_active Expired - Fee Related
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US3331133A (en) * | 1965-06-17 | 1967-07-18 | Grimmer Archibald Albert | Drawing instruments |
| EP0080316A2 (en) * | 1981-11-19 | 1983-06-01 | Gerald R. Witt | Scribing device for forming arcuate figures |
| US4790222A (en) * | 1987-10-29 | 1988-12-13 | Morgan Carey C | Apparatus for cutting various forms out of a picture frame mat or the like |
| CN2077802U (en) * | 1990-05-16 | 1991-05-29 | 叶俊 | Curve drawing instrument |
| CN2111202U (en) * | 1991-11-13 | 1992-07-29 | 龚永喜 | Universal curve compasses |
| CN2310683Y (en) * | 1997-11-06 | 1999-03-17 | 杨振起 | Ellipse gauge |
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| Publication number | Publication date |
|---|---|
| CN104309371A (en) | 2015-01-28 |
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Granted publication date: 20160330 Termination date: 20191028 |