CN1031968A

CN1031968A - The method for drafting of elliptic curve and elliptic curve instrument

Info

Publication number: CN1031968A
Application number: CN 87106361
Authority: CN
Inventors: 杨贵君
Original assignee: Individual
Current assignee: Individual
Priority date: 1987-09-14
Filing date: 1987-09-14
Publication date: 1989-03-29
Also published as: CN1016592B

Abstract

A kind of method and instrument thereof of drawing ellipse.Its method is that a moving some Q moves in a circle around another P that moves in a circle, and when satisfying specified conditions, the movement locus of moving some Q is ellipse.And having designed a kind of elliptic curve instrument with this principle, it is simple in structure, and is easy to use, according to specified criteria (major semiaxis and semi-minor axis), just can draw its ellipse.

Description

The method for drafting of elliptic curve and elliptic curve instrument

A kind of method and instrument of drawing elliptic curve, the method for drafting and the plotter class of genus curve.

Draw oval instrument, " middle school science teaching " the 3rd phase of editing by Beijing Normal University in 1978, introduced " tripod ellipsograph "; " conic-section plotter " of the Decree of Patent Office of China (CN85200874) and " round, ellipse, curve gauge " (CN86204400).They all design with planar interception cylinder, circular cone and the circle oval principle that is projected as in the plane.But structure is complicated, uses inconvenience; Draw specificly when oval, regulate difficulty.

The invention provides a kind of method for drafting of new ellipse, and designed a kind of elliptic curve instrument of simple in structure, easy to adjust, the ellipse that can draw different sizes and eccentricity according to this method.

Accompanying drawing 1 is the schematic diagram of a kind of new ellipse drawing method provided by the invention.

On the same plane, point P moves in a circle around an O take R as radius, point Q moves in a circle around a P take r as radius again, when satisfying: the opposite direction of (1) P, 2 motions of Q (a bit is clockwise motion, another point is counterclockwise motion), the angular speed (ω of (2) some Q_Q) be the angular speed (ω of some P_P) twice (ω_Q＝2ω _P), during (3) R＞r condition, the movement locus of some Q is ellipse (its major semiaxis is R+r, and semi-minor axis is R-r).

To this, prove as follows:

The p that sets up an office moves to arbitrfary point Pi (corresponding central angle is i), moves to a Qi (is 2 i to the corresponding central angle of a Pi) with time point Q.Cross some Pi and be Piq ₂//OP, then: ∠ q ₁P _iq ₂=∠ q ₂P _iQ _i= _iIn rectangular coordinate system XOY, the coordinate of some Qi is:

x＝RCosi+rCosi＝(R+r)Cosi..........(1)

Y=RSin i-rSin i=(R-r) Sin i.......... (2) can be got by (1), (2) two formulas:

x ²/ (R+r) ²+ y ²/ (R-r) ²=1................... (3) establishes R+r=a, R-r=b, then:

x ²/a ²+y ²/b ²＝1.......................(4)

(4) formula is oval normal equation, thus the card movement locus of putting Q is an ellipse.

Accompanying drawing 2 is structure charts of this elliptic curve instrument.

The elliptic curve instrument by rotating shaft [5], secondary sliding sleeve [6], secondary slide rail [7], the secondary slide block [8] of deciding pin [1], main sliding sleeve [2], main running rail [3], master slider [4], band boss of band boss, paint pen clip tool [9], paint pen [10], a transmission stay cord [11], slide block clamp-screw [12] and transmission stay cord trip bolt [13] and form.The outer diameter D of deciding pin [1] boss is the twice (D=2d) of secondary sliding sleeve [6] outside diameter d.

Main running rail [3] becomes fixedly connected with main sliding sleeve [2], or is welded as a whole, or twists solid with the yin, yang screw thread.

Painting pen clip tool [9] twists solid with secondary slide block [8] with screw thread.

Transmission stay cord [11] is a rigidity, and with identical winding on the boss of deciding pin [1] and secondary sliding sleeve [6], and fix it with trip bolt [13].

Paint pen [10] and can be lead core gripper, also can be duck and chew pen.

On main running rail [3] and the secondary slide rail [7], be carved with Yi Dingjiao [1] axis respectively and rotating shaft [5] axis is the length scale at zero point.On master slider [4] and secondary slide block [8], have the reading window, and be provided with the scale index line.

When drawing ellipse, by given major semiaxis (a) and semi-minor axis (b), with R+r=a, R-r=b two formulas calculate R and r value, regulate master slider [4] and secondary slide block [8], make it corresponding with the scale value on the secondary slide rail [7], and rotate main sliding sleeve [2], make stay cord [11] tension with R and r value at main running rail [3].Make and decide pin [1] and paint pen [10] to attach paper or other plane, rotate the handwheel on the main sliding sleeve [2], can draw desired ellipse.

The method for drafting of elliptic curve provided by the present invention, simple, principle is reliable; Elliptic curve instrument according to this method design is simple in structure, easy to use, according to given different condition, can draw the ellipse of different sizes and different eccentricities.

Claims

1, a kind of method for drafting of ellipse is characterized in that: at grade, some Q moves in a circle (radius is r) around another P of move in a circle (radius is R), and satisfies:

(1) 2 directions that move in a circle of P, Q are opposite;

(2) angular velocity omega of P, 2 motions of Q _Q=2 ω _P

(3)R＞r；

It is that R+r, semi-minor axis are the ellipse of R-r that the movement locus of some Q is major semiaxis.

2, a kind of elliptic curve instrument, except that the pin of deciding [1] is arranged and paint pen clip tool [9] and paint the pen [10], the invention is characterized in: it also is made up of main sliding sleeve [2], main running rail [3], master slider [4], rotating shaft [5], secondary sliding sleeve [6], secondary slide rail [7], secondary slide block [8], transmission stay cord [11] and its trip bolt [13] and slide block clamp-screw [12].Simultaneously:

(1) outer diameter D of deciding pin [1] boss is the twice of secondary sliding sleeve [6] outside diameter d, i.e. D=2d;

(2) transmission stay cord [11] is a rigidity, and with identical winding on the boss of deciding pin [1] and secondary sliding sleeve [6], fix it with trip bolt [13].

3, according to the described elliptic curve instrument of claim 2, its feature also is: on main running rail [3] and secondary slide rail [7], be carved with Yi Dingjiao [1] axis respectively and rotating shaft [5] axis is the length scale at zero point; On master slider [4] and secondary slide block [8], have reading window and scale index line.