CN201257853Y - Electric Archimedes spiral drawing instrument - Google Patents

Abstract

The utility model provides a drawing instrument for drawing Archimedes spirals. The drawing instrument consists of a main body structure and a bracket. The drawing instrument is characterized in that a motor 5 is inverted and tightly coupled with a circular panel at the top of 11, 10 is sleeved outside 11, 12 is fixed on 11, 6 is tightly coupled with a driving shaft 2 of 5 through 3, one internal thread hole is formed at each of the middle part and the lower part of 14, the internal thread holes are meshed with 15 and 19 respectively, a circular hole is formed at the upper part of 14 and allows 8 to pass through so as to connect 10 and 6, 16 is fixed on 15 and meshed with 12 orthogonally, 15 is loosely connected with 10 and 6, a drawing pen is mounted at the left end of 19, the motor 5 rotates clockwise, 6 is driven by 3 to reverse, 6 also drives 8 and 15 to rotate, 15 also drives 16 to automatically rotate on 12 when 15 revolves around 11, 15 automatically rotates with 16 synchronously and drives 14 to move along 8, a pen point on 19 rotates with 19 around 11 and travels along the straight line, and the track left by the pen point on a piece of drawing paper is an Archimedes spiral.

Description

Electronic Archimedes spiral drawing instrument

Technical field

The utility model relates to a kind of electronic Archimedes spiral drawing instrument

Technical background

The Ancient Greek Mathematics Archimedes of man (preceding 212 years of preceding 287--) provides the definition of helical (Archimedes spiral) in its works " opinion helical " book; Article one, ray at the uniform velocity rotates around its fixed endpoint, a moving point is arranged simultaneously from end points, and along the ray uniform motion, this moving point is just depicted a plane thread so.Position when ray begins is start line.Fixed endpoint is initial point.(beam ancestor monumental work " world's mathematics comprehensive history " first volume P ₃₅₇)

Senior middle school's textbook " plane analytic geometry " P of people education publishing house in 1984 _178-182Introduced the polar equation of Archimedes spiral: ρ=ρ ₀+ a θ (a〉0).Traditional method for drafting is a trace-point method.According to ρ=ρ ₀+ a θ provides a series of permissible values of θ, calculates the respective value of ρ, and again according to the respective value table, described point is drawn.

Login on August 7th, 2007 Baidu website acquired information: the first phase U.S. " science " magazine is reported recently, a postgraduate Peter Shandong of majoring in the physics master in Harvard University, studying one piece from high official's grave of The Spring and Autumn Period, after the Yuhuan that excavation is come out, reach a conclusion: the skillful craftsman of China, in the The Spring and Autumn Period, just can design and produce the machine of engraving Archimedes spiral.

Website login: www.sipo.gov.cn carries out the Searches of Patent Literature again, the input keyword: " Archimedes spiral ", find 6 of relevant patents.Wherein application number is 94312784.4 Archimedes spiral plotter, have only a word inequality with title of the present utility model, but both structures is completely different.

Operating computer utilizes U.S. wolfram company, and the mathematical software Mathematica of research and development has the function of the functional picture of rendering parameter and polar equation, can draw Archimedes spiral.(" mathematics communication " 13 phases in 2000)

Summary of the invention

The purpose of this utility model provides a kind of instrument that can directly draw Archimedes spiral.

The utility model is made up of agent structure shown in Figure 1 and Fig. 2, support shown in Figure 3.

Among Fig. 1, motor 5 is inverted, even it top down, with the top circular panel of fixed axis 11, by the fastening connection of screw 7 (totally 3).Bevel gear 12 is fixing with fixed axis 11 by bolt 13.Bevel gear 16 threaded 15 is fixing by bolt 17.The bevel gear 12 and 16 the number of teeth equate.Special-shaped nut 14 is enclosed within on screw rod 15 and the guide rail 8.The pitch of screw rod 15 and nut 14 all equals 7.4mm.Sleeve 10 is enclosed within outside the fixed axis 11.Screw rod 15 is with sleeve 10 loose couplings.Guide rail 8 tightly connects with sleeve 10.The 6th, cross section is the support bar apart from shape.The end of support bar 6 is equipped with scroll wheel 21, and the central shaft of scroll wheel is fastened with support bar 6 by nut 20 and 22.Screw rod 15 is with support bar 6 loose couplings, and guide rail 8 is tightly connect by nut 9 with support bar 6.Nut 1 cooperates with the driving shaft 2 upper end screws of motor 5.Coupling bar 3 left ends tightly connect with driving shaft 2, and right-hand member is tightly connect by nut 4 with support bar 6.The bottom of special-shaped nut 14 has a screw threaded 19 to cooperate.Nut 18 threaded 19 the left end threaded engagement, be used at screw rod 19 fixed installation drawing pens.

Fig. 2 is the front view of support, ratio 1:2, and height 160mm, the upper external screw thread of supporting leg 2 (totally 3) is with 3 of panel 1 The internal thread in hole tightly connects.The external screw thread of the end of supporting leg 2 tightly connects with the internal thread of magnet piece 3 (3) central authorities totally.The external diameter of panel 1 is 274mm.

The nut 1 of Fig. 1 is loosening, take off, Fig. 2 from Fig. 1 sky, is made

Centre bore, be inserted in the upper end that faces driving shaft 2, puts down.Again nut 1 is inserted in from the upper end of driving shaft 2, tightens.

Description of drawings

Fig. 1 is an agent structure of the present utility model, ratio 1:1.Among the figure 1,2,3 ... the 22nd, PT CODE.

Fig. 2 is the front view of support of the present utility model, ratio 1:2.Among the figure the 1,2, the 3rd, PT CODE.

Fig. 3 is the vertical view of support of the present utility model, ratio 1:2.

The specific embodiment

The step that the utility model is drawn an Archimedes spiral is as follows:

1. a drawing paper is layered on the magnet flat board.Take up an official post at paper and to get the limit of 1 O (0,0) as the Archimedes spiral that will draw.Make pole axis Ox, draw a ray l from O, l can regard the projection of the central shaft of screw rod 15 as.If the angle of l and Ox is θ, (initial position of l overlaps with Ox) gets 1 A (ρ on l ₀, O).

2. with whole electronic Archimedes spiral drawing instrument, place on the drawing paper, make the terminal needle point of fixed axis 11, aim at the O point.3 magnet pieces 3 of 6 terminal scroll wheel 21 and 3 supporting leg ends of support drop on the drawing paper simultaneously.Magnet piece 3 is attracted each other with the magnet flat board, clamps drawing paper firmly, and drawing paper can not be moved.Whole electronic Archimedes spiral drawing instrument also just is stabilized on the drawing paper.

3. from screw rod 19, take off nut 18, drawing pen (not drawing among the figure) is put into screw rod 19, refill top nut 18, and tighten.Drawing pen is fixed on the screw rod 19, and the position of adjusting screw(rod) 19 makes drawing pen nib drop on A point on the l, establishes nib and is a moving some M, A point (ρ ₀, O), establish ρ for the starting point of moving some M ₀=20mm.

4. with the power line of motor 5, connect with the mains, the forward and backward gauge tap (not drawing among the figure) of motor 5 is pulled to just changeing (clockwise) position, motor 5 starts, driving shaft 2 is just changeing and is driving connecting rod 3 inhours around driving shaft 2 rotations, coupling bar 3 drives support bar 6,6 and drives guide rail 8 and screw rod 15 again, rotates around fixed axis 11 inhours.Screw rod 15 drives sleeve 10 and also rotates around fixed axis 11 when fixed axis 11 revolution.

Because the bevel gear 16 that is fixed on screw rod 15 is with the engagement of bevel gear 12 quadratures, screw rod 15 drives bevel gear 16 rotation on bevel gear 12 around fixed axis 11 revolution and sleeve 10 time rotationals.Screw rod 15 is with bevel gear 16 synchronous rotations.Screw rod 15 time rotationals drive special-shaped nut 14 and outwards move along guide rail 8.Screw rod 15 is from turning around, and 14 move a pitch, and special-shaped obviously nut 14 had not only rotated but also moved along guide rail 8 around fixed axis 11.Screw rod on the special-shaped nut 14 19 drives drawing pen nibs at this moment, and promptly the M point is from A point setting in motion.Driving shaft 2 changes n circle (n=10 herein), establishes its angular speed Then the M point arrives the B point (l overlaps with Ox again) on the l, and θ then increases to 2n π by 0 °, closes power supply.The motion of nib (M point) is to be composited by at the uniform velocity moving around the O uniform rotation with along l.The track that M is ordered meets the given helical definition of Archimedes.So the AB curve is an Archimedes spiral.

The AB line segment length equals nt, and t is the known n=10 of the pitch=7.4mm. of screw rod 15, AB=74mm. linear velocity so

Because ρ ₀=20mm,

If

The equation of the Archimedes spiral of being drawn is: $\mathrm{\ρ}=20+\frac{7.4}{2\mathrm{\π}}\mathrm{\θ}$

Desire drafting θ gets negative value, about another Archimedes spiral of Ox symmetry.At first must make left hand thread to the screw thread of the screw thread of screw rod 15 and special-shaped nut 14 middle part screws.The forward and backward gauge tap of motor 5 need only be pulled to backward position during use, motor 5 is started.Can draw this Archimedes spiral out.

Claims (6)

1. an electronic Archimedes spiral drawing instrument is made up of main body and support.It is characterized in that inverted motor in the main body, connecting fixed axis, the fixed axis overcoat sleeve.

2. electronic Archimedes spiral drawing instrument according to claim 1 is characterized in that bevel gear of the tight connection in fixed axis lower end.

3. electronic Archimedes spiral drawing instrument according to claim 1 is characterized in that sleeve outreaches to be knotted a screw rod and a guide rail.

4. screw rod according to claim 3 is characterized in that bevel gear of the tight connection of screw rod left end, and this bevel gear is also overlapping a special-shaped nut with the engagement of the bevel gear quadrature on the fixed axis on the screw rod.

5. special-shaped nut according to claim 4 is characterized in that a small screw is installed on the special-shaped nut, and this screw rod left end is used to install drawing pen.

6. electronic Archimedes spiral drawing instrument according to claim 1 is characterized in that support has 3 legs, and the end of leg is respectively installed a magnet.

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