CN103085544B - A kind of ellipsograph - Google Patents

Abstract

The invention belongs to drawing appliance category, also culture and education office accommodations is related to, it is specially a kind of ellipsograph, it is one taking brand-new mathematical statements (" revolution rotation say ") as principle, realized the instrument of drawing function by the gear mechanism transmission mode of " two three grades, lines ", whole structure comprises manipulation, transmission, adjustment three part. Manipulation part comprises handle and drawing knob, and handle has the total platform function of machinery concurrently, the positive and negative 360 degree of operations of energy of drawing knob; Driving part is a system ensemble, specifically " two three grades, lines " pattern, " two lines " i.e. " revolution line " and " rotation line "; " three grades " i.e. " speed change level ", " speed and direction changing level ", " constant speed becomes to level ". Drawing adjustment is summarised as " one calculates two shiftings three opens " operation steps. The present invention innovates principle, optimizes structure, provides a kind of any simplicity of drawing standard ellipse and the drawing instrument of practicality to common people.

Description

A kind of ellipsograph

Technical field

The invention belongs to drawing appliance category, also relate to culture and education office accommodations, be specially a kind of ellipsograph.

Background technology

Ellipsograph is the long-expected instruments used for education of people and drawing instrument. If compasses have been adjoint human civilization history, so that the dream of ellipsograph is also long-standing. Do not know to have how many tireless pursuer at all times, except ancient china, ancient Greek and the Renaissance in addition of history load, some scientists at that time take part in the design design of ellipsograph, even Leonardo da Vinci just did design, such as " Leonardo da Vinci's ellipsograph " up to the present handed down from ancient times. Even to this day, still having many fans to be bent in this, the ellipsograph of research and development theory of machines, relevant patent emerges in an endless stream, and is wherein no lack of exquisite outstanding design. But, followed due to design design and do not broken through mathematics category traditional, classics with interdependent theoretical principle (i.e. mathematical definition, proposition), the process of machinery performance cannot be simplified thus embody its practicality, and then penetration and promotion, can only appreciate as " conceptual design ", object for appreciation, therefore, ellipsograph is also generally speaking a market vacancy. Although current design field has entered computer age, but still there is the demand to ellipsograph in production practice and education activities, especially a kind of can arbitrarily regulating parameter, accurately, ellipsograph easy and simple to handle, cheap.

Summary of the invention

The technical problem to be solved in the present invention be to provide a kind of structure simple, easy to operate, be easy to regulate, ellipsograph that tolerance range is high, to meet the demand of the aspects such as people's teaching, design, drawing, fill up a blank of drawing appliance.

In order to solve the problems of the technologies described above, contriver proposes and demonstrates a brand-new mathematical statements, i.e. " revolution rotation is said ", breaks through from theoretical principle, separately wards off path design and devises a kind of ellipsograph, greatly steps to practical aspect and goes a step further.

The particular content of " revolution rotation is said " is: " circle rotates (revolution) along a circular track; its rotation simultaneously; if rotation direction is contrary with revolution direction, and is the twice of revolution circular frequency from tarnsition velocity, and so the track of the upper point arbitrarily of this dynamic circle is oval. "

Based on the ellipsograph of this principle, make to realize the visual of mathematic curve by simple and mechanical motion and become possibility, " two three grades, lines " gear mechanism transmission mode in the present invention is one and relatively optimizes brief embodiment, it has not only fully demonstrated mathematical principle, there is utility function, also show the aesthetic feeling of a kind of physical construction and mechanical movement.

Ellipsograph of the present invention, structure is divided into manipulation, transmission and adjustment three part. Manipulation part comprises handle and drawing knob; Driving part is a system ensemble, is presented as " two lines " " three grades " transmission mode; Adjustment portion is summarised as the operation steps of " calculates two shiftings three opens ".

Further, manipulation shows as bimanualness Graphics Mode, a hand-held tight handle, and remain the vertical state of center of circle pin, rotate drawing knob on the other hand, due to the reversibility of geartransmission, user freely can draw as using common compasses, can positive and negative 360 degree of operations; Handle has the total platform function of machinery concurrently, and transmission system is in this, as dependence and starting point drops down.

Further, " two lines " of transmission system refers to " revolution line " and " rotation line ", the rotation energy of drawing knob is divided into two by two line layouts, passing to different demand points with two circuits: one is positive dirction rotation (revolution) of scale bar, two is opposite direction speed rotation (rotation) of penholder. " two lines " is parallel up and down, and by coaxial association, the first gear on two lines is active wheels, the company's of being arbor wheel, 2nd gear is driven wheels, upper for connecting arbor wheel, and lower is bearing wheel, bearing wheel case holds axle core, not synchronized in the same way with axle core, plays fulcrum and takes over from the past and sets a new course for the future.

Further, " revolution line " is positioned at structure upper strata, comprises company's shaft gear that two diameters arranged side by side are identical, one main one from, the axle core of driving toothed gear is upward through handle and the link of drawing knob; The axle core of follower gear extends downwards and scale bar and the link of center of circle pin, and the same body of three, rotates synchronous.

Further, " rotation line " is positioned at structure bottom, and parts comprise driving toothed gear, follower gear, change to tooth, conical gear, horizontal helical teeth bar, vertically twisted spur gear, rotation pen folder, wherein 1. become to the same body of tooth and follower gear, and one takes turns two teeth, is passed under upper; 2. conical gear and the horizontal same body of helical teeth bar, a bar amphitypy, front by rear biography; 3. vertically twisted spur gear presss from both sides same body with rotation pen, and a core two connects, and is passed under upper. " rotation line " omnidistance twice speed change (gear velocity of rotation), two secondary shafts (gear shaft core transforms anyhow), become to (gear sense of rotation) for three times, arrive sense of rotation when pen presss from both sides just contrary with the sense of rotation of scale bar, it coincide with mathematical principle.

Further, described " three grades " are the classifications of " rotation line ": the first step is " speed change level ", and the diameter ratio of driving toothed gear and follower gear is 2: 1, and rotating speed amplifies one times, rotate the angle brought with this supplementary scale bar and offset; The second stage is " speed and direction changing level ", and becoming to the gear ratio of tooth and conical gear is 2: 1, and rotating speed is exaggerated one times again, and this is caused by mathematical principle requirement, and this structure makes turning axle become to 90 degree simultaneously, horizontal by vertical transfer;The third stage is " constant speed becomes to level ", and the type of drive of horizontal helical teeth bar and vertical twisted spur gear makes rotating shaft become to 90 degree again, erects by horizontal turn, and tooth bar configuration is all identical with diameter, becomes constant-speed transmission. Horizontal helical teeth bar is parallel, on be placed in scale bar, scale bar two ends are provided with bearing support; The lower end of vertical twisted spur gear links rotation pen folder, and the rotation of pen folder drives penholder to rotate, it is achieved " rotation ", completes to draw.

Further, the drawing adjustment member of ellipsograph of the present invention comprises scale bar, slide block, rotation pen folder, opening and closing penholder, degree of tightness knob, auxiliary center of circle pin etc., and slide block is arranged on scale bar, regulates position by degree of tightness knob; Slide block built-in bearing, vertical helical gear shaft core passes from top to bottom, becames one with pen folder. Concrete mapping operation step summary is " one calculates two shiftings three opens ", according to known condition during use, first the mean value (a+b)/2 of length semiaxis is calculated, then moving slider, calculated value correspondence being implemented on scale bar, then opens penholder, the numerical value making nib correspond on scale bar equals semi-major axis a, complete to regulate, start to draw. Use or inadequate expert for first, the vertical state of center of circle pin can be maintained by auxiliary center of circle pin, ensure drawing quality.

Further, being sandwiched in the opening and closing penholder rotating pen folder, carry out opening and closing according to parameter, opening angle is more big, is painted ellipse more flat, and angle is more little, more close to circle, is positive round when angle is zero, uses so ellipsograph of the present invention can make common compasses.

Further: proof and the parameter conversion relation of the mathematical principle of ellipsograph of the present invention are as follows:

Prove: (Fig. 3) ⊙ Q rotates around initial point positive dirction, and circular frequency is θ, and himself is with the 2 reverse rotations of θ circular frequency. P (x, y) moves the point on circle for this reason, and it is by starting point M ' rotation so far, is also revolve round the sun so far by starting point M simultaneously.Track be oval.

In figure, extend M ' P and hand over x-axis in L, ∠ OLM '=90 degree can be demonstrate,proved

M ' P=2rsin θ (isosceles triangle base)

Y=PL=M ' L-M ' P

=Rsin θ-2rsin θ

=(R-2r) sin θ

X=OL=Rcos θ

$\stackrel{\·}{\·\·}\left\{\begin{array}{c}x=R\cos \mathrm{\θ}\\ y=(R-2r)\sin \mathrm{\θ}\end{array}\right.$

Meet elliptic parametric equation form. Card is finished.

Conversion relation: R=ar=(a-b)/2

Accompanying drawing explanation

Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail:

Fig. 1 is the stereographic map of the present invention's (a kind of ellipsograph);

Fig. 2 is the front view of the present invention's (a kind of ellipsograph);

1. handle 2. draw knob 3. driving toothed gear 14 follower gear 15. driving toothed gear 26. follower gear 27 become to the horizontal helical teeth bar 10. of tooth 8. conical gear 9. vertically twisted spur gear 11. scale bar 12. center of circle pin 13. rotate pen folder (being called for short pen folder) auxiliary pin 19. diagram parameter 20. penholder opening angle of 14. slide block 15. degree of tightness knob 16. bearing support 17. opening and closing penholder (abbreviation penholder) 18. center of circle pin

Fig. 3 is the mathematical principle figure of the present invention's (a kind of ellipsograph);

Fig. 4 is other purposes citing of the principle of the present invention's (a kind of ellipsograph).

Embodiment

As shown in Figure 2, the present invention provides a kind of ellipsograph, and by a brand-new mathematical statements " revolution rotation is said " use " two three grades, lines " gear mechanism transmission mode true representation out, whole structure comprises manipulation, transmission and adjustment three part.

Described manipulation part is one handle (1) and a drawing knob (2). Handle (2) has the total platform function of machinery concurrently, and transmission system is as dependence and starting point drops down.Ellipsograph of the present invention is bimanualness drawing instrument, and a hand-held tight handle (1) also remains vertical state, rotates drawing knob (2) on the other hand, can positive and negative 360 degree of operations.

Described driving part is a system ensemble, it is the main contents of the present invention, it is specially " two three grades, lines " gear mechanism transmission mode, " two lines " i.e. " revolution line " and " rotation line ", " three grades " are the classifications under " rotation line ", i.e. " speed change level ", " speed and direction changing level " and " constant speed becomes to level ". The rotary power of drawing knob (2) is divided into two by " two lines " layout, passing to different demand points by two circuits: one is positive dirction rotation (revolution) of scale bar (11), two is opposite direction speed rotation (rotation) of opening and closing penholder (17).

" revolution line " is positioned at structure upper strata, comprises company's shaft gear that two diameters arranged side by side are identical, one main one from, the axle core of driving toothed gear (3) is upward through handle (1) and links with drawing knob (2); The axle core of follower gear (4) extends downwards and scale bar (11) and center of circle pin (12) link, and the same body of three, rotates synchronous.

" rotation line " is positioned at the lower floor of structure, and parts comprise driving toothed gear (5), follower gear (6), become to tooth (7), conical gear (8), horizontal helical teeth bar (9), vertically twisted spur gear (10), rotate pen folder (13). Wherein becoming to tooth (7) and follower gear (6) same to body, one takes turns two teeth, is passed under upper; Conical gear (8) and the same body of horizontal helical teeth bar (9), a bar amphitypy, front by rear biography; Pen presss from both sides (13) same body to vertical twisted spur gear (10) with rotating, and a core two connects, and is passed under upper. " rotation line " omnidistance twice speed change (gear velocity of rotation), two secondary shafts (gear shaft core transforms anyhow), become to (gear sense of rotation) for three times, when arriving pen folder (13), sense of rotation is just contrary with the sense of rotation of scale bar (11), coincide with mathematical principle. " two lines " is parallel up and down, and by coaxial association, the first gear on two lines is active wheels, the company's of being arbor wheel, 2nd gear is driven wheels, upper for connecting arbor wheel, and lower is bearing wheel, bearing wheel case holds axle core, not synchronized in the same way with axle core, plays fulcrum and takes over from the past and sets a new course for the future.

" rotation line " lower point " three grades ", the first step is " speed change level ", driving toothed gear (5) is 2: 1 with the diameter ratio of follower gear (6), and rotating speed amplifies one times, rotates the angle brought with this supplementary scale bar (11) and offsets; The second stage is " speed and direction changing level ", and becoming to the gear ratio of tooth (7) Yu conical gear (8) is 2: 1, and rotating speed is exaggerated one times again, and this is caused by mathematical principle requirement, and this structure makes turning axle become to 90 degree simultaneously, horizontal by vertical transfer; The third stage is " constant speed becomes to level ", and horizontal helical teeth bar (9) makes rotating shaft become to 90 degree with the type of drive of vertical twisted spur gear (10) again, erects by horizontal turn, and tooth bar form is all identical with diameter, becomes constant-speed transmission. Scale bar (11) also has a platform function, and horizontal helical teeth bar (9) is set in parallel in upper end, and there is bearing support (16) at two ends, above has slide block (14) embedding folder, moves left and right; Slide block (14) built-in bearing, vertical twisted spur gear (10) and rotate pen folder (13) are coaxial is connected, upper and lower synchronous axial system; Pen folder (13) rotation resulting belt start writing bar (17) rotate, it is achieved " rotation ", complete draw.

Described adjustment portion refers to that diagram parameter calculates and operation regulates, and associated components comprises scale bar (11), slide block (14), rotates pen folder (13), opening and closing penholder (17), degree of tightness knob (15), auxiliary center of circle pin (18).Slide block (14) regulates position by degree of tightness knob (15), diagram parameter (19) correspondence of calculated in advance is implemented on scale bar (11). It is sandwiched in the opening and closing penholder (17) rotating pen folder (13), opening and closing are carried out according to parameter (19), opening angle (20) is more big, painted ellipse more flat, angle is more little, more close to circle, it is positive round when angle is zero, so ellipsograph of the present invention can be used as common compasses. The concrete steps regulated of drawing are summarised as " one calculates two shiftings three opens ", during use, according to known oval length semiaxis data, first calculating mean value (a+b)/2, then as shown in Figure 2, finding corresponding scale on scale bar (11), moving slider (14), alignment is tightened, open penholder (17) again, make the corresponding numerical value on scale bar of nib equal semi-major axis a, so far complete to regulate, start to draw. Use or inadequate expert for first, its vertical state can be maintained by auxiliary center of circle pin (18), ensure drawing quality.

Claims (1)

1. an ellipsograph, comprises handle (1), drawing knob (2), the first driving toothed gear (3), the first follower gear (4), the 2nd driving toothed gear (5), the 2nd follower gear (6), becomes to tooth (7), conical gear (8), horizontal helical teeth bar (9), vertically twisted spur gear (10), scale bar (11), center of circle pin (12), rotates pen folder (13), slide block (14), degree of tightness knob (15), bearing support (16), opening and closing penholder (17), auxiliary center of circle pin (18);

The structure of described ellipsograph is divided into manipulation part, driving part and adjustment portion,

Described manipulation part is one handle (1) and a drawing knob (2), and handle (1) has the total platform function of machinery concurrently, and driving part is as dependence and starting point drops down;

Described driving part is " two three grades, lines " gear mechanism transmission mode, " two lines " i.e. " revolution line " and " rotation line ", and " three grades " are the classifications under " rotation line ", i.e. " speed change level ", " speed and direction changing level " and " constant speed becomes to level ";

The rotary power of drawing knob (2) is divided into two by " two lines " layout, different demand points is passed to: one is the positive dirction revolution of scale bar (11), and two is the opposite direction speed rotation of opening and closing penholder (17) by two circuits;

" revolution line " is positioned at the upper strata of structure, comprises company's shaft gear that two diameters arranged side by side are identical, one main one from, the axle core of the first driving toothed gear (3) is upward through handle (1) and links with drawing knob (2); The axle core of the first follower gear (4) extends downwards and scale bar (11) and center of circle pin (12) link, and the same body of three, rotates synchronous;

" rotation line " is positioned at the lower floor of structure, comprises the 2nd driving toothed gear (5), the 2nd follower gear (6), becomes to tooth (7), conical gear (8), horizontal helical teeth bar (9), vertically twisted spur gear (10), rotates pen folder (13);

Wherein becoming to tooth (7) and the 2nd follower gear (6) same to body, one takes turns two teeth, is passed under upper; Conical gear (8) and the same body of horizontal helical teeth bar (9), a bar amphitypy, front by rear biography; Pen presss from both sides (13) same body to vertical twisted spur gear (10) with rotating, and a core two connects, and is passed under upper;

Kinetic energy transmission wherein is divided into " three grades ", the first step is " speed change level ", 2nd driving toothed gear (5) is 2: 1 with the diameter ratio of the 2nd follower gear (6), and rotating speed amplifies one times, rotates the angle brought with this supplementary scale bar (11) and offsets; The second stage is " speed and direction changing level ", and becoming to the gear ratio of tooth (7) Yu conical gear (8) is 2: 1, and rotating speed is exaggerated one times again, and this structure makes turning axle become to 90 degree simultaneously, horizontal by vertical transfer;The third stage is " constant speed becomes to level ", and horizontal helical teeth bar (9) makes rotating shaft become to 90 degree with the type of drive of vertical twisted spur gear (10) again, erects by horizontal turn, and tooth bar form is all identical with diameter, becomes constant-speed transmission;

Described adjustment portion comprises described scale bar (11), described slide block (14), described rotation pen folder (13), described opening and closing penholder (17), described degree of tightness knob (15) and described auxiliary center of circle pin (18);

Described scale bar (11) also has a platform function, described horizontal helical teeth bar (9) is set in parallel in the upper end of described scale bar (11), there is bearing support (16) at the two ends of described scale bar (11), described scale bar (11) has slide block (14) embedding folder, moves left and right; Described slide block (14) built-in bearing, described vertical twisted spur gear (10) presss from both sides with described rotation pen that (13) are coaxial to be connected, upper and lower synchronous axial system; The rotation of described rotation pen folder (13) finally drives described opening and closing penholder (17) to rotate, it is achieved " rotation ", completes to draw.