SU1689109A1 - Device for drawing conchoids and their equidistances - Google Patents

Abstract

The invention relates to instruments for drawing mathematical curves and used when drawing a Nichode conchoid, given by the boundary conditions, and its equidistant curves. The purpose of the invention is to improve ease of use by drawing on two boundary points and two tangents at these points. The device is equipped with a traverse and a connecting rod connected to the lever by means of a second pair of pivotally connected sliders, a protractor and a cruciform slide mounted movably on a horizontal guide and traverse and connected pivotally to the slide block. The protractor is fixed on the first pair of hinged sliders. In this case, the vertical and horizontal guides are connected by means of an additional cross-slider. The slider with the writing unit is movably mounted on the connecting rod with the possibility of fixation in a predetermined position. The curtain and the connecting rod are connected by means of a third pair of pivotally connected sliders, made with an additional writing unit. 1 il. WITH

Description

The invention relates to instruments for reproducing mathematical curves and can be used when drawing a conhoid of Nicomedes and its equidistants on the boundary conditions.

The purpose of the invention is to improve ease of use by drawing on two given boundary points and two tangents at these points.

The drawing shows the kinematic scheme of the proposed device.

On the vertical guide 1 with risk 2, the first double hinged slider 3 is fixed, equipped with a protractor 4 and a lever 5 that is orthogonal to the link 6, which slides freely in

double pivot slider 3. The lever 5 and the connecting rod 7 are connected by a second double pivot slider 8, in the hinge of which one end is fixed to the yoke 9, the free end of which slides in a cross-shaped orthogonal slider 10, which also slides along the horizontal guide 11 connected to a vertical guide 1 using a cross-shaped orthogonal slider 12 fixing at a distance I from risks 2 and at a distance a from a double pivot slide 3. The slider 10 is hingedly connected to the slider 13 in which the slide 6 slides. Tun 7 associated third slide double hinge 14, provided with a nib (not shown) for plotting of Nycomed conchoid.

Os 00

Yu

o you

On the connecting rod 7, a slider 15 is fixed with a writing unit (not shown) for drawing equidistants.

Let two boundary points A, B be given, one of which is a vertex, and the corresponding boundary normals of the PAS, nv of the desired arc of the Nichode conchoid. Let us prove that with such boundary conditions, it is possible to determine the parameters of the named curve with the polar equation

v, j

sinp

+ L.

ABOUT)

where a OK is the curve parameter, i.e. the distance from the pole to the basis;

p is the angular parameter of the curve in the polar coordinate system;

L IB is a curve parameter defining a constant distance from a basis to a curve, measured along a radius vector,

It is known that the polar subnormal of the OE for the radius vector of Vb OB of the Nichodes Nickel and the KI basis coincide, i.e. OECEV, EI1KI, and SHOCK.

Then, by the Sine Theorem, we can write down that

FROM BT

cos (g + p} cos p

where g is ATV; p TOE

or FROM BT (cos t - sin r, tg p) (2)

where two parameters are unknown:

OT, p.

From D AOW by the Sine Theorem, we can write down that

AB

a + L

TL5L ()

cozy cos ()

or a + L BT (cos and h-sin a. tan p) where the parameters are unknown; a + -, p.

From the LAVT by the Sine Theorem, we can write that

BT a + L-fOT

sin a

sin /

or a

.L-BTff FROM

where the parameters are unknown: a + - L, OT.

Thus, equations (2), (3) and (4) form a system of three equations with three unknowns, by solving which it can be determined that

p - di ag

(

cos t - A B cos a

Vsina 21V

7Sh sin a-W sin g

(3)

The construction of the desired arc using the proposed device is as follows.

Combine vertical guide 1 with the position of the initial normal, and

risk 2 with the starting point of the desired arc. Similarly, the connecting rod 7 is combined with the position of the final normal, and the double joint hinge slider 14 with the end point of the desired arc of the Nichode Conchoid. The value of the angle p for the given boundary conditions of the arc sought is determined by formula (3). The double pivot slider 3 is fixed on the vertical guide 1 at the point O (the polar focus of the arc being searched), when the angle

between the vertical guide 1 and the lever 5 is equal to the angle p, fixing the slider 13 on the link 6, and the cross-shaped orthogonal slider 12 on the vertical guide 1 brings the device into operation

condition. When the slider 10 is moved along the horizontal guide, the writing nodes of the slider 14 and 15 draw the desired arcs.

Claims (1)

Invention Formula Conchoid Tracer Nicomedes and its equidistant, containing a vertical guide and a link, connected by the first pair of hinged sliders, one of which is made with a lever fixed orthogonally to the wings, a horizontal guide, a slider mounted movably on the wings, and a slide made with a writing unit, characterized in that, in order to increase ease of use by tracing over a given two boundary points and two tangents at these points, it is equipped with a crossmember and a connecting rod connected to the lever by means of a second pair of pivotally connected sliders, and additionally contains a cross-shaped slide slidably mounted on a horizontal guide and traverse and pivotally connected to the slide of the slide, and a protractor attached to the first pair of pivotally connected sliders, while the vertical and horizontal guides are connected by means of an additional cross slide, the slide with the writing unit is movably mounted on the connecting rod with the possibility of fixation in a predetermined position, the slide and the connecting rod are connected by a third pair of sliders connected with an extra writing unit, Zhbidie / pantl KoHioufa Nycomed