SU914326A1 - Device for drawing arc - Google Patents

Description

The invention relates to drawing devices and can be used to draw arcs of circles of large radii when marking plasma.

A device for plotting arcs containing a carriage, consisting of two pivotally connected parts, each of which has a pair of wheels and writing and installation pins [13.

A disadvantage of the known device N is the inability to draw a circle through three given points with an unknown radius.

The purpose of the invention is the expansion of the range of tasks. * This goal is achieved by the fact that the device for plotting arcs containing a carriage, consisting of two articulated parts, each of which has a wheelset and writing ²¹ and mounting pins ·, has a means for installing wheel · pairs at a given angle relative to the parts of the carriage, and the latter are made in the form of rods, adjustable length.

In FIG. 1 shows a device, a General view; in FIG. 2 is an example of setting up a device to perform builds.

The device consists of two pivotally connected telescopic rods 1, at the ends of which wheel pairs 3 are fastened with rotation power. A limb 2 is located coaxially with the hinge of the rods 1, and the limbs 4 are also hinged with the wheel pairs 3. Also, a writing device 5 is located coaxially with the hinge of the rods. Pointers are mounted on the hinge of the rods and the axles of the wheelsets _{: the} hinges' of the device and the rods 1 are equipped with latches 7. The horizontal axles of the wheelsets have holes for. . fastening additional rods 8, fastened together by a mounting pin 9 ·

The operation of the device is explained fi g. 2.

^; 914326

Example 1. Let on the plane (a sheet of paper, steel, a plaza, etc.) be given three points A,, _ί C, through which it is necessary to draw an arc of a circle whose center lies obviously outside the plane of the sheet, and the radius is not known.

Set the points of the installation fonts to the specified points A, B, C 9. The lengths of the distances AB and BC are determined by the divisions on the rods 1 (or a ruler). Fix the position of the rods 1 relative to each other by the latch 7. Set the length of the rods 1 equal to half the distances AB and BC. The length of the rods indicates the distance between the pins 9. This position is fixed, the rods are fixed with 7 lengths, and the angle of the horizontal axis of the pair of 3 wheels with the axis of the corresponding rod 1 is set to 90 °. Fix this position. In the hinge of the rods, the installed pin 9 is replaced with a writing one, and the pins are removed from the hinges of the pair of 3 wheels.

Moving the device (it moves in a circle at the same time), draw an arc of a circle with a radius

From δΒΟΝ, where ΟΝΐΒ (Ζ and passes through the middle of the BC, determine ΒΝ = ОВ'дл β = Κ, -δίη (b.

From & AOM, where 0M1AC and ₅ passes through the middle of the AC, AM =

0Α5Ϊη (α ί + | b) = K-51n (cC + 1¾), a =

2K> 51Ps1, whence 5ϊη ¢ 1 = ΑΊΑ

B = 2K 5Ϊη '| ί>, whence 3ΐη £ = - $ £ 10 c = 2K 5Ϊη (ώ + (ΐ>), whence 31n (c1 + (b) =

In the same time

K. =

K. = a-bc with r + b / ¹ - a * ¹ · or where AB = a, BC = b; AC = s.

Set the lengths of the rods 1 equal to AB and BC, turn the horizontal axis of the pairs of wheels 3 by an angle

ά. = ags' soz + b

2bc ~ against

2K 5ΐηώ

B

2 & s1n) b

B. 31n (£ + (b)

Solving the last system of two equations, taking into account that cos o1 = 1-5111¾.

and szl (4. + 1b) = 51ps1-co5 [b + const x x 31n! b, get

POPs ά = c + b - a 2 bc% - b * +

2AC

P ₌ a-bc_ 1 _ a-b <c ___ ₍ c ^ + b ^ -a £ § <<. C ^^ ED + a ¹ f

Here 2 с4 is half the angle between for the sake of ³⁰ mustaches of AO and VO; half the angle between the radii of VO and OS.

Ex. 2. If the radius K of the circular arc is given, and the point (for example B) through which this arc must pass is known, then set the lengths of the rods 1 to the same (for example, equal to VK), and rotate the rods 1 relative to each other by an angle equal to 2ί, where o1 = ags 5ΐη (VK / 10 ° clockwise (for the left axis 3) and at an angle (6 = ags cos

L-b ^ ac + a · (for the right axis) clockwise. Dependencies for angles and radius are determined from the constructions in FIG. 2.55

Of. Δ A0K, where OCTA and passes through the middle of AB, determine AK =

Α0 -5ΪΙ1 ώ = K31P ά

In this case, the angle between the axles of the rods 1 and the horizontal axles of the wheelsets 3 should be 90 °.

Example 3. If there are two known points (for example A and C) and the radius K of the arc of a circle, then, setting the needles 9 at the given points (A and C) so that the lengths of both shtang 1 are equal to half the distance between the points (AC) , turn the horizontal bays of the wheelsets by an angle ώ = ags - 3ΐη G AM / K]

Example 4 (determination of the instantaneous center of rotation). To determine 5 2) 14326 6 the instantaneous center of rotation of the body, the law of motion of which is given by the graphic, analytical or coordinate method, proceed as follows. Let the law of motion of the body in time be given in the form of the movement of a point along a curve, part of which is ABC, and the nature of the curve of ABC is such (the points are located on the curve quite close to each other) that admits-> passing through these three points. Then, following the steps described in Example 1, additional rods 9 are inserted into the horizontal axles of the wheel pairs 3 and the point 0 is marked at the point of their intersection, which is the instantaneous center of rotation of the body when it moves along the ABC path. Having built a series of such points, semi-; read the distribution curve of instantaneous. centers of rotation when the body moves along some path depicted on a graph of a continuous curve.

The proposed device for drawing arcs makes it possible to solve the following construction problems:

- draw an arc of a circle of a given radius passing through a given point; ;

- draw an arc of a circle of a given radius passing through two given points;

- build an arc of a circle of a given and unknown radius, passing through three given points;

- build an arc of a circle passing through one, two and three given points, if the center of the circle is not. lies on the material plane;

- build an arc of a circle passing through three given points with an unknown radius in the center lying outside the material plane;

- determine the instantaneous centers of rotation of the body and build a distribution curve of the instantaneous centers of rotation of the body, if the law of motion is specified graphically or by the coordinate method.

In addition, the device allows for actually small dimensions to draw arcs of circles with a radius measured from centimeters to tens and hundreds of meters.

Claims (1)

Claim A device for plotting arcs containing a carriage consisting of two articulated parts, each of which has a wheelset and writing and positioning pins, which is characterized in that, in order to expand the range of tasks to be solved, it has means for installing wheel pairs under a given angle relative to the carriage parts, and the latter are made in the form of reg rods; walkable length.