DE114446C - - Google Patents

Description

IMPERIAL

PATENT OFFICE.

The subject of the present invention is a curve staking device.

The instrument (Fig. 1) consists of a horizontal disk divided into two equal halves, which is divided into degrees from the end points 1 and 2 of the dividing line to the right and left, and at the end points with diopters (sighting devices) 3 perpendicular to the dividing line and 4 and 5 and 6 is provided. These are so arranged that one. can see from the ends of the dividing line even after the graduation. The degree points part, approximately from 5 ⁰ to 5 ⁰ solid Diopterobjective are attached, which by sliding, loose or uhrzeigerartig associated with the endpoints of the Theilungslinie Objective - may be replaced - pointer. At both ends of the dividing line, in order to be able to set up the instrument with one of these ends above the starting point of the curve to be staked, loths are attached, unless the disc support point is to be placed under one end of the dividing line with the aid of a counterweight, in which case it is there Loth becomes dispensable. The instrument can be designed either as a full disk or as a half disk. But the degree of division always happens for the Scheibenhalbirungslinie and embraces course to the right and to the left in both cases only 90 per ^0th When the instrument is designed as a half disk, a disk counterweight must of course be attached in order to keep the latter in equilibrium.

When working out the disc to form a circular disc (Fig. 1), on the one hand, the Visor device 3-4 and on the other hand after the fixed ones attached to the graduation or sliding visors.

The round disc (full disc) can also be replaced by a square disc, since the graduation can be applied better and cheaper on angular discs. In this case, as FIG. 8 shows, the division is plotted on the hypotenuse of an isosceles right triangle b ac. The visor devices are attached at c d and α. This shape corresponds to a semicircle, but can also be designed as a square in accordance with the entire circular disk. Here, too, as with the other forms, the graduation goes from the disc center line to the right and left. This middle or dividing line is here the line from. At b , at most for the sake of universality, or when the disk is firmly connected to the stand, a sight perpendicular to the dividing line is pleasant, and one of the sighting devices 3-4 or 5-6 can also be dispensed with. Only with a must this vertical visor be present. The axes of the sighting device cd must be so directed that the sight is perpendicular to the division line α b .

The disc sits on a stick or other tripod and can be used with or without it rotatable.

The instrument serves:

i. for the construction and staking out of circular arcs by means of numerical

calculated ray lengths from the start or end point of the curve or finite from any point on the periphery - radiation method;

2. Likewise by means of mathematically obtained chord lengths from the periphery - cutting off equal tendons;

3. for the simplest and most precise calculation without further length or angle measurements:

a) the dimension and indentation when using the indentation method,

b) the diameter of the arcs constructed according to 1., 2. and 3a);

4. for constructing and staking out

Polygons from the perimeter or from their center;

5. to angle measurements.

If the instrument is made as a half disk, it can also be staked out use of slopes. The gradient percentages are to be attached to a scale, which perpendicular to the bisecting line. The pane is then hung freely floating.

The theory of the instrument rests first of all on the mathematical theorem that the triangle built over a circle diameter and inscribed in the semicircle on the Includes a right angle.

It is (Fig. 2):

cos χ = —j- > from this I = d cos χ , α

cos X ₁ = -j- ■> from this I ₁ = d cos X ₁ ,

therefore
therefore

as well

I: I ₁ = d cos χ : d cos X ₁ ,
I: I ₁ = cos χ : cos X ₁ ,

■ cos X ₁ = I ₁ cos x,

= L

In this way, any number of beams I ₁ Z ₂ Z ₃ . . . . of the circular arc are determined as soon as the length of the beam extremest Z and the angle χ X ₁ X ₂ X ₃ .... are known.

Every circular arc curve now consists of such a circular arc, where the curve span the outermost ray / represents. The values of the factors

cos χ

cos χ

cos X ₂
cos χ

cos X ₃ cos χ

can be now for all Winkelgröfsen, from about 5 ⁰ stepped to 5 ^0, and calculates the Verhältnifszahlen obtained thereby radially arranged in such a way on the instrument pane attached itself, that on each a given angular degrees corresponding jets the χ for each gradation of the variable supervisor angle relevant Number can be read off, as can be seen in FIG. 3 for the radii 65 ⁰ and 35 ⁰ .

cos

cos χ

cos X ₂

COS X

, cos χ, ·
L = I 2- etc

^ä COS X

Reading is made easier by the fact that the pointers are broken through and provided with a scale as well as with a movable mark, which can be moved to each division of the scale marked ⁰ ° to 90 ° corresponding to the outside angle χ. When the pointer is moved sideways, the respective ratio of each ray direction is shown by the mark with reference to the value of the curve outer angle χ set for the mark. For intermediate ^{values of the external angle χ graduated from 5 0} to 5 ⁰ , differential supplements must be added to the ratio numbers, which are calculated with reference to each difference between two successive ratio numbers for the intermediate degrees i °, 2 °, 3 ⁰ , 4 ^{0 can be} clearly displayed and read from a tablet.

By multiplying the ratio with the curve span / one then obtains the ray length of the angular directions X ₁ x ₂ x _s . .

Instead of using the length of the outermost ray / (the curve spans), the calculation of the ray system can also be based on one of the curved limbs, because it is in Fig. 2:

therefore

1 . 2

sin - ac b = ■>

2 ac

I = 2 α c sin - acb.

2 R,

But now is

A acb - \ - ^ _ cab - \ - ^ _ abc and

2 (Λ_cab -f AX) = ² R, consequently

A acb + A c from 4- A abc =

2 A_c from -j- 2 A_x, but there

A_c ab = A_a bc , so is

d. H. the outer angle of the curve is always half as great as that of the two sides of the curve formed angles. Therefore

Z = 2 α c sin x.

According to the foregoing, the value for

. cos x,

Z ₁ = 2 α c sin χ

Z ₂ = 2 α c sin χ

cos χ

cos X ₂ cos χ

u. s. w.

The values of the factors

cos x,. cos

2 a ν O a - w

olli · Α- J J * Olli Λ

cos χ

COS X

can then in the same way as above for the factors

cos χ

cos χ

has been carried out, calculated and compiled in tabular form. The ratios obtained in this way then relate to the leg ac of the curve.

The curve can also be constructed in those cases in which, as has not hitherto been assumed, the point of intersection of the two legs of the curve cannot or can only be determined with difficulty because of obstacles. This is done (FIG. 6) by looking for a connecting line which forms the same angle with both sides of the curve. For example, was first been visited at an angle of 45 ^0, such a connection line, but gave the rear, draw attention, that this line is not the same with the second leg direction, but an angle of 90 ⁰ forms, so is the arithmetic mean

45 * "

90 "

= 67 ⁰ 30 ¹

the right angle. The connecting line found then represents the curve span and the curve can thus be constructed.

In other words, this means:

If either the leg length or instead the curve span and furthermore the formed by the two legs or instead the outer angle of the curve span are measured, then, viewed theoretically, the entire curve can be mathematically exactly from the or end point from or from both towards each other easily without any auxiliary line and be safely designed directly. The intersection of the two curved legs can be indeterminate here.

The instrument must be set up in such a way that that the beginning or end point of the curve with an end point of the dividing line of the instrument coincides and the direction of the straight line passing through the start or end point of the curve coincides with the fixed direction of sight3,4 respectively 5.6 runs the same.

But if any point on the curve has already been determined in this way and should be obstacles Because of this, the curve is to be constructed to the end, then the connection between the beginning and the end point gives the first Curve with this. Curve points the new curve span for the relevant part the curve, while the curve outside angle of this curve part after the beginning. mentioned Theorem must always be right; The requirements for staking out the curve from a point on the periphery are thus fulfilled.

Specifically, the curve vertex d can be the specific point as soon as (Fig. 5) α d = dc = af = ce has been measured.

The methods of setting out curves that have been mentioned so far form the »radiation method «.

However, it is still possible to transfer the calculated beam lengths in the field there are other obstacles (Fig. 4). In this case the "cut off" has the same Tendons «to enter. This method consists in making the angle that one has already found ; Curve beam with the thigh (tan

direction of the curve or with a preceding ray, at ray endpoints recently plotted as a tangent angle and the last chord length in the one obtained Direction is measured again and continued in this way. The tangent angle is plotted by the fact that the two hands of the instrument are turned inward by the same number of degrees be moved when the tangent angle must be great, and then over the one pointer backwards to the last station point and across the other forwards.

The indentation method can be used instead of this procedure. Here, however, provided that the construction work is not to be a laborious and time-consuming trial, the lengths for the straight dimension ν (Fig. 7) and for the indentation e must first be determined. When using the circular curve constructor, the following formulas can be used as a basis (Fig. 7).

The straight-line dimension ν is calculated from the equation:

cos a =

~~ it

from which v = st cos

But now st can be viewed as a ray with the outside angle 90 ⁰ = α and, according to what has been said above, can be expressed by the outermost ray I. It is then

, cos (qo ° - a)

st = I A £; _,

cos χ

and after page 3 is

/ = 2 α c sin x,
therefore

sin α

ν = 2 α c sin χ cos α

cos χ

= 2 α c tang χ sin α cos α,

where α c is the side of the curve, χ is the outer angle of the curve and a. denotes the angle of the intended first indentation.

The first and last indentation quantity e is calculated from the equation: e = ν tang a.

Since the other indentations start from straight lines which intersect the arc of a circle, while the straight lines of the first and last station touch it tangentially , the results obtained here for the indentation quantity e are to be doubled at all other stations. The evidence may be waived as common knowledge ... . ■,

Finally, with the aid of the instrument, it is possible to determine the circle diameter of the curves in the simplest way using all the methods described above. In Fig. 2 are the. Circle diameter d, from the curve starting points from drawn-rays with / 1 _1/2. .., which denotes the angle corresponding to the latter with χ X ₁ x ₂ and the leg length with ac.

Now is

cos χ =

cos X ₁ =

therefore

d =

COS X

COS X,

or, as proved above,

/ = 2 α c sin χ

sin χ

a = 2 α c = 2 α c tang χ.

cos χ

Instead of the angle χ one can also use the one enclosed by the two legs of the curve Determine the angle, since, as mentioned, this is always twice as large as the former.

Regarding the ways of using the universal circle curve constructor specified under 4. and 5. no further explanation is required.

Due to terrain obstacles, the curve is staked out, as explained, when using the Instrument, since the same thing in all cases is the construction of a regular one Circular arc curve enables.

Claims (1)

Patent claim: Instrument for setting out, in particular, of circular arc curves, characterized in that, that there are two visor devices in a definite manner on a horizontal disk divided into degrees Distances from each other are attached, which allow it, both tangentially to the curve to be staked out, as well as to fixed or attached to the graduation sliding visors too. vising. 1 sheet of drawings.