Rulers. Bradis tables
To measure the quantity flat angle It is enough to add another side to the corner so that a right triangle is formed. By measuring the sides of the resulting triangle, you can get the value of any trigonometric function the angle whose value needs to be known. Knowing the value of the sine, cosine, tangent or cotangent of an angle, you can use the Bradis table to find out the size of the angle.There are certain known angles that can be measured using a school square ruler. They produce two types of such rulers, both types are right-angled triangles made of wood, plastic or metal. The first type of square is an isosceles right triangle, two angles of which measure 45 degrees. The second type is a right triangle, one of the angles of which is 30 degrees, and the second is 60 degrees, respectively. By aligning one of the vertices of the square with the vertex of the angle - with the side of the angle, when the other side of the angle coincides with the adjacent side of the square, you can find the corresponding value of the angle. Thus, using rulers-gons you can find angles of 30, 45, 60 and 90 degrees.
Theodolite
The tools listed in the previous paragraphs are used to measure angles on a plane. In practice - in construction, topography - a special device is used to measure the so-called horizontal and vertical angles called a theodolite. The main measuring elements of a theodolite are special cylindrical rings (limbs), on which degree markings are evenly applied. Installed using a special stand at the top of the corner, the device is aimed using a telescope, first at a point located on one side of the corner where the measurement is made, then on the other side of the corner, and the measurement is taken again. The difference in measurements determines the angle in the first half-step. Then the second half-reception is performed - in the opposite direction. The arithmetic mean of the values obtained in two half-steps is the value of the measured angle.Which are used when performing graphic works, to facilitate the work of the draftsman and create convenience and increase productivity:
- drawing board with drawing accessories located on it
- drawing board- serves for pinning a sheet of drawing paper (whatman paper) to it with buttons. She represents wooden shield, consisting of longitudinal planks, pulled together by external end strips and fastened with glue. The working surface consists of longitudinal planks made from soft wood - alder or linden. Boards are made various sizes. For example, drawing board No. 2 is 1000 mm long, 650 mm wide and 20 mm thick. For more comfortable work It is advisable to glue white celluloid strips onto the edges of the board with a rectilinear uniform scale with a division value of 1 mm.
Reisshin - consists of a long ruler and two short crossbars.
One of the crossbars is fixedly connected to the long ruler, the second can be rotated in relation to the large ruler at any angle. Thus, using a crossbar, you can draw parallel horizontal and inclined lines.
- measuring ruler- used to measure lengths in the drawing.
It is made of hard wood and has a symmetrical trapezoidal cross-section. The ruler is equipped with white celluloid strips glued on its inclined edges and having a straight, uniform scale with a division value of 1 mm.
- squares- are used to work with them separately or in combination with a crossbar. With their help, you can perform various geometric constructions: drawing a series of parallel lines, constructing mutually perpendicular lines, drawing angles and polygons, dividing a circle into a given number of equal sections.
- pattern- used for drawing curved lines.
It is a thin plate of a curvilinear outline, making it possible to draw curved lines that cannot be made using a compass. Patterns are made with different curvature of lines. To draw a pattern curve, the pattern is selected so that its edge coincides with at least four points of the curve; in this case, only two of them are connected with a line and then the pattern is moved to subsequent points.
- protractor- used to measure and plot angles in a drawing.
- stencils and templates- used to reduce labor costs and time for performing certain types of graphic work. They can be very different in form depending on their purpose. Using stencils and templates, inscriptions can be made, circles, rectangles, corners, and signs can be drawn.
intended for copying drawings
- Photocopier- used to reduce labor costs and time for performing graphic work.
The power of the light source should be 150 - 200 watts. The glass is 3 - 4 mm thick; its edges must be treated with emery stone. This measure will protect against cuts on your hands. The drawing sheets, the original and the copy, are fastened together to avoid shifting relative to each other and secured to the glass with tape or using magnets. The front panel can also be installed in a landscape position; this will require longer rear bars, which give the structure the necessary strength. Also, the front panel can have a position not only close to vertical, but also close to horizontal if the photocopier is placed on the rear bars.
Drawing device includes two rulers set at 90° to each other
Drawing supplies and instruments
Drawing supplies and instruments
- drawing instruments- serve to facilitate the work of the draftsman, reducing the time spent on graphic work. Currently, various designs of drawing devices are used. They allow you to replace a gauge, a protractor, a square, and a ruler at the same time.
A pantograph type device is shown in the top figure. Using a special rotating head, the rulers can be positioned under different angles inclination to given lines. The head is connected by a system of movable levers, which allows it to be moved around the drawing field, with a bracket-clamp, with the help of which it is attached to the drawing board. The carriage type device is shown in the lower figure. The head moves across the drawing field using carriages - one moves along the upper edge of the board, and the other along a movable vertical guide. The use of such a device reduces the time spent by approximately one quarter compared to the execution of drawings using a grid.
- hatching device- serves to draw a series of parallel lines that serve as shading for individual sections of the drawing. It consists of two rulers, one of which is hinged at its end to the other with the ability to move the hinge along the second ruler by a given amount.
In construction, various squares are used to measure angles, which can measure angles of 90, 45, 135 degrees.
The so-called square is used to measure right angles. To measure angles of 45 and 135 degrees, use a measuring rod. It consists of a base and a ruler attached to it at an angle of 45 degrees. This square is often used to mark miter joints.
And the last type of square for measuring angles is called a small square. There, the ruler is attached to the base in a hinged manner, thanks to which this tool can mark any angles. Using a small marker, angles can be marked on samples and then transferred to construction blanks.
All of these squares can be made of metal or wood.
This is a level square:
This is a combination square:
And this is the little one:
And finally, an electronic protractor - measuring device new generation:
Now there are quite a lot of tools on the market that measure angles quite accurately and almost all of them are described in the answer from Iranika. However, there is also such an easy-to-use and very old measuring tool, like a protractor, you can also use it to quite accurately measure and draw the required angles. 
A ruler is the simplest measuring instrument, also used for drawing, which is a thin long plate with a printed scale with marks in millimeters, centimeters and meters. Since the sides of the tool are completely straight, it is used in drawing to draw straight lines. Rulers are usually made of metal, plastic or wood.
Varieties of rulers
This tool may be in different designs. Its shape is adjusted to specific goals. There are several ruler designs:
- Regular.
- Check room.
- Logarithmic.
- Drobysheva.
- Pattern.
- Protractor.
- Square.
- Officer's.
Regular
Represents the simplest design. This tool is sold in office supplies. This is what schoolchildren use in geometry and drawing lessons. This tool is thin strip made of metal, wood or plastic. On one side there is a scale in millimeters and centimeters, which allows you to measure length over short distances. Often the part opposite the straight side is made in the form of a wave, for drawing wavy lines. The length of ordinary stationery rulers can be 10, 15, 20, 25 and 30 cm. Also, longer tools are sometimes made especially for drawing, adjusted to the parameters of whatman paper.
Checking
In mechanical engineering, as well as in the production of machine tools and other equipment, test rulers are used. Often they do not have a length scale, since their main purpose is to check the evenness of workpieces. Such a tool is applied closely to the surface, and a visual assessment of the presence of bends on it is carried out. These devices are made exclusively from metal or durable plastic, since wood can bend when in contact with water, so you cannot count on one hundred percent preservation of the geometry of the instrument. In addition, the rulers are thicker, so they do not bend as much as regular stationery rulers.
Logarithmic
It is a rather unusual ruler with many marks on its surface. This device can be used not only for drawing straight lines, but also for calculating the root of any number. This is a line of an old design, which is practically no longer used thanks to the advent of calculators.
Such rulers were used until the mid-eighties of the last century, after which they were replaced by calculators. Slide rules can be elongated in length or made in the shape of a circle. Now they are practically not produced. On some models of Swiss watches, the shape of the dial is made in the form of a round slide rule. The markings applied to the watch provide a wide range of calculation possibilities, in addition to determining the value of trigonometric functions.
Drobyshev's ruler
This is a tool that is designed to construct a coordinate grid. It is made in the form of a steel strip with slots applied, the distance between which is 10 cm. They are used for pencil marks. Using this device You can apply a grid to whatman paper much faster than applying a regular ruler. This design was invented in 1925 by Fedor Vasilyevich Drobyshev, in whose honor it received its name. Now this device, like the slide rule, is a thing of the past and is now of interest only to collectors who collect antiques.
Pattern
This is a figured ruler, which in most cases does not have a scale with markings. The instrument is a flat plate curved by waves. It is used as a template for the construction of various geometric shapes, such as parabola, ellipse, hyperbola, and also spirals. With the development of computer graphics, this tool has ceased to be used by engineers, and is now used only by clothing designers and seamstresses to create fabric patterns before stitching them.
Protractor
This is a special design of a ruler that is used to measure angles in degrees. The device can have different shapes. It is usually round, semicircular or triangular. With this tool you can not only measure angles, but also construct them. On the flat part of the protractor there is a scale as on a regular ruler, and also markings are made in a circle in degrees. Semicircular models have a scale from 0 to 180, and fully round ones from 0 to 360 degrees. The instrument is believed to have been invented in ancient Babylon. It is indispensable in geometry, and was also used in shipbuilding for correct laying ship routes. The protractor is still relevant and can be found in any office supply store. They are used by schoolchildren in geometry lessons, as well as by architects and engineers.
Corner
Angle ruler, or square, is a tool made in the form of a right triangle. It comes in two types. The first is made in the shape of an isosceles triangle, one angle of which is 90 degrees, and the other two are 45 degrees. There are also tools with angles of 90, 30 and 60 degrees. Squares are used to construct angles when drawing, but only those in the shape of which it is made. Typically, such a tool is used for drawing with high precision. With its help you can draw perpendicular and parallel lines.
The square found its use not only in drawing, but also in carpentry. Joiners and carpenters use it to assemble furniture and other wooden structures when it is necessary to maintain a 90-degree angle between the parts being connected. The carpenter's square is much larger than the one used in drawing. In addition, its design is much stronger, since often when assembling furniture, the ruler takes on the function of supporting the workpieces, so the flimsy plate can become deformed, which will lead to failure of the correct angle.
It is worth noting that in carpentry, a construction corner is also used, which consists of two strips connected to each other at right angles. This design is inferior to the square, since with prolonged use, play may appear at the connection of the plates, which changes the shape by several degrees.
Officer's
This line is multifunctional tool for carrying out various measurements and drawings. It is made of transparent plastic, which can have different dimensions. Most often, such rulers are a plate measuring 20 by 10 cm. On two sides, which form a right angle, there are markings in millimeters and centimeters. The rest of the part is made in the form of a stencil, outlining the contours of which you can draw various figures, as well as numbers in large printed fonts. This tool is used to determine coordinates, as well as calculations on topographic maps. This design is designed specifically for military officers. Its dimensions are adjusted for convenient placement in a tablet with documents and office supplies. Most officer rulers that are now on sale also have a scale scale.
The best material for rulers
Rulers are usually made of metal, wood or plastic. The properties of these materials are different, so tools made from them have different properties. Metal rulers are considered the best because they can withstand deformation and are not destroyed by impacts. Such tools fully comply with GOST standards and can be used to perform precise drawings.
Wooden rulers quickly become dirty, so the scale printed on them may be difficult to see. When struck, they crumple and can also crack. In addition, upon contact with moisture, the wood becomes wet and begins to bend. The main advantage of such rulers is their pleasant surface, but the service life of this tool is minimal. If you place a wooden ruler unevenly and press it down with some kind of weight, then if you remain in this position for a long time, it will bend and retain its irregular shape.
Plastic rulers are the cheapest. They are lightweight and are not at all afraid of moisture, unlike wooden and metal ones, not made from of stainless steel. Their only drawback is their low impact resistance. Such a ruler can be broken, and when struck by an edge, small fragments of plastic break off from it, so further use of the tool for drawing straight lines becomes impossible.
Goniometer is precision instrument, designed to measure angles between two surfaces or their inclination relative to the horizon. The results obtained are expressed in degrees. Goniometers have a similar design to a construction or carpenter's angle, but they can show not only an angle of 90 degrees, but also be adjustable.
The simplest design of a protractor
The design of the protractor itself in simple form consists of two plates (rulers). They are fixed together on one side, fixed with an axis that allows you to change the angle between them. On the surface of the instrument there is a scale expressed in degrees. It can be ruled or rounded. There are both fully movable protractors and those with fixed measurements. The latter are used in cases where only the measurement of the most important angles is required - 90, 45 and 30 degrees. This tool falls more into the category of templates.
In which industries is the goniometer used?
This device is widely used in construction. It is used by joiners, carpenters and installers. With its help, you can set the planes perfectly straight before fixing them. The vast majority of objects that are used in everyday life and at industrial facilities have angles of 90 degrees. This is installed international standard which provides maximum convenience. In addition, failure to maintain a 90 degree angle in construction vertical elements increases the load on the structure.
For example: Due to the fact that the corners of buildings are measured accurately, during installation corner bath, there is no gap under the wall and when hanging cabinets and shelves everything looks even. There are thousands more examples that allow you to visualize the benefits of precise angles. The use of goniometers allows for accurate transfer of the parameters shown in the drawing to the real object.
Protractors are also used in route planning, military affairs, geometry and astronomy. Due to the demand for this instrument, its design has been adapted to various measurement purposes.
Goniometers can be divided into types:
- Building.
- Locksmith.
- Plotnitsky.
- Mountain.
- Astronomical.
- Nautical.
- Artillery.
Building The protractor is the most common. It is used to control the level of walls, foundations and other structures. Such devices are quite large. The length of each measuring part is usually at least 50 cm.
Locksmith have high accuracy. They are quite compact, but at the same time they have quite sensitive adjustment, allowing measurements to be taken with the display of fractions of a degree. This is necessary because the slightest deviations from the norm are unacceptable. With such inclinometers, you can safely measure the parameters of parts that will be used in rotary mechanisms.
Plotnitsky Protractors have low measurement accuracy. They are used in woodworking when precise adherence to angles and fractions of degrees does not matter. This tool belongs to the low price category. Often the adjustment mechanisms have backlash, which also leads to errors. Despite this, similar variety protractor is quite acceptable for fulfilling the purposes for which it is intended.
Mountain Protractors, unlike previous types of these instruments, are not used for direct contact with the surfaces being measured. This tool allows you to visually determine vertical and horizontal angles in the spaces of mines and mine workings. This equipment belongs to the imprecision class. Nowadays it is practically not used due to the advent of more high-precision electronic equipment, such as total stations, etc.
Astronomical are the most accurate. They are used to measure the angle between the surface of the earth and points in the sky. With their help, the trajectory of movement of celestial bodies is calculated, the speed of their movement is determined, and the size of the object is estimated. Such devices are often integrated into telescopes, which expands the range of their measurements, since the object of study can be not only objects visible in the sky, but also distant stars and planets.
Seaworthy Protractors are also called navigation meters. With their help, geographic latitude is determined using a special table. These devices work on the principle that the celestial body (sun, moon or stars) on a certain day and time is above the horizon at a special angle, relative to geographic latitude. Thus, using this device and table, the observer can determine the latitude at which he is currently located.
This device was widely used by sailors in the past, but with the development of satellite technology, its use has faded into the background. Despite this, similar protractors are available on board many ships, since in the event of failure of the electronic equipment, the use of a hand-held device will be the only way to obtain the exact coordinates of the ship.
Artillery goniometer used for installing artillery guns and adjusting salvo fire. The use of such a tool allows for precise aiming and changes in the direction of the shot after preliminary zeroing.
Types of goniometers according to the measurement principle
According to the measurement principle, goniometers are divided into the following types:
- Mechanical.
- Pendulum.
- Optical.
- Laser.
- Electronic.
Mechanical The protractor is a contact device. To carry out measurements, it is necessary to apply both surfaces of the tool to those objects, the angle between which you want to measure. The device has a special scale that allows you to determine what angle is obtained between the sides of the tool. Since the sides fit tightly to the surfaces being measured, their angle will therefore also be equal to the scale.
Pendulum The goniometer looks like a clock. The round dial of the instrument has markings corresponding to the angles. The needle of such a protractor always stands perfectly vertical, regardless of how curved the device itself is. There is a small ruler at the bottom of the device. It is applied to the surface that needs to be measured, after which you need to look at the indicator of the formed angle between the “0” mark on the dial and the arrow. Using such a device, you can measure the level of inclination of one surface.
Optic The protractor has an unusual shape for this type of equipment. You can recognize optical protractors by their eye, which acts as a magnifying glass. Optical instruments have a measuring range of 360 degrees. They are very accurate because the scale has many marks not only in degrees, but also in fractions of them. In this regard, it is difficult to visually determine which indicator the arrow is pointing to. Optical ones have a magnifying loupe. Thanks to it, it is much easier to count the marks that the arrow points to on the scale.
Laser The protractor has in its design two laser beams directed at the surface between which it is necessary to measure the angle. The angle between points is measured visually or using a computational electronic element, which is integrated into the design of the device. This device works well at night, as well as indoors. On daylight laser ray almost invisible.
Electronic or digital inclinometers are similar in principle to mechanical ones. With the exception that they have a dial in the form of an LCD display, which displays the indicator in numbers. This is very accurate equipment that allows you to determine tenths of degrees. To power such a device, a regular finger-type power supply is used. Such tools are used by builders and installers.
How to use contact protractors
Contact type goniometers are the most common and inexpensive. They are used everywhere. To take a measurement, you need to place the tool on the corner you want to measure. One ruler of the protractor is pressed against one surface, and the second against the other. If necessary, the device must be adjusted by increasing or decreasing the angle between its sides. The measurement results are displayed on a mechanical or electronic scale. In order for the data to be as accurate as possible, it is necessary that the surfaces at the contact points are smooth. If, for example, the angle between the floor and the wall is measured, it is necessary that there are no layers on them in the form of stuck lumps mortar or glue. Such a grain under one of the rulers will disrupt the received data by several degrees.
How to choose a protractor
When choosing, you should pay attention to the material. If it is made of very thin metal, then you should not take such a tool. Over time, it will deform, so the accuracy of measurements will be compromised. The cheaper range often has a painted scale. As a result, over time the paint begins to peel off. After this, it is impossible to determine how many degrees the instrument indicates.
The cost of a protractor depends not only on its design features, but also accuracy. The higher the accuracy, the less play there is on the tuning axis, which requires more expensive production. For carpentry or low-rise construction, it is quite possible to get by with tools of a lower category, but for the manufacture of critical parts, you need precise equipment.
