In history, people developed different types of coordinate systems. According to the application, we can select a suitable one. You can find out detailed information about them in this article.
Coordinate System Types
Cartesian Coordinate Systems
We use the right-hand rule for general ones. The cartesian coordinate system is the most common type that we apply the right-hand rule. We use CAD programs and the cartesian coordinate systems for positioning.
According to the right-hand rule;
- When you align your right thumb to the positive X-axis direction,
- The index finger shows the positive Y-axis direction.
- If we curl the other fingers 90 degrees according to the index finger, they show the positive Z-axis direction.
Rotations are also very important and we define rotations according to the X, Y, and Z axes. According to the right-hand rule, if we direct the thumb along the positive side of an axis, the other finger’s curl shows the positive direction of rotation.
Unlike the cartesian, we make the positioning of the points differently. Here you can find brief information to understand the general logic of the polar coordinate systems.
The positioning in the polar type has a different notation. Also, to define the position of a point in polar coordinates, we must define the length and an angle value. Moreover, the length value is the minimum distance between the origin point where we define the polar coordinate system and the main point. The angle value is the angular position of the line between these points, according to the positive X-axis.
For example, (45, 145) shows the polar coordinates of a point. The first notation is the distance between two points. And the second notation is the angle between the positive X-axis and the line between these points.
Absolute and relative positionings are also possible in the polar type.
Cylindrical Coordinate Systems
The Cylindrical-coordinate system is the same as the polar coordinate system. So, we use the polar type for the 2D situations in which we make the specification of a place with an angle and distance value.
We develop the cylindrical coordinate system for positioning in 3D space. In cylindrical type;
- The first element is the radius value which gives the distance between the point and the origin(center).
- The second element is the angle value which gives the angle of the line between these points and the X-axis.
- Furthermore, the third element is the distance of the point to the Z-axis in a perpendicular position.
So you can understand that the third element of the cylindrical type is the additional element to define the exact position in 3D space.
For example, if a coordinate of a point is given as (45 145 30). As you understand that the distance between the point and the center is 45 units. And also the angle between this line with the X-axis is 145 degrees. The distance from that point to the Z-axis is 30 units again.
Spherical Coordinate Systems
Also, for 3D positionings, they developed different kinds of them and one of these coordinate systems is the spherical type. So, as you understand from its name, we make the positioning on a sphere in 3D space. We make this positioning with these elements;
- And also, the first indicator of the spherical type is the radius. This radius gives the distance between the point to be positioned and the center(origin) of the sphere.
- And then the second indicator is the angle. This is the angle between the radius and the X-axis.
- The third and last indicator is the angle between the radius line and the X-Y plane. X-Y plane is the Ecuador plane of the sphere.
For example, if we give a location as (100, 50, 40) for a spherical coordinate system, you can understand that the length of the radius line is 100 units. The angle between the radius line and the X-axis is 50 degrees and the angle between the radius line and the X-Y plane is 40 degrees.
Also, absolute positioning is one of the most used methods in coordinate systems. In absolute coordinates, there is a point which is called the origin. And origin’s coordinates are (0, 0, 0) in each directions(X, Y and Z). So, if you specify a point on that absolute coordinate system, the absolute coordinates show the distance between the point and the X, Y, and Z rays. Also, this distance is a perpendicular distance. These distances are the coordinates of the point.
For example, if you have a point on an absolute coordinate system, say it is (4, 5, 6). The perpendicular distance of this point to the X-axis is 4 units. And to the Y-axis is 5 units. And this is 6 for the Z-axis. This is very simple like that.
For different situations, the use of relative coordinates can be useful. So, relative coordinates of a point are defined according to the previous coordinates which must be known. If the given relative coordinates are added to the previous coordinates, the exact location will be found.
For example, you want to define the location of a point, according to another point. The first point’s coordinates are (4, 5, 6). And if you define the second point’s coordinates (2, 3, 4) with respect to the first point you can find the absolute location of the second point’s as (6, 8, 10) which is the addition of the given coordinates.
Relative coordinates are useful if the origin point is not known.
These are the general coordinate system types that are used in different calculations in engineering.
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