In astronomy, a galactic latitude or longitude, useful for describing the relative positions and motions of components of the Milky Way Galaxy. Galactic latitude is measured in degrees north or south of the plane of the Milky Way. Galactic longitude is measured in degrees east of the galactic centre in the constellation Sagittarius.

Learn more about galactic coordinate with a free trial on Britannica.com.

Investigation of geometric objects using coordinate systems. Because René Descartes was the first to apply algebra to geometry, it is also known as Cartesian geometry. It springs from the idea that any point in two-dimensional space can be represented by two numbers and any point in three-dimensional space by three. Because lines, circles, spheres, and other figures can be thought of as collections of points in space that satisfy certain equations, they can be explored via equations and formulas rather than graphs. Most of analytic geometry deals with the conic sections. Because these are defined using the notion of fixed distance, each section can be represented by a general equation derived from the distance formula.

Learn more about analytic geometry with a free trial on Britannica.com.

A 'coordinate measuring machine' (CMM) is a device for measuring the physical geometrical characteristics of an object. This machine may be manually controlled by an operator or it may be computer controlled. Measurements are defined by a probe attached to the third moving axis of this machine. This probe touches the part of interest and allows collecting discrete points on the object's surface.

The typical CMM is composed of three axes, an X, Y and Z. These axes are orthogonal to each other in a typical three dimensional coordinate system. Each axis has a very accurate scale system that indicates the location of that axis. All three axes are displayed on a digital readout. The probe is used to touch different spots on the part being measured. The machine then uses the X,Y,Z coordinates of each of these points to determine size and position. There are newer models that have probes that drag along the surface of the part taking points at specified intervals. This method of CMM inspection is more accurate than the conventional touch-probe method and most times faster as well. The next generation of scanning, known as laser scanning, is advancing very quickly. This method uses laser beams that are projected against the surface of the part. Many thousands of points can then be taken and used to not only check size and position, but to create a 3D image of the part as well. This "point-cloud data" can then be transferred to CAD software to create a working 3D model of the part. The laser scanner is often used to facilitate the "reverse engineering" process. This is the process of taking an existing part, measuring it to determine its size, and creating engineering drawings from these measurements. This is most often necessary in cases where engineering drawings may no longer exist or are unavailable for the particular part that needs replacement.

A coordinate measuring machine (CMM) is also a device used in manufacturing and assembly processes to test a part or assembly against the design intent. By precisely recording the X, Y, and Z coordinates of the target, points are generated which can then be analyzed via regression algorithms for the construction of features. These points are collected by using a probe that is positioned manually by an operator or automatically via Direct Computer Control (DCC).

Technical details

Parts

Coordinate-measuring machines include three main components:

• The main structure which include three axes of motion
• Probing system
• Data collection and Reduction system - typically includes a machine controller, desktop computer and application software.

Uses

They are often used for:

• Dimensional measurement
• Profile measurement
• Angularity or orientation measurement
• Depth mapping
• Digitizing or imaging
• Shaft measurement

Features

They are offered with features like:

• Crash protection
• Offline programming
• Reverse engineering
• Shop floor suitability
• SPC software and temperature compensation.
• CAD Model import capability

The machines are available in a wide range of sizes and designs with a variety of different probe technologies. They can be controlled and operated manually, or by CNC or PC controls. They are offered in various configurations such as benchtop, free-standing, handheld and portable.

Specific parts

Machine body

The first CMM was developed by the Ferranti company of Scotland in the 1950s as the result of a direct need to measure precision components in their military products. One of the subsequent coordinate measuring devices was the UMS 500 (Zeiss/Germany). Leitz/Germany subsequently produced a fixed machine structure with moving table. In modern machines, the gantry type superstructure has two legs and is often called a bridge. This moves freely along the granite table with one leg (often referred to as the inside leg) following a guide rail attached to one side of the granite table. The opposite leg (often outside leg) simply rests on the granite table following the vertical surface contour. Air bearings are the chosen method for ensuring friction free travel. In these, compressed air is forced through a series of very small holes in a flat bearing surface to provide a smooth but controlled air cushion on which the CMM can move. The movement of the bridge or gantry along the granite table forms one axis of the XY plane. The bridge of the gantry contains a carriage which traverses between the inside and outside legs and forms the other X or Y horizontal axis. The third axis of movement (Z axis) is provided by the addition of a vertical quill or spindle which moves up and down through the centre of the carriage. The touch probe forms the sensing device on the end of the quill. The movement of the X, Y and Z axes fully describes the measuring envelope. Optional rotary tables can be used to enhance the approachability of the measuring probe to complicated workpieces. The rotary table as a forth drive axis does not enhance the measuring dimensions, which remain 3D, but it does provide a degree of flexibility. Some touch probes are themselves powered rotary devices with the probe tip able to swivel vertically through 90 degrees and through a full 360 degree rotation.

As well as the traditional three axis machines (as pictured above), CMMs are now also available in a variety of other forms. These include CMM arms that use angular measurements taken at the joints of the arm to calculate the position of the stylus tip. Such arm CMMs are often used where their portablity is an advantage over traditional fixed bed CMMs. Because CMM arms imitate the flexibility of a human arm they are also often able to reach the insides of complex parts that could not be probed using a standard three axis machine.

Mechanical probe

In the early days of coordinate measurement mechanical probes were fitted into a special holder on the end of the quill. A very common probe was made by soldering a hard ball to the end of a shaft. This was ideal for measuring a whole range of flat, cylindrical or spherical surfaces. Other probes were ground to specific shapes, for example a quadrant, to enable measurement of special features. These probes were physically held against the workpiece with the position in space being read from a 3-Axis digital readout (DRO) or, in more advanced systems, being logged into a computer by means of a footswitch or similar device. Measurements taken by this contact method were often unreliable as machines were moved by hand and each machine operator applied different amounts of pressure on the probe or adopted differing techniques for the measurement.

A further development was the addition of motors for driving each axis. Operators no longer had to physically touch the machine but could drive each axis using a handbox with joysticks in much the same way as with modern remote controlled cars. Measurement accuracy and precision improved dramatically with the invention of the electronic touch trigger probe. The pioneer of this new probe device was David McMurtry who subsequently formed what is now Renishaw Plc, even today the driving force behind many developments in the CMM field. Although still a contact device, the probe had a spring loaded steel ball (later ruby ball) stylus. As the probe touched the surface of the component the stylus deflected and simultaneously sent the X.Y,Z coordinate information to the computer. Measurement errors caused by individual operators became fewer and the stage was set for the introduction of CNC operations and the coming of age of CMM's.

Optical probes are lens-CCD-systems, which are moved like the mechanical ones, and are aimed at the point of interest, instead of touching the material. The captured image of the surface will be enclosed in the borders of a measuring window, until the residue is adequate to contrast between black and white zones. The dividing curve can be calculated to a point, which is the wanted measuring point in space. The horizontal information on the CCD is 2D (XY) and the vertical position is the position of the complete probing system on the stand Z-drive (or other device component). This allows entire 3D-probing.

Physical Principles:

Optical probes and/or laser probes can be used (if possible in combination), which change CMM's to measuring microscopes or multi sensor measuring machines. Fringe projection systems, theodolite triangulation systems or laser distant and triangulation systems are not called measuring machines, but the measuring result is the same: a space point. Laser probes are used to detect the distance between the surface and the reference point on the end of the kinematic chain (i.e.: end of the Z-drive component). This can use an interferometrical, a light deflection or half beam shadowing principle.