CNC Programming Handbook: A Comprehensive Guide to Practical CNC Programming, Second Edition

Chapter 4: Coordinate Geometry

The major step towards the basic understanding of CNC principles and geometrical concepts is the understanding of a subject known in mathematics as the system of coordinates. System of coordinates is founded on a number of mathematical principles dating back over four hundred years. The most important of these principles are those that can be applied to the CNC technology of today. In various publications on mathematics and geometry, these principles are listed under the headings like the real number system and the rectangular coordinates.

REAL NUMBER SYSTEM

The key to understanding the rectangular coordinates is the knowledge of arithmetic, algebra and geometry. The key knowledge in this area is the knowledge of the real number system. Within the real number system, there are ten available numerals (digits), 0 to 9 (zero to nine), that can be used in any of the following groups:

  • Zero integer

0

? Positive integers
(with or without sign)

1, 2, +3, 10, 12943, +45

? Negative integers
(minus sign required)

?4, ?381, ?25, ?77

? Fractions

1/8, 3/16, 9/32, 35/64

? Decimal fractions

0.185, .2, .546875, 3.5

All groups are used almost daily. These groups represent the mainstream of just about all applications of numbers in modern life. In CNC programming, the primary goal is to use the numbers to translate the drawing, based on its dimensions, into a cutter path.

Computerized Numerical Control means control...

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