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What is X Y Z System? Cartesian Coordinates

Basics

A basic understanding of the three-dimensional cartesian co-ordinate system is needed for machining. For the purpose of this course, let us quickly refresh the basic concepts starting with the 2-dimentional followed by the three dimensional system.

Please note that all measurements in this course is in the metric system.

 The left-right (horizontal) direction is commonly called X.

The forward – backward direction is commonly called Y.

When we put them together on a graph, we get a representation of a two dimensional plane.

Where they cross over is the 0 point, It is called ‘the origin‘, and we generally measure the relative distance of every other point in the plane from here.

Top Tip – In the context of our CNC machine, the origin is called the ‘the home’ position.

Directions

Note that in the above diagram, the X-axis runs horizontally through zero and the Y-axis runs vertically through the zero.

As X increases, the point moves further right, and when X decreases, the point moves to the left.

The forward – backward direction is commonly called Y.

When we put them together on a graph, we get a representation of a two dimensional plane.

What About Negative Values of X and Y?

 Yes, we can have negative values and therefore, when the value of X or Y is negative, start at zero and move in the opposite direction. Negative X goes to the left of the origin, and negative Y goes below the origin.

Source – https://www.mathsisfun.com/data/cartesian-coordinates-interactive.html

3rd Dimension

The two-dimensional system gives us the ability to define a point in a two-dimensional plane, in order to do the same in three directional spaces, we add a third dimension as shown below –

Exercise – Measure different objects in the room using 3-D cartesian co-ordinates. Use both meters and feet. Choose different origins each time. 

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