CNC Coordinate System | Cartesian Coordinate System

CNC machines Axis:

The real parts of a CNC program involves the input of co-ordinates of the tool endpoint to produce any machining profile, subsequently it is necessary to follow a proper co-ordinate system.

01 - CNC milling axis - Cartesian coordinate system01 - CNC turning axis - cartesian coordinate system

Cartesian Co-ordinate System:

All the machine tools make use of the Cartesian coordinate system for the purpose of simplicity. The guiding coordinate system followed for assigning the axes is the familiar right hand coordinate system. The fundamental axes to be assigned are the rectangular axes and the rotary axes. One could use his right hand to arrive at these alternate variable positions of the same right hand coordinate system.

Designating the axes:

Z-Axis and Motion:


The Z-Axis movement is either along the shaft pivot axle or parallel to the shaft pivot axle. In the case of machine without a shaft / spindle such as shapers and planers, it is identified as the one perpendicular to the table, which passing through the controlled point (e.g., the cutting tooltip).


The tool moving far from the work-holding surface towards the cutting tool is assigned as the positive Z direction. This means in a drilling machine the drill moving into the workpiece is the negative (-) Z direction. This aids in decreasing the possible accidents because of the wrong part program entry in the coordinate signs.

When there are several shafts and slide ways:

In such cases, one of the shafts, preferably the one perpendicular to the work holding surface may be chosen as the standard shaft. The primary Z movement is then close to the primary shaft. The tool movements of other spindle quills or sometimes slides, these movements are termed as secondary and tertiary movements, and they are designated as U, V, W and P, Q, R respectively. For other machines such as shaper, planer etc., the positive (+) Z movement increases the clearance between the work surface and the tool holder.

01 - Vertical Axis Milling Machine Cartesian coordinate system

X – Axis:

The X – Axis is the principle motion direction in the positioning plane of the cutting tool or the workpiece.


It is perpendicular to the Z – Axis and should be horizontal and parallel to the work holding surface wherever possible.


When looking from the principle spindle to the column, the positive (+) X is to the right. For turning machines, it is radial and parallel to the cross slide. X motion is positive when the tool withdraws from the axis of rotation of the workpiece. For other machine tools, the X – Axis is parallel to and positive along the principle direction of movement of the cutting or the guided point.

Y – Axis:

It is perpendicular to both X – and Z – axis and the direction is identified by the right hand Cartesian coordinate system.

Rotary Motions:

A, B and C movements define the primary rotary motions.


These movements are located about the axis parallel to X, Y and Z respectively. If it in count to the above mentioned primary rotary motions, there are secondary rotary motions. These should be designated as D or E regardless of whether they are parallel or not to A, B and C motions.


Positive A, B and C are in the directions which advance right hand screws in the positive X, Y and Z directions respectively. The fingers of the right hand point towards the positive direction of the rotary motions. All the above mentioned (e.g., X, Y, Z; U, V, W; P, Q, R; A, B, C and D, E) is the reference to a point, the movement of which is sought to be controlled. This point is generally the tip of the cutting tool. Often the tool point may not move in some directions, e.g., the quill of the spindle of a vertical milling machine moves in the Z direction but not in the X and Y directions. In such problems, the work surface is usually motioned in a direction opposite to the one projected for the tool, e.g., the table of the milling machine holding the workpiece may be moved in – X and – Y directions. Such movements of machine elements, – X or –Y are signified as + X or + Y respectively. Prepared letters can thus be used for all the afore-mentioned motions to show the corresponding reversed directions for moving work surfaces.

Principle Parts of a Shaper Machine | Shaper Machine Mechanism


The different parts of a shaper are given and described below.

01 - parts of shaper machine - shaper machine


        The base is a heavy and robust in construction which is made of cast iron by casting process. It is the only part to support all other parts because all parts are mounted on the top of this base. So, it should be made to absorb vibrations due to load and cutting forces while machining.


        The column has a box type structure which is made of cast iron. The inside surface is made as hollow to reduce the total weight of the shaper. It is mounted on the base. The ram driving (Quick return) mechanism is housed. The two guide ways are supplied on the top. The ram reciprocates on the supplied guide ways. Similarly, there are two guide ways at the front vertical face of the column to move the cross rail along these guide ways.

Cross rail

        It is also a heavy cast iron construction. It glides on the front vertical ways of the column with two mechanisms. One is aimed at elevating the table and the other one is for cross travel of the table. A saddle slides over two guide ways already provided in the front face of the cross slide. The crosswise movement of the table is obtained by cross feed screw and the vertical movement of the cross rail is obtained by an elevating screw.


      It is attached on the cross rail which holds the table in position on its top without any shake.


     It is also a box type rectangular hollow cast iron block. This table slides along the horizontal guide ways of the cross rail. The work is held in the table. The table has machined surfaces on the top and sides of T-slots for clamping work. It can be moved vertically by the elevating screw. An adjustable table supports the front face of the table.


     Ram of cast iron has cross ribs for rigidity. Generally, it is a reciprocating type which slides over the guide ways on the top of the column. It is linked to driving mechanism of any one and also it carries the tool head at the front end.

Tool Head

     It holds the tool rigidly having swivel base with degree graduation. So, the tool head can be swiveled to any angle as required. The tool head has a vertical slide and apron to provide vertical and angular feed to the tool. A feed screw with graduated dial moves the vertical slide vertically to set the accurate movement.

     Apron is clamped upon the vertical slide which can be titled to right or left and also clamped at a correct position. The clapper box hinges a tool block previously fixed with apron. The tool block holds a tool post to hold the tool. The tool block fits inside the clapper box rigidly. In the return stroke, the tool block lifts out of clapper box to minimizing rubbing of the tool on the job.