Cartesian Coordinates for CNC: XY & XYZ Systems Explained

In CNC programming, G90 (Absolute Method) defines all coordinates from a fixed origin point, while G91 (Incremental Method) defines movements relative to the current position. For example, with G90, a command like 'X50 Y-15' moves to absolute coordinates (50, -15), whereas with G91, the same command moves 50 units in X and -15 units in Y from the current position. The video demonstrates this difference through practical programming examples showing how the same coordinate values produce different results depending on which method is active.

In CNC programming, absolute positioning (G90) measures all dimensions from a fixed datum point (X0;Y0;Z0), while incremental positioning (G91) measures dimensions from the tool's last known position, effectively making the tool the new datum after each move; programmers often switch between these modes using G90 and G91 commands, with incremental being particularly useful for drilling multiple holes where only the distance between holes needs to be specified rather than absolute positions from the machine origin.

G91 is the G-code that sets the program in incremental mode. In incremental mode, all coordinates are based off of the current tool position rather than the part origin. This is the opposite of absolute mode (G90).

G90 sets absolute positioning mode where all movements go to specific coordinates in the printer's coordinate system. For example, G0 X50 Y50 moves to X50, Y50, and subsequent G0 X100 Y100 moves to X100, Y100 regardless of previous position. G91 sets relative positioning mode where movements are incremental from the last position. Starting at origin (0,0), G0 X50 Y50 moves to (50,50), then G0 X100 Y100 moves to (150,150). Absolute positioning is standard for most movements, while relative positioning is useful for end G-code to lift the nozzle consistently regardless of print height.

G90 sets absolute coordinate system where coordinates are measured from the machine origin (zero point). G91 sets incremental coordinate system where coordinates are measured from the current position. When programming, the choice between absolute and incremental affects how the machine moves and positions the tool relative to the workpiece.

The work coordinate system (WCS) is a logical system that can be positioned anywhere on the machine. The programmer does not need to know the exact physical workpiece location on the table. The WCS is typically set with X and Y origin at a corner or center of the workpiece, and Z origin at the top surface. Modern CNC controllers store multiple WCS (G54, G55, G56, etc.), allowing the same program to process multiple workpieces at different locations by simply shifting the WCS origin. The G54 command activates the first WCS.

The Work Coordinate System (WCS) in CNC machines, designated as G54-G59, defines the working origin for machining operations, allowing users to set up multiple coordinate systems for different workpieces or setups. To setup G54, the operator uses a dial indicator to measure the distance from the machine's reference point to the workpiece surface, then enters this value (typically negative) into the machine's coordinate system. Tool length compensation (G43 H1) is essential for accurate machining, where each tool's length is measured relative to the workpiece surface and entered into the machine's tool offset table. This enables the CNC machine to automatically adjust the Z-axis position for each tool, ensuring precise cutting depths regardless of tool length variations.

The Work Coordinate System (WCS) allows CNC programmers to define an arbitrary origin point on the workpiece, called the Program Origin Point. This system simplifies programming by enabling the use of drawing dimensions instead of machine coordinates. To set WCS, the user moves the tool to the desired origin point and selects G54-G59 codes, then enters the machine coordinate values (X, Y, Z) for that point. The machine then uses these values to translate program coordinates to actual positions. CNC machines typically provide 6 basic work coordinate systems (G54-G59), with options to expand to 48 or 200 systems.

Work coordinate systems (G54-G59) in CNC milling machines allow operators to define a convenient origin point for programming by storing offset values that shift the machine's coordinate system to align with the workpiece, eliminating the need for complex negative coordinates and simplifying programming when the workpiece is positioned at a convenient location on the machine bed.

In CNC machining, G54, G55, G56, and G57 are work coordinate systems that define the position of the workpiece zero point relative to the machine's machine zero. When machining multiple identical workpieces on a CNC machine, each workpiece can be assigned a different work coordinate system (G54 for piece 1, G55 for piece 2, G56 for piece 3, G57 for piece 4). The operator measures the distance from the machine zero to each workpiece zero point and enters these values into the machine's coordinate system settings. This allows the same CNC program to be used for all workpieces by simply changing the work coordinate system selection (e.g., G00 G54, G00 G55, G00 G56, G00 G57), enabling efficient batch production without modifying the program for each workpiece.

In CNC programming, letters A, B, and C are used to control rotary axes: A is used when the rotary table is positioned on the X-axis, B when on the Y-axis, and C when on the Z-axis, allowing operators to rotate the fourth axis by 360 degrees for precise machining operations.

CNC machine tools use auxiliary rotational axes (A, B, C) for complex machining. A-axis rotates around X-axis, B-axis around Y-axis, C-axis around Z-axis. Positive/negative directions follow clock face rules: A-axis counterclockwise=positive, B-axis clockwise=positive, C-axis counterclockwise=positive. Horizontal machine tools have Z-axis horizontal and Y-axis vertical, with A and B axes as auxiliaries. CNC lathes use C-axis for spindle rotation and Y-axis for linear auxiliary movement.

CNC (Computer Numerical Control) machining uses programmed computer software to control cutting tools for material removal, with machines classified by their axis count: 3-axis CNC machines operate along X, Y, and Z axes with the workpiece stationary, suitable for basic drilling and milling; 4-axis CNC machines add rotational capability around one axis (typically A-axis) for side machining; and 5-axis CNC machines utilize all three rotational axes (A, B, C) along with X, Y, and Z axes, enabling machining from five directions for complex parts, though requiring more programming time.

The A, B, and C axes are rotational axes that rotate around the X, Y, and Z axes respectively. On milling machines, A rotates around X (commonly used for rotary tables), B rotates around Y (often controls pallet rotation), and C rotates around Z (like a turntable). However, on CNC lathes, these axes function differently: the C-axis controls spindle rotation (essential for live tooling where the spindle can be positioned at precise angles like 0° or 180°), while the B-axis typically controls the subspindle's Z-axis movement for part transfer between spindles. This demonstrates how axis functions vary significantly between machine types.

CNC machines include three rotary axes corresponding to rotation around the linear axes. The A-axis represents rotation around the X-axis, where clockwise rotation is considered positive and counterclockwise is negative. The B-axis represents rotation around the Y-axis, following the same sign convention. The C-axis represents rotation around the Z-axis. These rotary axes enable complex five-axis machining operations, allowing tools to approach workpieces from multiple angles simultaneously. The direction conventions apply consistently to both vertical and horizontal machining centers.