Coordinates for the CNC Lathe 221

Coordinates for the CNC Lathe provides an overview of the coordinates used to program cutting operations on CNC lathes or turning centers. It introduces the systems of both Cartesian and polar coordinates and describes how Cartesian axes are used on a CNC lathe. The class describes both how coordinates are used on blueprints and how they are applied as machine movements. This includes concepts such as incremental vs. absolute coordinates, linear and circular interpolation, machine zero, and program zero.

Coordinates and axis movements are at the core of operations for a CNC machine. A foundational knowledge of these topics is necessary to understand how and why parts can be successfully made on the CNC lathe or turning center.

  • Difficulty Intermediate

  • Format Online

  • Number of Lessons 16

  • Language English


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Course Outline
  • CNC Coordinates
  • The Origin and Positive and Negative Movement
  • Blueprints and Coordinates
  • Blueprints and Coordinates
  • Polar and Spherical Coordinates
  • CNC Coordinate Basics
  • Axis Locations
  • Axes on the Turning Center
  • Rotational Axes
  • Axes on the Turning Center
  • Review of Turning Center Axes
  • Linear and Circular Interpolation
  • Machine Zero and Program Zero
  • Incremental and Absolute Coordinates
  • Incremental vs. Absolute Coordinates
  • Machine Movement Review
  • Describe the Cartesian coordinate system.
  • Identify the origin and the positive and negative directions of the Cartesian coordinate system.
  • Describe blueprints and computer-aided design.
  • Describe blueprints and computer-aided design.
  • Describe the polar and spherical coordinate systems.
  • Describe the general guidelines for locating axes on CNC machines.
  • Describe axes on the CNC turning center.
  • Identify the A, B, and C rotational axes.
  • Describe axes on the CNC turning center.
  • Describe linear and circular interpolation.
  • Describe the role and location of machine zero. Describe the role and location of program zero.
  • Describe incremental and absolute coordinates.
  • Distinguish between incremental and absolute coordinates.
Vocabulary Term

A axis

A rotational axis that describes motion around, or about, the X axis. The A axis allows the tool to tilt in order to machine hard-to-reach areas.

absolute coordinates

A series of numerical positions that are calculated from a fixed point of origin. Absolute coordinates are the most conventional and commonly used.


A figure formed by the intersection of two lines. Angles are also used to measure distances around a circle.


An imaginary line that passes through the center of a point or object. Axes are used to describe the positions of objects on the Cartesian coordinate system.

B axis

A rotational axis that describes motion around, or about, the Y axis. The B axis is not present on all lathes.


A design representing the dimensions of a specific finished part. A blueprint is used to create a part program.

C axis

A rotational axis that describes motion around, or about, the Z axis. The C axis describes the rotation of the workpiece.

Cartesian coordinate system

The system that describes the position of any point or object in three-dimensional space by numerically expressing its distance from a fixed position along three linear axes. The Cartesian coordinate system is used to describe measurements in CNC milling and turning.

circular interpolation

A circular cutting path that requires tool motion on multiple axes. Circular interpolation is used to cut curved shapes.

CNC lathe

A lathe that is controlled by a computer running programs driven by numerical data. CNC lathes are much more precise than their manual counterparts.

computer numerical control

CNC. A programmable control system for a machine tool, directed by mathematical data, which uses microcomputers to machine parts. A computer numerical control operation is much quicker and more precise than its manual counterpart.

computer-aided design

CAD. The use of computers for the design and drawing of a part or other product. Computer-aided design drawings are precise and can be made quickly compared to blueprints.

computer-aided manufacturing

CAM. The use of a computer to assist in part manufacture. Computer-aided manufacturing uses CAD data to generate coded instructions for machining a part.


Tool movement along two or more axes simultaneously. Contouring is used to create curved, non-linear features.

cutting variables

Variables that impact cutting during machining operations. Cutting variables include speed, feed, and depth.


Any object which has a circular top and bottom connected by parallel walls that follow the circumference of the circles. Cylindrical parts can be easily created using a CNC mill.


The distance of the tool's penetration into a part. Depth is measured from the centerline of the workpiece.

diametrical dimensions

Measurements made along the diameter of a part. Diametrical dimension measurements are commonly used for the CNC lathe.


The desired measurement of a feature on a part. Dimensions typically indicate length, width, and height.

incremental coordinates

A series of numerical positions that use each current position as the point of origin for the next position. Incremental coordinates can pass errors on from position to position, which makes them less reliable than absolute coordinates.

linear interpolation

A movement along two or more axes simultaneously that creates a straight line. Linear interpolation can be used to create tapered parts.


In turning, a motion or action that occurs parallel to the axis of a cylindrical workpiece. Tool feed in turning is longitudinal.

machine zero

The starting position that is permanently set by the manufacturer of each particular CNC machine. Machine zero is typically used for loading and unloading parts.


A numerical value stored in the CNC controls that is used to reposition machine components. Offsets are used to move the machine tool from machine zero to program zero as well as to adjust for variations in tool geometry, part size, and other factors.


The fixed, central point in the Cartesian coordinate system. The origin has a numerical value of zero.

part program

A series of numerical instructions or commands that direct a CNC machine to perform the necessary sequence of operations to set program zero from machine zero and to machine specific workpiece features. Multiple part programs can be stored in a CNC machine at the same time.

part programmer

The person responsible for the creation of a part program. The part programmer translates the workpiece design into program instructions for the CNC machine.

polar coordinate system

A system that describes positions in three-dimensional space using locations on a sphere or ball. The polar coordinate system uses the angle of an object's location to describe it.

program zero

The position that acts as the origin for the part program of a particular workpiece. Program zero is unique to each workpiece design and is selected by the part programmer.

right angles

An angle measuring 90° and formed by two lines that are perpendicular to one another. Right angles form the corners of squares and rectangles.

right-hand rule

A quick reference that shows the location of the X, Y, and Z axes. A person displays his or her right hand and the first three fingers from the right each represent the X, Y, and Z axis respectively.

rotational axes

An axis that describes turning or rotation around the linear axes. The rotational axes are designated as the A, B, and C axes.


The rate at which the cutting edge of a tool moves past the workpiece surface at the point of contact. Speed must be carefully selected in order to ensure a good cut.

spherical coordinate system

A coordinate system which locates points based on their angles from two of the three axes as well as distance from the origin. The spherical coordinate system can be useful for circular or spherical parts.


The component that holds and rotates the workpiece in the CNC lathe. The spindle is always parallel with the Z axis.


An object which has length, width, and depth. Three-dimensional objects can be represented by the spherical coordinate system or Cartesian coordinate system.


Any device used to accomplish a task. Tools for CNC lathes include drills and cutting tips.


An object which has length and width but not depth. Two-dimensional coordinates can be represented using the polar coordinate system or Cartesian coordinate system.


A part or component that is being machined. Workpieces in CNC machining are the raw materials that are shaped by the machine.

X axis

A linear axis in the Cartesian system that is perpendicular to the Z and Y axes. On the CNC lathe, the X axis describes turret motion toward and away from the spindle centerline and controls workpiece diameter.

Y axis

A linear axis in the Cartesian system that is perpendicular to the Z and X axes. The Y axis is typically not programmable on a basic CNC lathe.

Z axis

The linear axis that represents motions and positions perpendicular to the X axis and parallel to the machine spindle. On a CNC lathe, the workpiece typically rotates around the Z axis.