Hello, I am Hide Arai from the Research and Development Department at XEBEC.
The year 2026 marks the 430th anniversary of the birth of René Descartes. To recognize the occasion, let us look at the connection between Descartes, Cartesian coordinates, NC machining, and automated back-burr removal.
The X, Y, and Z axes are now fundamental to engineering, architecture, computer science, and many other fields.
Their name comes from René Descartes, whose Latin name was Cartesius. His work helped establish analytic geometry, connecting geometric shapes with algebra and numerical coordinates.
Descartes was a French philosopher, mathematician, and scientist. He is also known for the statement “I think, therefore I am.” His philosophy began by questioning everything that could possibly be doubted. He concluded that the act of thinking itself proved the existence of the person doing the thinking.
This confidence in reason and mathematical thinking also influenced his approach to science. Descartes believed that the physical world could be described using numbers.
A well-known story connects the development of Cartesian coordinates with a fly.
While resting in bed, Descartes reportedly watched a fly moving across the ceiling. He wondered how he could describe its exact position to another person.
Saying that the fly was “near the middle of the ceiling” would not be precise. However, if everyone used the same corner as a fixed reference point, its position could be expressed by measuring its distance along different directions.
The story may have been added later rather than being a literal historical event. Even so, it illustrates the central value of coordinates: they turn an unclear position into information that other people and machines can understand.
The same principle is fundamental to modern manufacturing.
An NC program controls a machine tool by describing where and how the cutting tool should move. Several coordinate systems may be used:
For example, the command below instructs the machine to move rapidly to a specific position using absolute coordinates:
G90 G00 X10.0 Y20.0 Z-5.0
The machine interprets this as an exact destination: X equals 10 millimeters, Y equals 20 millimeters, and Z equals minus 5 millimeters.
In this sense, an NC program is a language that describes tool movement through coordinates.
XEBEC Back Burr Cutter & Deburring Tool Path uses this coordinate-based approach to remove burrs from the exit side of drilled holes.
The shape and size of a burr can vary depending on the material and machining conditions. The burr itself is therefore difficult to define precisely. One fact remains reliable, however: a back burr forms along an edge.
Instead of trying to measure the changing shape of the burr, XEBEC defines the position and geometry of the edge. We then provide a spherical deburring cutter together with a custom-made Tool Path created for the customer’s workpiece.
The Tool Path contains the coordinate data required to guide the cutter along the edge. This allows the tool to trace complex intersecting-hole geometry and remove back burrs automatically inside the CNC machine.
Just as coordinates can describe the position of a fly, they can also describe the path required to reach a hard-to-see edge inside a metal component.
Centuries after Descartes helped connect geometry with numbers, Cartesian coordinates remain at the heart of manufacturing technology.
They allow NC machines to translate an abstract position into precise physical movement. With XEBEC Back Burr Cutter & Deburring Tool Path, that principle helps manufacturers automate a difficult process and remove back burrs accurately and consistently.
An idea from the history of mathematics is still helping solve practical challenges on the factory floor today.
Learn more about XEBEC Back Burr Cutter & Deburring Tool Path.
