3D Rotation of CAD Parts

From robotic joint translations to advanced video game-level physics modeling, DMC has done some fun 3D applications over the years.  A recent example of a fun application of the non-flat kind involves AIM, Inc., a manufacturer 2D and 3D CNC wire bending machines.  AIM has been designing state-of-the-art wire benders used in a variety of applications for more than two decades and DMC's relationship with AIM goes back to some of our first projects.

Often times these bending machines are used to by end clients to manufacture a single part over and over again.  Yet some applications are more artistic such as creating the wire frame for a concrete sculpture.   These machines create parts that, when brought together, form amazing geometries that the most creative designers can imagine. 

AIM, Inc. has developed an easy-to-use software called Smart Editor that allows users to import design files and control the machine.   DMC partnered with AIM to further automate custom applications using a DXF Batch Importer.  One of the goals of the DXF Batch Importer is to use a 2D wire bending machine to manufacture parts from a 3D DXF file. This leads to the question, how does one create parts for a 2D wire bending machine from a 3D CAD design?

A slow, tedious option is for the CAD model designer to go through the file and recreate the parts on the XY-plane. Fortunately much of this process can be automated through the use of the DXF Batch Importer coupled with AIM's Smart Editor.  While the math (3D matrix calculations) is fairly simple and can be found in places like Wikipedia, visualizing what is happening is important. The following visuals step through a simplified process of transforming a 3D part onto the XY-plane.

1. It is easiest to visualize if we begin by translating the part to have a point on the absolute origin. As you can see this part consists of 2 line segments that are not on any of the standard planes (XY, XZ, or YZ).


2. Rotate the part about the Z-Axis until a line segment is on the XZ-plane.


3. Rotate the part about the Y-Axis until one segment is on the X-Axis.


4. Rotate the part about the X-Axis until the other line segments are on the XY-Plane.


5.  

With a few simple rotations (using basic Rotation Matrices), the part moves from 3D space to the XY-plane. It takes a long time for a designer to go through all the parts in a file they create and complete this transformation. A computer, on the other hand, can complete this very quickly.

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