Instead, we'll just focus on the 8 simple steps required for the tool that will be used to 'cut' the threads in our making of the bolt for 3D printing.
To create a thread with a 3D design application, like Cubify Invent or Moment of Inspiration, requires creating a "Cutting Tool" shape that is used with a Helix tool ((Coiled Line) to make the threads.
STEP 1: Create the Primary Reference Triangle at the Thread Pitch size
While it is not absolutely required that the triangle used to form the thread cutter be an equilateral triangle, it is the most common form. What is required is that the height of one side of the triangle is exactly the length of the desired "Thread Pitch". In our case, this would be 20 threads per inch, or 0.05". our starting triangle would look like this sample.
|Equalterial Triangle with 0.05" Sides|
Each of the tips of the base triangle will be truncated for reasons explained in the Wikipedia article. To facilitate the design of the trucation, we copy the primary triangle and then scale the copy to 1/4 the size of the original. We then place that second triangle right into the tip of the first as shown below. We'll call this the "Tip Triangle". It's colored red in this sample.
|Create the Tip Triangle at 1/4 Scale of the Base Triangle.|
STEP 3: Create a "Corner Triangles"
We next make two copies of the "Tip Triangle" and scale them to 1/2 the size of the Tip Triangle. Each of the copies is moved into either the upper left tip or lower left tip of the primary triangle. All of these triangles are merely reference objects to help us actually draw the cutting tool itself.
|Back Triangles 1/2 Scale of the Tip Triangle|
STEP 4: Create a Truncation Arc inside the Tip Triangle
The goal of this step is to create two 90 degree reference lines that intersect the side of the Tip Triangle at a point that is 1/4 along the side of the triangle. We then draw an arc whose center is at the center of the back line of the triangle and that extends from the points where the lines intersect the triangle.
|Adding the Trucation Arc|
STEP 5: Add Reference Lines that divide each back triangle.
These lines will aid us in drawing the final cutting tool by giving us snap-to points.
|Add Reference Lines to Facilitate Drawing|
Step 6: Using Continuous Lines Draw the Cutter Outline
Notice that we do not draw to the tips of the primary triangle. Beginning at the intersection of one end of the arc we draw a series of connected line (Blue Sample) until we get to the intersection of the arc on the opposite side of the triangle. We then JOIN the arc and lines to form a single object.
|Using the Reference Lines, Draw the Cutter Tool Outline|
Step 6: Remove the Reference Lines (Invisible) to Reveal the Cutting Tool
As we make the reference triangles and lines invisible, the outline of the cutting tool is revealed. The front tip is rounded and the back tips have been truncated to result in gaps so that the final thread will not be too pointed.
|Remove References to Reveal the Cutting Tool|
Step 7: Add References to Aid Connecting to the Helix
The final step is to add a line and a point, which we have exaggerated for clarity, to aid in positioning the Cutting Tool relative to the Helix path. Notice that it is NOT attach the cutter to the Helix along the back side of the cutting tool. We move the attachment point forward to a point along a line anchored at the tips of the small back triangles. This means that the thread is slightly more shallow then the thread pitch.
|Add a Reference to Center the Attachment to the Helix|
As the cutter moves around the shaft of the bolt, it removes material to form the threads. The thing to note is that the tips of the thread ends up being somewhat flat, rather than sharp. And, the valleys of the thread are also not sharply pointed. This makes for a stronger, smoother turning thread with less potential for binding up..
It's been very interesting, to me, to explore the more technical aspects of thread design. Once grasped. it allows us to design any sized threaded bolt or accessory. But, knowing how to design it is not enough if we are to use a 3D printer to realize those designs. And, this is going to take some experimentation in scaling, etc.