There is no one-step method to align a non-rectangular workpiece on a laser cutter bed. When lots of similarly shaped objects are going to be engraved, a custom-cut jig is often employed to ensure that the alignment is consistent, but for a one-off job that can be overkill, and requires a fair amount of time to design and test the jig. All that is needed is a way to identify the center of object to be etched and line the laser up to that point. A piece of paper, some tape, and a pencil are all the tools required. I'll show you how I was able to etch the bottom of a shot glass, and you can apply the technique to your own project!
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Step 1: Make a Rubbing of the Surface to Be Engraved
Get a blank piece of paper that is at least the size of the surface you are engraving. Having a larger piece of paper will help you get a more accurate center since your measurements can be more accurate.
Affix the paper to the surface to be engraved. I used single-sided tape stuck in a loop, but double-sided tape is less likely to move. Rubber cement would work fine too, I'm sure.
Using a graphite pencil, lightly rub around the edge of your object. This should transfer the outline of your object onto the paper. Use the side of the pencil when making the rubbing, not the tip, or you'll just poke holes in the paper.
Step 2: Find the Center of the Template
Now it's time to employ some junior-high geometry. There are several ways to find the center of a circle. I present two ways here:
Method 1: Use a compass
We will call the circle we're finding the center of circle 1. Any other circles/arcs we will call A, B, C, D. These additional circles that we will draw need to have the same radius as each other, but do not have to match the radius of circle 1. I like to make them as big as the paper will allow because it makes it easier for me to scribe accurate lines.
Pick any point on the circle's circumference as the center of a new circle A. Draw a circle A (or an arc that is guaranteed to include the center of the circle 1). Pick a second point as the center of circle B on the circle 1's circumference on the opposite side of the circle 1 from circle A's center. Don't worry about getting it exactly opposite point A, you just need some distance between the two.
The two circles you just drew should intersect at two points. A line drawn between those two points is guaranteed to cross through the center of circle 1.
Repeat the process you did for circles A and B, but pick two new points so they will create a line roughly perpendicular to the line drawn for A and B. Any two points will work, but the closer the resulting lines are to being perpendicular to each other, the more accurately you can find the center of circle 1.
Once you have drawn the line between the intersections of the circles C and D, you will have a nice X drawn through the middle of circle 1. The point where they intersect will be the middle of the circle.
Method 2: Use the corner of another piece of paper as a 90 degree angle. (harder to get accurate results, no images provided)
Place a second sheet of paper over the rubbing you made earlier so that a corner of the new sheet is inside the circle of the rubbing. Slide the new sheet so the corner new piece of paper just touches the inside of the curve of the circle, with the circle extending to the left and right. Now most of the circle will be covered by the new sheet of paper. Mark on the sheet with the rubbing where the edges of the second sheet of paper cross the circumference of the circle. Draw a line between these two points.
Repeat the process, moving the corner of the sheet of paper to a new location (preferably around 90 degrees from the first point. Using one of the marks you just made is as good a place as any) and mark two new points on the circumference of the circle. Draw a line connecting these two new points. Where the two lines cross will be the middle of the circle.
Step 3: Put the Piece in the Cutter and Affix the Template
Put the piece to be engraved on the cutting bed of the laser cutter and focus the laser to the surface you will be engraving. If the piece is small, be sure to attach it to a stable base so it does not shift or tip during the engraving process.
Once the laser has been properly focused, lay the template on top of the piece to be engraved so that the template lines up exactly with the rubbing you made.
I cut my template along the outside edge of the rubbing that I made so that I could visually align the template to the edge of the piece. As I was cutting, I left some overhanging tabs and bent them downward to help auto-center the template and keep it in place as I adjusted the laser head position.
Do not use adhesive to attach the template to the object since this time you will need to remove the template before etching, and you would likely disturb the placement of your piece while trying to unstick the template. It would theoretically be possible to leave the template affixed to the piece and just burn through it while etching, but I would imagine the quality of the etching would be inconsistent, not to mention it would destroy your template if you had plans to use it on multiple pieces.
Step 4: Center the Laser Over the Piece
Use the directional arrows on the trotec control panel to position the cutting head so that the laser pointer dot is centered on the intersecting lines that indicate the center of the circle on your template.
Remove the template being careful not to disturb either the laser or the piece to be etched.
In the Job Control software, position the job to be engraved so that its center 'snaps' to the crosshairs indicating the position of the laser head. For rectangular stock people usually position the top left or bottom left corner of the job at the print head ... make sure you position the CENTER of the job at the print head! If the print job is too small, the JobControl software will only snap to the corners of the job, not the middle. If you find you cannot snap to the middle of the job, adding a bounding box to your artwork in a non-printing color will let you increase the size of your job without rescaling your artwork. Just be sure the bounding box is centered around your existing artwork.
Double check to make sure you removed the template, hit print, and you're done!
I made mine at http://techshop.ws!