Makerspace laser cutters are good at both engraving and cutting, and this Instructable uses both! You can choose some public domain art or use your own, then use the jigsaw template to make a puzzle.
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Step 1: Find Some Art You Like and Test It on Your Laser
Optimize your art for your material and your laser cutter. For more information on that, see these other Instructables:
Finding public domain art: https://www.instructables.com/id/Public-Domain-Imag...
Setting up your art for laser engraving: https://www.instructables.com/id/Optimize-Your-Art-...
Step 2: Combine Your Image and Your Puzzle Template
The attached files are different formats of a vector 20-piece jigsaw puzzle. Choose your favorite and modify it in your favorite drawing program, or open it in your laser cutter software and resize it to fit around your art.
Step 3: Test Your Puzzle Material and Size
A laser cutter will burn away a little bit of material as it cuts, so your jigsaw puzzle will be a bit loose compared to a factory-made puzzle. A thicker material - quarter-inch plywood instead of eighth-inch - will minimize the looseness. But it will make a thick puzzle.
In this photo, the big puzzle is about 8 by 5 inches (20 by 13 cm) and the smaller one is about 4 by 2 ½ inches (10 by 6 cm). The smaller one feels really loose when it’s assembled.
Step 4: Cut Your Puzzle!
This example is cut from eighth-inch plywood, then shellaced to make the engraved surface stronger.
Here’s the art shown in the example puzzles:
Hercules abducting Iole: http://collections.artsmia.org/art/124319/hercule...
Hercules Carrying the Columns of Gaza: http://collections.artsmia.org/art/124319/hercule...
More public domain art by Sebald Beham: http://collections.artsmia.org/art/124319/hercule...