What should I look for in a laser cutter intended to cut 3mm plywood with the aim of making custom shelves to display painted miniatures or to make the base structure for table top gaming.
For example, laser type, laser power.
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The typical hobbyist laser will either be a diode laser or a CO2 laser, when the focus is 3 mm plywood. I have both, with the diode laser having an optical output power of 5 Watts at 100% power. The CO2 laser is a 60 Watt unit.
The diode laser will cut laser-grade 3 mm plywood but can take up to seven passes at fairly slow travel speeds, along with substantial charring of the edges.
The CO2 laser will easily cut the same laser-grade 3 mm plywood in a single pass, at reasonably fast speed and minimal to zero charring of the edges.
I can't recall the travel speed of my diode laser as it's become a dust collector, but the first job that was done on both machines went from a duration of forty-five minutes on the diode laser to about five, perhaps ten on the CO2 machine.
Cost plays quite a factor in these machines. A reasonably powerful CO2 machine will require some means of liquid (distilled water) cooling, while the diode versions are almost always air cooled.
The CO2 lasers generate smoke, as do the diode lasers, but the cabinet of a CO2 machine has an exhaust port to which an exhaust blower is connected, with the exhaust directed to a window or similar vent. A diode laser usually has none of the above, unless a specific product is selected for this feature. Glowforge may have that feature, but it is not a popular machine in the laser community, due to mandatory internet connectivity for operation.
Software for using either type of laser varies, with LightBurn rapidly becoming the program of choice. It works with both types, is well supported and tremendously easy to use. Consider to visit the LightBurn forum for discussions regarding both types of lasers as well as the program features. YouTube has a number of videos from the creator which may be of value.
Other information to assist your decision can be found on various forums and involve much discussion regarding accessories for CO2 laser machines, cooling options for CO2 machines. Too much to cover in this resource, in my opinion.