Had a go this morning cutting a living hinge using the laser on 3mm birch plywood.
Actually works rather well. I managed to break one part while getting it out of the material but that is easily solved by cutting a couple more passes. Should transfer to acrylic quite well too.
More info. on this and some test SVG files you can use can be found over on this blog on the Deferred Procrastination site: http://www.deferredprocrastination.co.uk/blog/2012/lattice-hinge-design-choosing-torsional-stress/
Pictures of my attempt below.