I have been cutting vinyl using a CB09 cutter from e-bay, with a penny to give some scale. It has a tiny drag blade which rotates in the smallest bearings I have ever seen and the height can be adjusted for different thicknesses. The blade comes in three angles for different materials 30, 45 and 60 degrees, I am using the 45.
The parts for the slide made from the old Z-axis leftovers. The slide puts pressure on the blade using gravity and will follow the vinyl even if the base board is uneven.
Parts
CB09 Vinyl cutter, blades and springs.
Aluminium plate 4mm thick.
SC12UU 12mm rail bearings 4off.
12mm optical linear rails 100mm long 2off.
SK12 12mm support brackets 4off.
SK16 16mm support bracket 1off.
M5 Bolts.
To set the height of the drag blade, screw it all the way in and then back out so you can just feel it with your finger (remember it's a knife!). Pull it over a bit of scrap vinyl and adjust the blade up or down so it just cuts through the vinyl but dos not cut the backing paper. Different vinyls have different thicknesses, so the depth will need to be re-set for each.
My daughters name was created using F-Engrave software and posted to G-Code for the CNC controller.
After using the CNC machine to cut out the design, carefully peal off the unwanted vinyl leaving only the parts that are needed.
Transfer film or pound shop masking tape is then used to cover the vinyl before pealing off the backing paper.
Apply the vinyl and transfer tape to it's final location and peal off the masking tape to reveal the finished design. In this case my daughters name on her over sized make-up box.