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Just use a length of NICROME (or similar) wire starched between 2 posts. Nicrome is a resistive wire that will get hot when power is run through it. It is often found in wire wound resistors or pots.
Connect it to a variac or variable supply and turn up the voltage until it is hot enough to cut.
Take a nicrome wire (one of those used with 220V AC line,you can find one in every electrical materials shop, usually come in spiral form)
Cut a part of it about 25 cm longand make it a straight line.
Then fix the ends of this part with the positive and negative terminals of a PC power supply,yellow and black wire so you use +12v voltage.It would be better if you fix initially also a ampermeter in series to monitor the current,too much of it would burn the wire whether a very low current wouldn't make the wire hot enaugh to cut the polystyrene,that's why i told to use a piece of 25 cm about for me it worked.
I fixed the ends of the nicrome wire in a vertical colon,one of those used for the driiling machines,the lower side in the basement of the colon and the upper in the moving part which i keep under mechanical tension by lowering it a litle while fixing the nicrome wire and then releasing it.In this way the wire will be perfectly straight as it is pulled from both sides.
Power on and start cutting.
P.s. If the wire isn't hot enaugh or you want to cut a little bit faster just make the nicrom wire a little bit shorter.
regards
maXer
Added after 6 minutes:
whoops this was not what you wanted ...
anyway maybe somebody else needs it...
i did not understand very well what you wanted to do ...
Here are a couple of links to CNC foam cutters. May be that is what you are
looking for:
h**p://www.rcgroups.com/forums/showthread.php?t=3792637926
h**p://www.8linx.com/cnc/cnc.htm
use an old electric fire element {spring of resistance wire}
the wire they use is special formular dosnt burn in air so fast if it glows hot
so use a single strand 6" long has a resistance of about 1R per 12"{33cm}
and connect this to a 12v car battery or a good quality lead acid gel cell{for alarms}
or you can use a 1 - ~30v supply 3-4 amps youll need some form of adjustment
for current ,
i used in the past just the battery and limit the current on the cutter tool
with the rest of the left over element
i used a copper band to slide up and down
if you look around you can find resistance cable for old valve radio's
cant remember its name
but this wire has a built in resistance of 10R per 1' {foot} or so and was used as the 'mains dropper' to lower the ac to 150v or less for the radio to then use
to use as a leed to a tool made up to fit your jobs needs
{bits of wood with metal ends to protect from fire risk}
letter cutting and writing on poly is done using mainly a pulse laser diode
around 5 watts
however most carton stuff is premolded beeds
{done in the same factory as makers products from makers molds and beeds}
other than this a matrix of fine wires to cut it
is needed as a jig that gets made up for the job
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