I think this would be the safest option if you don't have a diagram or picture.

http://www.myetymology.com/italian/falcione.html

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cythe - Wikipedia, the free encyclopedia
- [ Μετάφραση αυτής της σελίδας ]
A scythe (pronounced /ˈsaɪð/) is an agricultural hand tool for mowing grass or reaping crops. It was largely replaced by horse-drawn and then tractor ...
Etymology - Structure - Use - History
en.wikipedia.org/wiki/Scythe - Προσωρινά αποθηκευμένη - Παρόμοιες
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War scythe - Wikipedia, the free encyclopedia
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A war scythe is a kind of improvised pole weapon, similar to a fauchard, usually created from standard scythes. The blade of the scythe is transformed so as ...
en.wikipedia.org/.../War_scythe

Literally

falcione s.m. (agri.) hay-cutter
[source La Biblioteca di Republica's l'Enciclopedia Dizionario di Italian-Inglese]

Alternatives

1. mower
2. scythe (not in this case) (hand operated)
3. sickle (hand held)

falciatura s.f.>7i> mowing, sickling, scything

In this machine, it sounds like they're talking about the mower blades. Since it's probably not just for hay, I suspect 'hay-cutte' is too literal. 'Mower blades' seems a reasonable comprimise.

Plus, falcione is literally the 'blade of a sword' or cutting device - not the whole instrument (i.e. handle, support, etc).

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Note added at 15 mins (2010-07-12 12:56:51 GMT)
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Since there's no reference to their shape - straight, round, arched, bent - I didn't add an adjective for their shape. I did't see any reference to their form in the word to be translated or the translation text.