Collins Russian Dictionary 2nd Edition © HarperCollins Publishers 2000, 1997:
brink [brɪŋk] n (of disaster, war etc) грань f
on the brink of doing чуть не +infin
she was on the brink of tears она́ е́ле сде́рживала слёзы
* is used to mark translations which have irregular inflections. The Russian-English side of the dictionary gives inflectional information.
Русский: