Almost, it's a tricky one because of the font that Duolingo uses. :-)
If there was short "i" in the pronoun (jejich) and not long one (jejích; with the acute accent above í), your sentence would be correct.
"dotknout se něčeho"/"to touch something" uses genitive
Note it is the form that used to be originally dual, because here the arm is a body part and not a part of a machine or a crane.