Can PC controller or gamepad support toribash
to connect them?

This would be no help at all to this game there is no point at all
not saying your idea is dumb or anything its just
I would maybe do it for like a challenge video or something
like that.

You'd be better of trying to coax someone into making a script for it, although you'd probably need something to sit between the controller & the game (eg joy2key, xpadder etc)

I can see this work somehow by using the left stick as a dial to switch between joints in a circular fashion. The buttons are for holding, relaxing, extending and contracting. Maybe then the triggers as left grab right grab, and the bumpers as hold all and relax all. Start will be the menu button obviously, and the right stick is used to look around. Not sure how to get the camera closer and further away.

It might work. But I doubt it'll be convenient.