I sent this to a friend whose father has parkinson's - a gov't agency bought him a tricycle bike a bit ago (they're in Belgium)...

He says his father can still ride a bicycle fine, but has trouble steering a bicycle - so this may not be a universal parkinson's phenomena. I'm not sure what stage parkinson's he is considered, last time I saw him he was still moving about, just slow to get started walking, etc.

His parents are looking into buying a tandem with a motor assist - his mother's convinced that the father is not peddling enough in the back to help them get up hills or against headwinds. (but since they're renting tandems, maybe the gearing just isn't ideal for her)