I have a co-worker who's seems to hate me for some unknow reason.?

so you want to do the right things here i hope. then accept first off that the person does have some handicap. next the person is a person and a co worker. treat them as such. it is disrespectful not to treat them as you would others at the work place . except if the matter is in direct relation to the handicap like the swinging arm or bent spine.