No grannie, if your right leg is the bad one (arthritic knee) use the stick in your left hand. When people walk, they swing the opposite arm forward to the leg that is swinging forward.
Like this
http://www.google.co.uk/imgres?imgurl=http:/
/www.worldofstock.com/slides/TAI1072.jpg&imgr
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so you want the stick in the hand that swings forward at the same time as your bad leg which will be your LEFT hand.