Abstract: A crank mechanism is provided which has a first driven member constituted by a first shaft, and a second driven member constituted by a sleeve member-disposed around said first shaft. The sleeve member is retained in support means such that the sleeve member and the first shaft can rotate relatively to one another. A rotating arm is connected to the sleeve member, and attachment means is slidable along said rotating arm. First linkage means is provided between said attachment means and said first shaft, and second linkage means is provided between said sleeve member and said first shaft, whereby said attachment means can selectively describe any of a range of circular or elliptical paths. In the preferred embodiment, the linkage means are adjustable and include a counter-rotating arm associated with said first shaft, and a second shaft and a third shaft and gears associated therewith and with said first shaft, which gears transmit rotational movement from said first shaft to said sleeve member.