On the completeness of kinematic chains of mobility unity

A complete kinematic chain is a chain in which every link of the chain makes contact at a joint with every other link of the chain. Simple closed-loop chains, semicomplete, and complete chains of mobility unity are investigated topologically to determine the limits within which it is possible for all these three kinds of chains to exist. A study is made mainly in terms of: (a) the number of links, <I>l</I>; (b) the number of joints, <I>j</I>; and (c) the degree of that link of the chain whose degree is greatest, Δ. Some brief remarks are made on the application of these ideas to the field of practical machine design.