11.9  Spring balancing

An arm that stays where it is put has a potential energy that does not change with its position. Counterweights do this exactly and add mass; springs do it without the mass, exactly for a zero-free-length spring (the Anglepoise lamp, George Carwardine 1932) and approximately for a real one. The gas spring of a car tailgate, its force curve and its mounting points, chosen so the moment of the spring follows the moment of the weight; the torsion springs of a garage door. Energy as the design method: make \(U_\text{gravity} + U_\text{spring}\) flat. Example: a printed lamp arm with a zero-free-length spring made from a cord over a pulley.