Two short and direct methods of exact analysis of the spring-and-lever balancing mechanism are presented. It is shown that perfect balance can be achieved by the use of a close-coiled spring whose free length is effectively zero and whose stiffness is chosen appropriately. The two-degree-of-freedom balancing mechanism, commonly seen in desk lamps but useful in many other situations, is then analysed. The treatment is extended to allow for the weight of the components of the mechanism itself.
The originator of these devices was George Carwardine, whose patents over the period 1931–35 show the evolution of his ideas on this subject. A short biographical note is included as an appendix.
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