The analytical formulation from a companion paper is extended to allow the concept of multiply separated positions to be applied to the spring-energy problem. A major change in perspective for mechanisms is accomplished by the ability to presume that the mechanism pre-exists. Heretofore it has always been necessary to deal with mechanisms on a positional basis where higher-order motion could not be considered without also including the location of the mechanism. The set of analytics applied to springs is not affected by ignoring positional information. Utilization of the mechanism-spring system in the proposed manner creates a dynamic tool for the enhancement of machine operations.

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