Past work in mechanisms synthesis has been primarily position-dependent. Here, the problem of coordinating time and geometric states up to the fourth order simultaneously for several functions is accomplished with all classes of multiply separated specifications. The previous algebraic formulation for geometric Burmester theory based on a set of Amt coefficients is now transformed into a time-dependent Burmester theory by using an expanded set of tabulated coefficients Dmt. New problems of complex geometric coordination of three functions relative to some position parameter are now solvable, and it is shown that geometric synthesis is a special case of time synthesis. This generalized theory vastly increases the range of solvable problems for industrial application in terms of the 4-, 5-, and 6-bar mechanisms.

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