One of the primary objectives of synthesis is the reduction of the number of controlling parameters facing the designer in the optimization phase of the design process while at the same time forcing the remaining parameters to generate solutions which are acceptable in some prescribed sense. In this paper, the four mass parameters m, k, u, v of any link moving in coplanar motion are used to meet specified torque (or energy) levels or specified shaking moment values for up to four positions of the system. The origin of these specifications for the synthesis procedure may be due to inertia in the rest of the system or due to a work function such as those generated by springs. The dimensions of the mechanism are considered to pre-exist or are due to an earlier motion synthesis stage of the design [5]. Springs may have been obtained by a synthesis procedure outlined in reference [6]. Finally, once the values of m, k, u, v for one link are met by means of procedures introduced here, they may then be used directly in shaking force criteria of Berkof and Lowen [2] to further balance the system or those in reference [3] for additional refinement. The total objective of this serial use of synthesis procedures is to minimize the number of independent design parameters while still retaining a set of solutions containing the global optimum in terms of some prescribed qualitative requirements. Some of these qualitative criteria were outlined in the very interesting and complete work [4] on characterization of the dynamic state of real machines by Artobolevskii and Loschchinin. The synthesis procedure is validated by a design example of a throwing mechanism. The object being thrown is specified in four finitely separated velocity states of an existing mechanism. The resulting dynamic response of the system meets these arbitrary specifications within an error of 0.05 percent.

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