In an important chemical apparatus, admission of three fluids had to be made in quantities required by the correct reaction cycle. For the control of the fluid admission valves, four-bar linkages were to be used. The dimensions of the linkages were determined from the reaction curves and the valve opening curves by means of a digital computer. It was found that, during the cycle, the links of the two driven linkages used came into a coincidence position each, in which their motions were indeterminate. They were made determinate by auxiliary pin tooth and mating gap mechanisms added to the respective links at the polodes in these coincidence positions. This required finding a new and simple kinematic-algebraic solution for determining the poles in the general case of a four-bar linkage in these coincidence positions. A new geometrical solution is added. An outline for the practical design is presented. In an Appendix, the formulas derived were tested by application to cases for which the poles are known or can be found easily.

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