This paper considers the relationship between the three-position function-generation problem and the solution space for planar four-bar mechanisms. The two infinities of solutions possible are mapped in a plane to determine the locations where particular types of mechanisms occur. It is possible to generate a contour in the mapping plane which joins together all solutions which possess a common characteristic in regard to their link lengths. This same contour can be displayed in the solution space to ascertain the overall characteristics of potential solutions to the design problem. A numerical example is used for illustrative purposes, but the results can be applied to any three-position function-generation problem.

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