A general method is presented for synthesizing plane, linked mechanisms obtainable from a single, closed kinematic chain. Using complex numbers and the matrix theory of linear systems, these methods have been applied to 4-link mechanisms for generating a path through up to five arbitrary points with prescribed corresponding crank rotations. The five-point synthesis is programmed for automatic computation on the IBM 650 digital computer, which determines all existing solutions (a maximum of 12 linkages), selects one on the basis of a quality index, and completes the generated path.

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