Synthesis of Multi-Variable Function-Generator Linkages Using Point Position Reduction

A graphical method based on point position reduction is presented for synthesis of multivariable function-generator linkages to satisfy a set of arbitrarily selected precision positions. The method is illustrated for 10-link, three-variable and 13-link, four-variable function-generator linkages. The maximum number of precision positions satisfied in these cases are, respectively, six and eight for linkages with rotary inputs and output, five and seven for linkages with sliding inputs and output. The number of positions satisfied can be increased by combining point position reduction with, for example, the theory of finitely separated positions. The method is also applicable for synthesis of multidegree-of-freedom linkages for point-path generation or rigid body guidance as a function of several independent inputs.