Multi-modal Continuous Approximate Algebraic Input-Output Synthesis of Planar Four-Bar Function Generators

Abstract

This paper introduces a novel multi-modal function generator synthesis algorithm for planar four-bar mechanisms. Multi-modal in this sense means concurrently optimising multiple functions approximately generated between different joint parameters in a four-bar linkage over the desired continuous input-output ranges. Every planar four-bar function generator explicitly generates six functions uniquely determined by the relationships among the constant link parameters. We will instead investigate the simultaneous synthesis of two distinct functions between different joint variables. An example is described where two different functions in a planar RRRP linkage are generated over continuous ranges between the ground-fixed R-pair and the R-pair connected to the P-pair, as well as between the same ground-fixed R-pair and the P-pair. The multi-modal synthesis equation is the sum of the squared input-output equations integrated over the desired ranges. We compare the generated continuous approximate synthesis algorithm results and the multi-modal continuous synthesis results by comparing the areas between the synthesised planar algebraic curves in the parameter planes of the input and output joint variables to those of the desired input-output functions over their continuous ranges, thereby evaluating the structural error.