A restatement of the optimum synthesis of function generators with planar four-bar and slider-crank mechanisms examples

Abstract

The problem of optimum synthesising of a mechanism to best approximate a function, while simultaneously ensuring good motion transmission characteristics is discussed. Distinction is made between the design variables that determine the shape of the input-output (I/O) function of the mechanism, and the design variables that affect the degree of overlap between this I/O function and the function to be mechanised, through scaling, mirroring and rotations in 90o increments. Examples are given of designing the planar four-bar and slider-crank linkages of a logarithmic scale, and that of a tangent-function generator. These are performed on modified mechanisms with an added degree-of-freedom, which substantially simplify the synthesis problem.