Function generation with planar four-bar mechanisms as a mixed problem of correlation of crank angles and dead center design

Abstract

Function generation synthesis of mechanisms can be considered as the design of correlation of crank angles and dead dead-center position design. These two problems have been clearly defined and solved separately. But some problems may require both correlation of crank angles and dead dead-center design at different configurations. Such problems are called mixed function generation problems. In this paper, an overview of these mixed function generation problems for the planar four-bar mechanism are given and the problems are solved analytically or semi-analytically. Except three of them, all presented mixed function generation problem formulations are novel. The solutions of all problems including three positions for the four-bar mechanism and the solution of a problem including four positions for a four-bar mechanism are addressed. All problems are first reduced to a univariate equation and a fast solution is found. Thus, link lengths can be found quickly by changing the problem definition problems, and several design iterations can be performed in a short time. Numerical solutions of all problems have been demonstrated using Excel.