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

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.