A Logical Function Method for Dynamic and Design Sensitivity Analysis of Mechanical Systems With Intermittent Motion

Abstract

Dynamic and design sensitivity analysis of mechanisms and machines with intermittent motion are accomplished through introduction of “logical functions” to approximate discontinuities and special features of system motion. The Heaviside step function and the delta and unit doublet distributions are introduced to represent discontinuities and to determine the values of certain functions of isolated times. These functions and distributions are approximated by smooth functions, and validity of the approximation is argued both mathematically and physically. A numerical method is then presented for analysis of the approximate problem. An elementary and a complex, realistic example are presented to illustrate applications of the method.