Dynamic Stability Considerations in Elastic Closed Loop Linkage Systems

Abstract

In this work a theoretical method is developed to identify critical speeds for elastic linkage systems. Critical speeds are input operating speeds where the response of the system is larger when compared to neighboring noncritical speeds. A survey of the literature reveals that theoretical methods of determining the critical operating speeds with experimental verification have not been applied by researchers for linkage systems with large number of elastic degrees of freedom and with all links considered as elastic members. Research works that address this problem are usually limited to mechanisms with only one link treated as an elastic member. The method of determining critical speeds in this work is an efficient implementation of Floquet theory, and is applicable for mechanism systems with large numbers of elastic degrees of freedom and with all links considered as elastic members. Experimental verification for the results obtained using this approach is provided in Nagarajan and Turcic (1991).