Investigation and Comparison of Possible Boundary Conditions and System Vibration Modes in Two-Link Flexible Manipulators

In the slewing multi-link flexible robot systems, the natural frequencies and mode shapes have been determined using the assumed component mode method with clamped-joint condition, in which the system modes is reconstructed by the series of assumed modes of each link. This method, however, requires large number of assumed modes to accurately describe the system and even more, sometimes, the results are erroneous. The direct analytic solution of entire system vibration mode which is a comparative concept of assumed mode method can accurately account for the entire vibration with a few number of significant modes. This paper deals with system vibration modes of two-link flexible robot and their appropriate boundary conditions. There are four possible set of boundary conditions, that is, clamped-clamped, clamped-spring, spring-clamped, spring-spring, according to joint servo condition, and we compare mode shapes and modal frequencies of each case by numerical and experimental results. We also provide important characteristics of natural mode when imposed certain kind of boundary conditions.