Dynamics of Planar, Elastic, High-Speed Mechanisms Considering Three-Dimensional Offset Geometry: Analytical and Experimental Investigations

Abstract

Mechanisms in industrial applications in general operate as three-dimensional elastic systems, including planar mechanisms due to offsets between the planes of motion of links. This article investigates dynamic behaviors of planar mechanisms with offset geometry analytically and experimentally for dynamic stress and critical speed levels. Three-dimensional line element with irregular freedoms is used and generalized digital computer programs are prepared to perform kineto-elasto-static, dynamic stress, frequency, and critical speed analyses of three-dimensional mechanisms including the planar mechanisms with three-dimensional offsets. An experimental planar four-bar mechanism was tested for critical speed and elastodynamic stress levels with three levels of offsets. It has been determined that a mechanism experiences integer divisions of the integrated average of the three-dimensional fundamental natural frequency, ωinavg, within a cycle of the mechanism as critical speeds as well as its multiples. Recommended operating speeds of a mechanism are those in between two integer divisions of ωinavg at lower levels. Elastodynamic stress levels at these recommended speed levels are predicted analytically by kineto-elasto-static analysis and very conservatively even in the shock loading zones of the mechanism. The validity of the highly economical CGKES (Critical Geometry Kineto-Elasto-Statics) method for mechanisms having three-dimensional geometry is also verified by the experimental results.