Kineto-elastic modeling and optimization of compound bows

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Most improvements and re-designs of compound bows apparently use or partly apply empirical methods to determine bow performance characteristics. A kineto-elastic analysis procedure of a compound bow which in each side of the limbs has two stacked eccentric cams connected by two inextensible cables and one inextensible string is presented in this thesis. With the principle of finite element method, a large deformation cantilever beam model was created by combining small deflections of segmented cantilever beam elements to determine the trajectories of limbs, end points where the cams are installed. A quasi-static model was constructed to simulate the draw process. The displacements of cams, cables and string were analyzed and the required draw force as a function of draw length was obtained by gradually drawing the bow string. A commercial finite element analysis software was employed to verify the precision of the elastic limb model. The other arbitrary cam system was simulated by the revised kineto-elastic model. Three cases of optimal cam profile designs were studied by this integral model. Several design variables were discussed in the optimization to accomplish three different objectives, which are interesting to archers. The modeling, simulation and optimization procedure used for combining elastic components, flexible but inextensible string-cable components, and rigid component in a precision dynamic model of a mechanical system can also be applied to archery bows with more complex configuration, and to other similar mechanical systems.