Kineto-Elastic Analysis of a Compound Bow

This paper presents the kineto-elastic analysis 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. A large deformation cantilever beam model was created to determine the center trajectories of the cams. The principle of finite element method was applied to calculate the deformation of the limbs by combining small deflections of segmented cantilever beam elements. Another part of this work is the construction of a quasi-static model to simulate the draw process. The displacements of cams, cables and string were analyzed by gradually drawing the bow string. The required draw force as a function of draw length was obtained, and verified by experiments. The kineto-elastic analysis procedure described in this paper can be used later for the optimal design of the shapes of the cams and limbs. The modeling and simulation 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.