Modelling the twin-cam compound bow

In this thesis, the statics of the archery twin-cam compound bow is investigated with the help of mathematical models. The simplest case is the model of the round-wheel compound bow, which is then advanced with the Euler-Bernoulli (EB) beam model for the limb deformation. Further, a generalization of the round-wheel compound bow model is examined, and also the twin-cam compound bow with non-round cams is studied. The force-draw curves of the round-wheel and the twin-cam compound bows are measured and compared to the predictions of the respective models. The extended offset-eccentric model is tested with the help of the round-wheel model, and also by using the twin-cam bow model. The path of the limb tip of the compound bow is checked with both bows by measurements. The Young's modulus of the round-wheel bow limb is determined, and the effects of the shape of the limb on the force-draw curve are also considered. Furthermore, an approximation on the path of the tip of the straight limb with constant bending stiffness for small deformations is derived. In the twin-cam bow model, the non-round cams are modelled with the help of cubic splines. In all models of this thesis, the derived non-linear equations are simplified and solved numerically. The consistency and the validity of all the models were also checked in several ways. Two static quality coefficients for the compound bow are presented. A limit for the force-draw curve of the compound bow is concluded. As an example, the cams of the compound bow are virtually modified in order to improve the effectiveness of the bow. All the models presented in this thesis may be used for adjusting and designing twin-cam compound bows.