Compound archery bow asymmetry in the vertical plane

Abstract

The aim of the research was to create a mechanical and mathematical model of a compound bow and analyse its work without any prior hypothesis about the symmetry of limb deflection. The method of the research was based on the methods of theoretical mechanics, applied and computer mathematics. A pair and shift mechanism with cams and levels was used as a basis of the mechanical and mathematical model of a compound bow. The difference between results of modelling and measurement was near 7 %, while the error due to digital image deformation was evaluated to be near 1 % which was considered as acceptable. The calculated results indicated noticeable differences from simulations using the constraint of symmetrical limb deformation. Comparison of symmetrical and asymmetrical simulations with experimental data revealed that the asymmetrical simulation gave a closer match to the measured values for cam angles; the simulated and measured cam angle asymmetry was much greater than any measurement errors. Realisation of a process of solving the problem using computer mathematical system MathCAD makes it possible for specialists of physical education and sports (coaches and sport archers), who do not have a mathematical background, to use the mechanical and mathematical model that was p