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 proposed in the research for a study and training process.
Highlights
The results in archery, like other sports of shooting, are strongly dependent on the quality of the sports weapon and its tuning
Scientific research of compound archery bow mechanics assuming symmetrical bending of upper and lower limbs was described by Park [8]
Considering a compound archery bow designed with a symmetrical twin cam and cable system a limb can be modelled with a solid shaft jointed to a handle using an Archimedean spring
Summary
The results in archery, like other sports of shooting, are strongly dependent on the quality of the sports weapon and its tuning. In comparison with other archery bows, the compound bow is able to store more energy and give higher accuracy in shooting. They are more resistant to temperature and humidity changes due to the incorporation of string limbs in their design. Scientific research of compound archery bow mechanics assuming symmetrical bending of upper and lower limbs was described by Park [8]. His basic mechanical and mathematical model of the compound bow needs to be developed. The aim of this research was to create a mechanical and mathematical model of a compound bow and analyse its work without of any prior hypothesis about the symmetry of limbs’ deflection
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