Prediction of belt sag on a non-motorized curved treadmill

A non-motorized curved treadmill is completely self-powered equipment operated by human movement. As a walkway, the top surface of its belt has U-shaped concave sag that enables the belt to rotate freely through human footsteps. The concave sag on the upper belt is produced by also allowing the unnecessary sag on the lower belt, which is yet to be known. This study suggests a design method for the curved treadmill accompanied by a mathematical model that enables the prediction of the exact extent of the upper and lower belt sags according to design factors. The mathematical model is presented using the approximated parabola curve instead of the catenary curve, the belt tension, and the wheel friction. An experimental belt system is produced. The extent of the upper and lower belt sags is also measured to compare with the calculated values from algebraic expressions. The theoretical values match the actual measurements, which confirm the validity of the mathematical model. The results of this study will be useful in designing curved treadmills with various geometries.