INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 18, No. 3, pp. 359-365 MARCH 2017 / 359 © KSPE and Springer 2017 Prediction of Belt Sag on a Non-Motorized Curved Treadmill Sayup Kim , Joonho Hyeong , Jongryun Roh , Ohung Kwon , and Youngho Kim 1 Human and Culture Convergence Technology R&D Group, Korea Institute of Industrial Technology, 143, Hanggaul-ro, Sangnok-gu, Ansan-si, Gyeonggi-do, 15588, South Korea 2 Department of Biomedical Engineering, Yonsei University, 1, Yeonsedae-gil, Heungeop-myeon, Wonju-si, Gangwon-do, 26493, South Korea # Corresponding Author / E-mail: younghokim@yonsei.ac.kr, TEL: +82-33-760-2492, Fax: +82-33-760-2852 KEYWORDS: Belt sag, Catenary, Conveyer belt, Curved treadmill, Non-motorized, Parabola 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. Manuscript received: April 11, 2016 / Revised: September 8, 2016 / Accepted: September 27, 2016 1. Introduction The excessive dietary habits and sedentary lifestyle of modern people have brought about various metabolic diseases, such as obesity, and have led to social issues. In response, many people engage in aerobic exercises to burn surplus calories and stay healthy. One of the most representative fitness equipment that helps with aerobic exercises, such as walking or running, is the ‘treadmill.’ A treadmill is provided with a conveyor belt rotated by an electric motor to enable the users to walk or run according to the rotating speed of the belt, which they have set. Traditional electric-powered treadmills require users to control buttons to adjust their moving pace, which is quite inconvenient and sometimes unsafe, especially when having to manipulate the button while running NOMENCLATURE D = wheel diameter (mm) S = belt's total length (mm) S = upper belt length (mm) S = lower belt length (mm) S = belt length of the wind section on the wheel (mm) L = distance between wheels (mm) L = maximal distance between wheels (mm) L = upper catenary belt span (mm) L = lower catenary belt span (mm) H = upper belt sag (mm) H = lower belt sag (mm) h = upper belt sag within the catenary section (mm) h = lower belt sag within the catenary section (mm) θ = wheel tangent angle of the upper belt (°) θ = wheel tangent angle of the lower belt (°) T = upper belt tension (kgf) T = lower belt tension (kgf) T = horizontal component of the upper belt tension (kgf) T= horizontal component of the lower belt tension (kgf) w = weight of belt per unit length (kgf/mm) μ = friction coefficient of wheel rotation REGULAR PAPER DOI: 10.1007/s12541-017-0043-2 ISSN 2234-7593 (Print) / 2005-4602 (Online)