Research on hand rope knot based on energy theory
                      ZHANG Dongdong1, DONG Yijia1, HUANG Songtan2,LV Junjie3, YANG Huijie3, YING Fuqiang2

（1.Department of Mechanical Engineering, Zhejang Institute of Mechanical and electrical Engineering,Hangzhou 310053, China; 2.College of Mechanical Engineering, Zhejiang University of Technology,Hangzhou 310014, China; 3.Equipment Engineering Company, China United Engineering Corporation Limited, Hangzhou 310052, China）

Abstract: Aiming at the problem of high labor intensity and low efficiency of human knotting, and the problem of low knotting rate of current mechanical knotting, the minimum energy state of hand rope during knotting was studied, the research object was proposed combined the differential theory for hand rope to be tied under the suspended condition, winding rope（170°～400°）and move into knot, a mathematical model of hand rope was established. Through the arc length formula and the variational method, the minimum potential energy of hand rope at the catenary state was disproved. Through the plane curve theory, the theory of the bending and torsional energy, the bending energy and torsional energy of knotted rope segments was analyzed, results were obtained that more circular the rope used for knotting was, the less bending energy would occur, and the less twisting number of the rope itself, the less torsional energy would occur, the hand rope would be more stable. Through the above energy analysis, the method of rotating around a shaft to carried out the knot test was determined, and the robustness test was done. The results indicate that the successful rate of hand rope diameter between 2.8 mm to 5.3 mm is above 90%.

Key words: hand rope mathematical model; bending energy; torsional energy; knotting test