The work aims to analyze the relationship between the energy and the knotting state of the hand rope, in order to design an automatic hand rope knotting machine. The catenary theory was used to propose a two-dimensional mathematical model of hand rope based on the analysis of hand rope in the state of suspension, one turn winding and knotting. The arc length equation and the Euler-Lagrange equation of the variational method, etc. were used to analyze the potential energy of the hand rope in the catenary state. The bending energy and torsional energy of the rope segment used for knotting were analyzed by the Frenet equation of the plane curve, the bending energy equation and the tor-sional energy equation. A knotting test was carried out for the verification. The hand rope had the lowest potential energy in the state of the catenary. In the winding process, the closer the curved shape was to the regular circle, the less the twisting number of the hand rope itself, the smaller the energy of the rope. The state selection of the hand rope in the knotting process determines the energy of the rope. The smaller the energy, the more stable the rope will be, and the higher the knotting success rate.