基于能量分析的拎手绳打结研究

Knotting of Hand Rope Based on Energy Analysis

中文关键词: 悬链线理论  拎手绳建模  重力势能  弯曲能量  扭转能量

英文关键词: catenary theory  hand rope modeling  gravitational potential energy  bending energy  torsional energy

中文摘要:

      目的 为了设计拎手绳自动打结机而分析能量与拎手绳打结状态的关系。方法 分别以悬垂约束时，缠绕1圈后和成结时的拎手绳为分析对象，利用悬链线理论建立拎手绳的二维数学模型；通过弧长方程、变分法里的Euler-Lagrange方程等，分析拎手绳在悬链线状态下的势能；通过平面曲线的Frenet方程、弯曲能量方程及扭转能量方程等，对用于打结的绳段弯曲能量和扭转能量进行分析，并进行打结试验验证。结果 拎手绳在悬链线状态下势能最小；拎手绳在缠绕过程中，弯曲的形状越接近规则圆、拎手绳自身的扭转数越少，绳子的能量就越小。结论 打结过程中拎手绳的状态选择决定了绳子能量的大小，能量越小绳子就越趋于稳定，打结成功率越高。

英文摘要:

      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.