Research On The Formation Principle Of Rope Knots And New Knotting Device

The knotting operation of flexible objects is filled in and closely linked with almost every aspect of people’s life,such as the knotting of a hand rope,shoelace and so on.Knotting devices are mostly used in medical,husbandry and other special fields,and there is still a urgent demand for automatic knotting device that can be used in daily life with market applications.In order to improve people’s life quality and satisfaction,the new knotting device is necessary to be studied.Taking shoelace knotting as an example,focusing on the scientific problem of the operation of rigid mechanism to flexible rope,this paper abstracts shoelace knotting as the operation of overhand knotting based on knot theory,carries out the research on the principle of shoelace knotting and the new knotting device.The main work and results of this paper are as follows:1.Propose the equivalent closed-loop knot model of rope knot and the method of overhand-knot tyingBased on the knot theory,the shoelace is transformed into the closed-loop knot model of rope,and the invariants of the rope belt equivalent knot are analyzed,such as twists number,writhing number and link number.Based on the actual knotting process and the basic transformation of Reidemeister,the forming mechanism that the rope belt forms the rope ring and the rope end moves to cross the rope ring is proposed.The bending energy and torsion energy of the rope ring are further studied,combined with the theoretical analysis of the method of the knot forming,an operable method of the overhand knotting method “the knotting method of rotating and crossing the axis ” is proposed,which can overcome the uncertainty of the flexible rope belt and obtain high-quality knotting.2.Overall design scheme and composition of the new knotting deviceCombining with the knotting method and the forming mechanism,a new knotting device is proposed and developed.A new knotting mechanism is built with the non-integral hollow gear disk driving rope belt rotation winding and arc facade cam supporting rope belt,while the movable arm gripper picks up and fixes the rope belt.The motion planning and timing sequence coordination are carried out for the rope picking clamping mechanism,the rotating crossing knot mechanism and the supporting platform mechanism,so as to realize the knot operation of the device on the rope belt.3.Proposing of the combination index of topology and geometry combining the number of intersection and extremum points and the division of knotting stageIn view of the description of the knot forming process of the rope and the control of the rope shape,a new index combining the number of intersection and extremum points is proposed based on the catenary theory.The knot-forming process of the rotations is divided into four stages.By extracting the key characteristic transients of the rope,the balance model of catenary force is used to solve and sketch the geometric spatial morphology of the characteristic transients of the rope belt.The qualitative and quantitative description of the forming process of the overhand-knot is realized.4.Simulation of overhand-knot forming process of rotating crossing knot mechanism based on IPS softwareIn view of the stability of knot forming,IPS Cable Simulation is used for the first time to simulate the movement of knot forming.By establishing the model of rotating crossing knot mechanism and the rope to analyze the bending energy of rope ring,the stability of rope ring and the feasibility and rationality of knotting method are verified.Through the simulation results of IPS,the low axial energy density of the formed rope loop can be obtained.Therefore,the optimized design of the rope belt support plate of the knotting mechanism is carried out,and finally the rope ring with high axial energy density is obtained to improve the knotting success rate.5.Forward and inverse kinematics analysis of the supporting arm of the rope belt pickup operationAiming at the realization of rope picking and fixing during the knotted movement,the D-H model of the rope picking mechanism is constructed and the solution of forward and inverse kinematics is carried out.The characteristic points of the posture transformation trajectory picked up and fixed by the mechanism arm against the rope belt are taken as the target posture points.By solving the joint variables,the mechanism arm can move according to the preset motion trajectory,and laying a foundation for the trajectory optimization and mechanism control of subsequent devices.