Study Of The Multi-rigid Body Modeling For Vertical Take-off Action On Trampoline

Trampoline gymnastics is an exercise that a trampolinist performs a series of difficult yet beautiful movements on the elastic trampoline bed.The beauty of a trampoline performance is highly dependent on the vertical bouncing,which is the key factor in trampoline gymnastics and directly determines the scoring of this gymnastics.The purpose of this dissertation is to study how a trampolinist gets the optimum kicking force and achieves the optimum hight utilizing the elastic property of the bed during the landing-bouncing process.In this work,we tested and analyzed the mechanical property of the trampoline bed and the kinematics of the vertical bouncing of athletes;we also created the finite element model of trampoline bed and multi-rigid body dynamical models(i.e.,two-rigid body model and seven-rigid body model)for an athlete.The main contents are as follows:(1)We measured and analyzed the mechanical property of the standard trampoline bed.First,the static load-displacement curves and the corresponding vertical stiffness at various bed locations were obtained and the stiffness distribution function of quarter bed was fitted.Second,the equivalent elastic modulus was obtained by inverse analysis method of FEM simulation(ABAQUS).The results showed that the vertical stiffness decreased from edges to the center.The displacements and stresses were decreased from the action point of bed to the edges;the greater values were obtained in the diagonals,and stress concentration occurred in the edges of the bed.According to the equivalent elastic modulus,the calculated load-displacement curves by FEM were well fitted with the experimental data.The results could not only provide the mechanical parameters for dynamical analysis for trampoline but also the theoretical basis for improving the techniques of athletes.(2)The kinematic parameters of the vertical bouncing of a national level athlete were measured using two-dimensional measurement techniques(HD cameras)and three-dimensional motion capturing system(Vicon 2.1),respectively.The displacement,velocity and acceleration of the centroid of different part of the athlete,during the touching period,were collected.The duration time of touching process costed 0.15 s and the deepest of the bed was 0.85 m obtained by HD cameras(falling height was 4.03 m),while the corresponding data collected by Vicon 2.1(falling height was 4.12 m)were 0.17 s and 0.86 m.The data obtained by the two different methods were almost same considering the different falling heights.(3)A two-rigid body kinematic model was created to analyze and solve the control force of the athlete when he got the deepest kicking displacement.The model was divided into upper-part and down-part by the knee of the athlete,and we defined the control force was the muscle force between the two parts.In modeling,there was an assumption that the control forces were simplified into two step loads.The dynamic equations were established and solved.The numerical analysis results showed that when the falling height was 4.0 m,the deepest kicking length and the optimum duration time of the athlete were 92.65 m and was 0.14 s,respectively;and the optimum control forces for the first and the second stages were 1.3 kN and 3.4 kN,respectively.The validity of the two-rigid body model was verified by comparing the simulation results with the experimental results.This modeling of two-rigid body could theoretically guide the vertical bouncing of the athlete and offer an analyzing idea for the further accurate model.(4)We established a seven-rigid body model(dividing the body of the athlete into seven parts,i.e.,head,torso,thigh,leg,foot,arm,and forearm)to analyze the vertical bouncing and derive the corresponding motion differential equations.Substituting the corresponding kinematic data of each part of human body collected by Vicon 2.1 system in section(2)into above differential equations,we obtained the relationship between the athlete's kicking force and the touching depth.This calculation well fitted to the elastic reaction force practically measured according to the mechanical characteristics of the bed,which verified the validity of the model in one aspect.This model could be treated as an analysis basis for the technique of vertical bouncing in trampoline and provide a valuable reference for guiding the training and competion.In addition,we also analyzed the sensibility how the accuracy of the model was affected by the mass variation of rigid body.