Hwang K-H., Kim Y-S., Choi D-C. Choi M-I.: DYNAMIC MODELLIN FOR THE SECOND… Vol. 12 Issue 2: 163 - 171 Science of Gymnastics Journal 163 Science of Gymnastics Journal DYNAMIC MODELLING FOR THE SECOND FLIGHT PHASE OF THE YURCHENKO LAYOUT VAULT BASED ON MSC. ADAMS Kum-Hyok Hwang1, Yong-Song Kim1, Dong-Chol Choi1, Mun-Il Choi2 1Faculty of Mechanics, Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea 2Korea Sports CollegePyongyang, Democratic People’s Republic of Korea Original article Abstract Gymnasts attempt to increase the angles of rotation about transversal and longitudinal axes during the post-flight of vaulting, and these angles are related to different mechanical properties. The present study uses a 3D angle-driven computer simulation model of a gymnast who performs Yurchenko layout vault using ADAMS software. Simulation initial conditions are horizontal and vertical velocities of gymnast’s pelvis center and angular velocities about the transversal and longitudinal axes which can be easily measured. The initial linear and angular velocity conditions of the simulation model are each changed in certain increments from measurement data collected from an elite woman gymnast. Increasing initial horizontal velocity results in an increased horizontal flight distance, but has no connection with the duration of flight and angle of twists. The overall angle of twists is concerned with initial vertical velocity and angular velocities about the transversal and longitudinal axes. Also, increasing initial vertical velocity and angular velocity about transverse axis leads to increase in touchdown angle between ground’s horizontal axis and gymnast’s longitudinal axis. Keywords: vault, aerial movement, multibody dynamics, ADAMS. INTRODUCTION Gymnasts get marks which consist of difficulty and performance values of their vaulting in artistic gymnastics. The vault difficulty values are already defined at FIG Code of Points. These difficulty values depend on body configuration and rotation angles about transversal and longitudinal body axes in gymnast’s flight performance (Atiković, 2011). The rotations around the transversal and longitudinal body axes are mainly performed in the second flight phase and the gymnasts change body configuration purposely for rotation in this phase. The second flight of gymnast is related to various mechanical initial conditions at take-off from table and gymnast’s body configuration during flight. The elements of successful vaults are vertical velocity at takeoff from the table, angular momentum about the mass center, and moment of inertia about the mass center (Čuk & Karacsony,2004; Prassas, 2002; Takei, 1998). To simulate human movement, a human body can be divided by several rigid segments which are connected with various joints (Yeadon & King, 2008). Huang (1998) Hwang K-H., Kim Y-S., Choi D-C. Choi M-I.: DYNAMIC MODELLIN FOR THE SECOND… Vol. 12 Issue 2: 163 - 171 Science of Gymnastics Journal 164 Science of Gymnastics Journal presented a three dimensional human body model to simulate human response within rear-end impact vehicle. This model consisted of 15 rigid bodies which were connected with spherical and revolute joints. King and Yeadon (2015) presented various simulation models of different sports movements with their detailed information. Angle-driven models were simpler to control human body configuration than torque-driven models, so these models were used to simulate complex movements having many degree of freedoms (DOFs). Yurchenko layout vaults include rotations about transversal and longitudinal axes in the second flight phase. Koh (2003a, 2003b) studied optimized performance at table contact phase by using a five segment model of a gymnast in order to obtain maximum flight height and good performance vault. This five segment model was driven by joint angles and angular velocities. Rotations about longitudinal axis can be produced during contact phase at table and during the flight phase by means of asymmetric movements of arm and hip. To simulate this kind of aerial movements, an angle-driven model that comprised four leg segments, four arm segments and three body segments was used (Yeadon 1990, 1993c, 1999). The study of human movements needs to find joint angles from video data applying inverse kinematics theory. The measured global Cartesian coordinates should be transferred to generalized coordinates including all joint angles by the methods of inverse kinematics. Yeadon and Hiley (2003) collected the global position of the joint centers from two synchronized video data and determined joint angle histories using the Direct Linear Transformation method. Reinbolt (2011) presented an inverse kinematics method to minimize weighted square error between experimental and simulated global positions of markers. Also, Koh and Jennings (2003) used an optimization procedure to solve the inverse dynamics problem for Yurchenko layout vault. This objective function was composed of differences between computed and measured segment angles and between computed and measured center of mass (CM) positions of a gymnast. MSC. ADAMS is a widely used software based on multibody dynamics, and it can help to simulate kinematics, statics and dynamics problems with its convenient interface. It has the capability to import various types of geometry files such as SolidWorks, IGES and Parasolid files. Once a simulation model is given by users, it builds a dynamic equation of the model automatically, and so users can simulate easily by inputting only simulation duration and interval. Liu and et al (2013) analyzed inverse and forward dynamic problems of bicycle riding human model using LifeMOD and ADAMS software, and presented the effect of bicycle suspension systems to human body. The purpose of this study is to build a 3D angle-driven simulation model using ADAMS software and simulate the second flight movement of Yurchenko layout vault in various initial conditions. This model has an exclusive user interface to change initial conditions and joint angle trajectories for gymnasts and coaches. METHODS A computer simulation model has been built for an elite woman gymnast who performed Yurchenko layout vault using SolidWorks and ADAMS software. This model was driven by joint angle trajectories which were obtained from video data of gymnast’s movement. To verify this model, the measured CM positions were compared with computed CM positions presented by simulation under measured initial conditions. Then, the model was repeatedly simulated to find how each of initial conditions influences the angle of twists and somersaults. A 15 segment simulation model was built comprising head, torso, pelvis, hands, foot and the upper and lower arm and leg Hwang K-H., Kim Y-S., Choi D-C. Choi M-I.: DYNAMIC MODELLIN FOR THE SECOND… Vol. 12 Issue 2: 163 - 171 Science of Gymnastics Journal 165 Science of Gymnastics Journal segments. During aerial flight phase, twist can be generated by asymmetric arm of hip movement, so the upper and lower arms and hands are each considered as a different segment, and the upper and lower legs and foot are also different segments (Yeadon, 1993c). Each segment was built from measured geometric properties of the gymnast and combined into a whole body geometric model using SolidWorks software. Then, this whole body model was imported to ADAMS, and inertia properties of the model were calculated automatically by density of segments (Winter, 2005). The bodies (parts of ADAMS model) should be connected with suitable joints. Generally, the multibody model of human body is considered as tree-type system whose root is the pelvis and each body connects its parent bodies with a joint. Table 1 shows the joints of model and their DOFs. As the pelvis body has 6 DOFs, this model has 36 DOFs. Table 1 Type of joint used for the model Position Adjoining bodies Type of Joint DOF Spine Pelvis- Torso Spherical 3 Neck Torso- Head Spherical 3 Shoulder(L, R) Torso- Upper Arm Spherical 3 Elbow(L, R) Upper Arm- Lower Arm Revolute 1 Wrist(L, R) Lower Arm- Hand Spherical 3 Pelvis(L, R) Pelvis- Upper Leg Spherical 3 Knee(L, R) Upper leg- Lower leg Revolute 1 Ankle(L, R) Lower leg-Feet Revolute 1 Generally, angles of joints are determined from global positions of markers which are attached to the body (Delbridge, 2015). These markers disturb aerial movement of gymnasts, so they cannot complete their vault to the best of their own physical abilities. Therefore, the movement was recorded using two video cameras (1920×1080 pixels, 400Hz), and global positions of joint points were determined by analyzing video data (Fig 1). As the revolute joint has only one rotational DOF, the angles of elbows and knees can be easily determined. But the spherical joint has three rotational DOFs and the angle coordinates of spherical joints are Cardan angles in ADAMS software. To determine Cardan angles of joints, nonlinear least square method in which Eq. (1) is a minimized objective function was used (Reinbolt, 2011).           ni iiiq qxxw ,,1 2expmin  (1) where iw are weighted coefficients, exp ix are measured global coordinates of joint points, q are Cardan angles of spherical joints and calculated global coordinates of joint points  qxi are functions of q . These Cardan angles of joints are considered as nonstationary kinematical constraints using AKISPL function of ADAMS software. Figure 1. Locations of Cameras Neglecting friction and resistance forces in the air, the external force acting on gymnast is only gravity, so the trajectory of mass center is closely approximated to a parabola. This parabolic movement is related to initial horizontal and vertical Hwang K-H., Kim Y-S., Choi D-C. Choi M-I.: DYNAMIC MODELLIN FOR THE SECOND… Vol. 12 Issue 2: 163 - 171 Science of Gymnastics Journal 166 Science of Gymnastics Journal velocities (Takei, 1998). And the rotations around the transversal and longitudinal body axes are related to initial angular velocities (Čuk & Karacsony,2004; Prassas, 2002). The CM position of human body governed by CM positions of body segments cannot be directly measured. So, instead of CM velocity of whole human body, the CM velocity of pelvis segment is used as initial linear velocity conditions. And the angular velocities around the transversal and longitudinal body axes at take-off from table are also initial conditions. For the convenience of users, the customized simulation dialog box was built using the ADAMS Dialog-Box Builder (Fig 2). Users can change initial conditions, trajectories of angle joints and simulation settings in this dialog box. A trajectory of angle joint was defined as a spline curve, so users can change configurations of body in the air by changing it. Also, this dialog box has animation controls and a graph display button to display simulation results such as the total rotation angle of twists, CM position and velocity trajectories of whole body using ADAMS View command language. Figure 2. Customized Simulation Dialog Box. Computer simulation result of the Yurchenko layout vault is shown in Fig. 3. The gymnast performed Yurchenko stretched with 2/1 turns. At the take-off from table, the horizontal velocity of gymnast’s pelvis center is 3.0m/s and vertical velocity is 4.3m/s. The angular velocities around longitudinal and transversal axes are respectively 525°/s and 250°/s. Figure 3. Computer graphics result of the model used in evaluation. The flight durations of video and simulation are 1.0575s and 1.068s, respectively. The difference of flight duration is 10.5ms and its relative error is about 1%. Fig. 4 shows a comparison between CM position trajectories obtained from simulation result and video. The marker ‘o’s are CM positions which were calculated from video sequences. It can be seen from Fig. 4 that the simulation result closely matches the video result and its relative error is 8.6%. This error may partly occur in measuring marker positions of body segment to calculate whole body CM position from video sequences, and also partly in inertial parameters of body segments which were determined by their densities. Figure 4. CM trajectories from simulation and video. Hwang K-H., Kim Y-S., Choi D-C. Choi M-I.: DYNAMIC MODELLIN FOR THE SECOND… Vol. 12 Issue 2: 163 - 171 Science of Gymnastics Journal 167 Science of Gymnastics Journal maxX and height maxY , touchdown twist angle about longitudinal axis of body T and touchdown somersault angle between horizontal axis of ground and longitudinal axis of body at flight end time end . To compare simulation results in various initial conditions, simulations are terminated when the distance from CM position of pelvis to ground is 0.9 meter. In this simulation model, the orientation angles of the human body can be determined by measuring the CM marker’s orientation of the torso segment. Fig. 5 shows the trajectory of the body’s somersault, tilt and twist angles when initial velocity conditions are sssmVsmV xzyx /250,/525,/3.4,/3 000   RESULTS The simulation results are flight duration endT , maximal flight distance Figure 5. The trajectory of the body’s orientation angles during simulation when initial conditions are sssmVsmV xzyx /250,/525,/3.4,/3 000   . Table 2 shows simulation results when initial horizontal velocity 0xV varies from 2.6m/s to 3.2m/s with an increment of 0.2m/s. Increasing initial horizontal velocity results in an increased maximal flight distance maxX , but has no connection with endT , maxY , T and end . Table 2 Simulation results with the variation of 0xV sssmV xzy /250,/525,/3.4 000   0xV endT maxX maxY T end 2.6 1.068 2.087 2.906 740.7 60.09 2.8 1.067 2.299 2.906 740.2 60.09 3 1.068 2.514 2.906 740.7 60.09 3.2 1.068 2.727 2.906 740.9 60.15 The flight duration of a particle is related with its vertical velocity in parabolic movement. Simulation results show the initial vertical velocity of pelvis segment 0yV effects on every five resultant variables (Table 3). Table 3 Hwang K-H., Kim Y-S., Choi D-C. Choi M-I.: DYNAMIC MODELLIN FOR THE SECOND… Vol. 12 Issue 2: 163 - 171 Science of Gymnastics Journal 168 Science of Gymnastics Journal Simulation results with the variation of 0yV . sssmV xzx /250,/525,/3 000   0yV endT maxX maxY T end 3.9 1.007 2.398 2.7485 698.3 30.36 4 1.022 2.431 2.7842 704.4 38.03 4.1 1.037 2.461 2.822 713.3 45.5 4.2 1.052 2.488 2.863 725.3 52.68 4.3 1.068 2.514 2.906 740.7 60.09 4.4 1.084 2.542 2.9525 756.4 66.93 4.5 1.101 2.569 2.9995 769.5 74.24 4.6 1.12 2.603 3.0473 782.2 82.68 4.7 1.135 2.628 3.096 796.2 92.29 The simulation results, as changing the other two initial angular velocity conditions, are shown in Table 4 and 5, respectively. If the initial angular velocity about transversal axis 0z increases, the flight duration endT , maximal flight distance maxX and maximal flight height maxY are decreased., but the twist angle T and touchdown angle end are increased. Also, the total rotation angle T is related with initial angular velocity about longitudinal axis 0x . Table 4 Simulation results with the variation of 0z . ssmVsmV xyx /250,/3.4,/3 000   0z endT maxX maxY T end 450 1.087 2.758 2.937 692.6 -20.22 475 1.08 2.683 2.923 704.2 0.63 500 1.073 2.6 2.912 714.8 34.24 525 1.068 2.514 2.906 740.7 60.09 550 1.07 2.442 2.9053 753.3 82.54 575 1.058 2.318 2.9059 774.1 109.1 600 1.059 2.212 2.907 803 142.7 Table 5 Simulation results with the variation of 0x . ssmVsmV zyx /525,/3.4,/3 000   0x endT maxX maxY T end 200 1.066 2.489 2.9079 691.7 63.03 225 1.067 2.505 2.9076 712.5 58.98 250 1.068 2.514 2.906 740.7 60.09 275 1.067 2.517 2.9057 756.4 58.62 300 1.068 2.525 2.9059 756.2 52.92 325 1.068 2.527 2.9065 761.7 51.01 From simulation results for various initial conditions, the cross correlation coefficients between initial conditions and flight results are obtained (Table 6). If the variation of flight result, when changing an initial condition was very small, this correlation coefficient was neglected (marker ‘- ‘s). Hwang K-H., Kim Y-S., Choi D-C. Choi M-I.: DYNAMIC MODELLIN FOR THE SECOND… Vol. 12 Issue 2: 163 - 171 Science of Gymnastics Journal 169 Science of Gymnastics Journal Table 6 The cross correlation coefficients between initial conditions and flight results. endT maxX maxY T end 0xV - 1.000 - - - 0yV 1.000 1.000 0.999 0.995 0.999 0x -0.961 -0.996 -0.838 0.937 0.999 0z - 0.958 - 0.937 -0.936 DISCUSSION The aim of the present study was to build a simulation model of the gymnast who performed Yurchenko layout vault by using ADAMS software and to study relations between initial conditions and flight results in the second flight phase. The customized dialog box was designed for gymnasts and coaches to use the simulation model easily and conveniently. Initial conditions of second flight are related to linear and angular velocities at vault table touchdown and their changes in contact with the table. Among these initial conditions, the linear velocities and angular velocity about transversal axis are concerned with the first flight phase, while the angular velocity about longitudinal axis is related with body configuration during table contact phase (Yeadon 1993a, b). The results show that the initial horizontal velocity does not affect a gymnast’s vaulting performance, but it is related to maximal flight distance in second flight phase. When the gymnast lands on mat, the landing position should be at appropriate distance from the vault table to avoid accidents, so this horizontal velocity condition cannot be reduced to zero. The one of important flight results is the rotation angle about longitudinal axis of body which is associated with initial vertical velocity and angular velocities (Table 6). Consequently, the flight duration gets increased by an average of 16 ms and the twist angle about longitudinal axis by an average of 12°, as the initial vertical velocity gets increased by 0.1m/s. And the twist angle gets almost increased by 28°, when both initial angular velocities about transversal and longitudinal axes are increased by 50°/s. Simulation results also shows that the flight duration was decreased with increase of initial angular velocity about transversal axis. Generally, the flight duration is related with the initial vertical velocity of a body’s CM. The linear initial velocities used in this paper are horizontal and vertical velocities of gymnast’s pelvis CM, not those of the whole human body’s CM. The vertical velocity of the whole human body’s CM can be determined by pelvis CM velocities and angular velocity about transversal axis, hence the flight duration may be related with this initial angular velocity. The landing on mat is a final phase of vault and the suitable touchdown angle is important for successful landing. The touchdown angle is increased with increase of initial vertical velocity and angular velocity about transversal axis of gymnast, but when the angular velocity about longitudinal axis increases, this angle is decreased slightly. CONCLUSION From these results, it can be seen that the important technique on vault table is to change the linear horizontal momentum of the first flight phase to the linear vertical momentum of the second flight. Hwang K-H., Kim Y-S., Choi D-C. Choi M-I.: DYNAMIC MODELLIN FOR THE SECOND… Vol. 12 Issue 2: 163 - 171 Science of Gymnastics Journal 170 Science of Gymnastics Journal Through the simulation model in this paper, the twist somersaulting flight result can be shown by intuition, as the initial conditions and flight body configurations are changed by users. 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Choi M-I.: DYNAMIC MODELLIN FOR THE SECOND… Vol. 12 Issue 2: 163 - 171 Science of Gymnastics Journal 171 Science of Gymnastics Journal Yeadon, M.R. & Kerwin, D.G (1999). Contributions of twisting techniques used in backward somersaults with one twist. Journal of Applied Biomechanics, 15, 152-165. Corresponding author: Kum-Hyok Hwang Faculty of Mechanics Kim Il Sung University Pyongyang, Democratic People’s Republic of Korea Email: mech2@ryongnamsan.edu.kp Hwang K-H., Kim Y-S., Choi D-C. Choi M-I.: DYNAMIC MODELLIN FOR THE SECOND… Vol. 12 Issue 2: 163 - 171 Science of Gymnastics Journal 172 Science of Gymnastics Journal