MAEC Web of Conferences, 0 5 04 ( 05 DOI: 0.05/ matec conf / 0 5 0 5 04 C Owned by the authors, ublished by EDP Sciences, 05 Biomechanical Analysis of Contemorary hrowing echnique heory Jian Chen Deartment of Physical Education, Ocean Uniersity of China, Qingdao, Shandong, China ABSRAC: Based on the moement rocess of throwing and in order to further imroe the throwing technique of our country, this aer will first illustrate the main influence factors which will affect the shot distance ia the mutual combination of moement equation and geometrical analysis. And then, it will gie the equation of the acting force that the throwing athletes hae to bear during throwing moement; and will reach the seed relationshi between each arthrosis during throwing and batting based on the kinetic analysis of the throwing athletes arms while throwing. his aer will obtain the momentum relationshi of the athletes each arthrosis by means of rotational inertia analysis; and then establish a restricted article dynamics equation from the Lagrange equation. he obtained result shows that the momentum of throwing deends on the momentum of the athletes wrist joints while batting. Keywords: analysis of throwing technique; mechanical analysis; biodynamic analysis; rotational inertia and tensor INRODUCION As the times rogress, the technologies of track & field and throwing sorts hae been gradually imroed and obtained great breakthrough. he current world records hae exceeded the reious ones by a great extent. During the deeloment of throwing in China, the achieement had neer been good before the founding of New China. With the founding of New China, our nation has been liberated and our strength in each sort has achieed remarkably imroement. After the establishment of the reform and oening-u olicy, China s comrehensie national strength has been in continuous rise and our status in sorts field is becoming increasingly higher. Our enhanced learning and mastering of sort techniques hae laid a solid foundation for the lea in our throwing field. In order to further imroe our techniques in throwing, this aer will analyze the influence that shot seed and shot angle hae on throwing erformance according to the moement rocess of throwing. It will also offer the study and analysis of the imact that human biomechanics has on the shot seed and angle of release, so as to roide better corresonding exercise for the athletes and hel them imroe their erformance. ESABLISHMEN AND SOLVING OF MODEL. Princile of hrowing he moement rocess of throwing can be diided into two arts: after the shot and before the shot. Before the shot, the thrown object gets initial elocity from the athlete s own moement. After the shot, the thrown object moes in arabolic motion that only bears graity effect. he final result is related to the shot seed, the angle of release and the shot height of the weight throw. herefore, if a throwing athlete wants to get ideal erformance, he/she must find the best shot height and angle of release. he distance between the shot sot and the landing sot of the thrown object is comosed of two arts: distance before the shot and distance after the shot. he factors influencing these two arts are shown in Figure below. he thrown weight throw only does arabolic motion after the shot due to graity effect. he equation is as follows: x0x t 0cos t y 0y t gt 0sin t gt he equation of t can be soled by y and can be brought into the equation aboe to obtain the following calculating equation of throwing distance: sin cos 0 cos ( 0 sin x g gh 0 It can be seen from the calculating equation of throwing result that the angle of release, shot height and final shot seed can leae great influence on the throwing distance among which the final shot seed is the first influencing factor.. Analysis of the Final Shot Seed his aer will first analyze the influence that the final shot seed has on the final result with the condition that both the angle of release and shot height are fixed. his is an Oen Access article distributed under the terms of the Creatie Commons Attribution License 4.0, which ermits unrestricted use, distribution, and reroduction in any medium, roided the original work is roerly cited. Article aailable at htt://www.matec-conferences.org or htt://dx.doi.org/0.05/matecconf/050504
MAEC Web of Conferences Figure. Analysis of the Influence Factors of Distance able. he Influence that the Final Shot Seed Has on the Result Seed( m s 4 0 3 4 5 6 7 8 9 30 Result( m 5.45 4.57 50.83 55.46 60.03 65. 70.4 8.3 87.88 93.4 97.5 able. he Influence that Different Angles of Release Hae on the Distance Angle 30 35 38 40 43 45 48 50 55 58 60 Distance(m 66.9 7.98 74.05 75.00 75.78 75.86 78.63 74.89 70.68 68.3 65.4 Fixed arameters: the angle of release is 43and the shot height is.6m. See able for the results. It can be seen from the table aboe that the final shot seed has obious influence on the throwing results. When the seed is 4m/s, the throwing distance is about 5m. Howeer, when the final shot seed of an ordinary athlete is within 6~30m/s, the throwing distance can be 70m if the shot seed can reach 6m/s. When the final shot seed is 7m/s or 8m/s, the throwing distance can be 80m or een 90m. As a result, the imroement of the final shot seed can lead to the imroement in the athletes final throwing erformance. When there s little air friction, the moement of the thrown weight throw can be regarded as standard oblique rojectile motion. Set the seed and the initial sot as constant alues, different angles of release can make large differences in the athletes throwing results. See the arabolic aths formed by different angles of release in Figure. It can be seen from Figure that the angle of release can only lead to the best distance within a certain range. When there s no influence from air friction, the arabola san can reach its maximum alue if the angle of release is 45. ake weight throw as an examle; and see the relationshi between the angle of release and the distance in able..3 Analysis of the Angle of Release and the Shot Height Figure. he relation between angle of release and distance In the hysical situation, besides the graity effect, the weight throw will also be affected by the resistance formed in air streaming. For simlification, regard the weight throw as a material oint. In accordance with Newton s laws of motion, the motion mode of the weight throw is shown in Figure 3. 0504-.
ICEA 05 Figure 3. he Schematic Diagram of the Weight hrow Moement in the Air In the figure, S refers to the radius ector while R refers to the air friction. herefore, the weight throw moement can be exressed by the differential equation shown as follows: d s m G R According to hydromechanics, we also know that wake flow will aear when the weight throw flies in the air, and it will form streaming resistance to the air. he streaming resistance and the air dynamical ressure are in direct roortion. he exression is gien below: V R ca Among which, c refers to the resistance coefficient; A d 4 ; refers to the air density; refers to the seed of the weight throw; and d refers to the diameter of the weight throw. he equation set gien below can be obtained by bringing equation ( into equation (: d x ca m ( x y x d y ca m mg ( x y y While soling the aboe equation set, set dx dy z x, z, z3 y, z4 in order to simlify the aboe equation set into four differential equations of first order: dz z dz ca ( z z4 z m dz3 z4 dz 4 ca g ( z z4 z m Aly Runge-kutta numerical integration to sole the aboe equations and obtain the relationshi between the flying distance of the weight throw and the angle of release, the shot height, the shot seed and the air friction coefficient. he results show that the angle of release, the shot height, the final shot seed and the air friction coefficient can leae different influences on the athletes final erformance. And among the influence factors, the final shot seed has the greatest influence. With the increasing of the final shot seed, the flying distance of the weight throw can be greatly imroed. Howeer, the influences that the shot height and the air friction coefficient hae on the athletes final erformance are not so obious. In the hysical condition, the athletes stand in the basically same enironment and share the same aerage height. As a result, the best choice to imroe the throwing erformance is to enhance the training for the final shot seed and the control of the angle of release..4 Kinetic Analysis of hrowing Regard the uer arm and the forearm that an athlete uses while throwing as two rigid bodies with different olumes; and integrate the shoulder joint, elbow joint and wrist joint into a model with three degrees of freedom as shown in Figure 4. Figure 4. he Schematic Diagram of the Degrees of Freedom of the hrowing Athlete s hrowing Arm Set the throwing athlete s shoulder joint, elbow 4 0504-.3
MAEC Web of Conferences joint and wrist joint as, and 3 resectiely; set the uer arm and the forearm as L, L ; and set the dissection angles as,. Among which, the three dimensional ectors of and are, acting as the angular elocities of the athlete s throwing uer arm and forearm relatie to the earth. he seed of is and its alue can be calculated as follows: When a throwing athlete does throwing, the shot seed and the momentum of the thrown object deend on the seed of the wrist at the moment of throwing. Howeer, the angle seeds of the uer arm and the forearm which do the throwing motion and the angle seed of can leae influence on the angle seed of 3.As leads L to do translation and rotation during its circling motion, the seed of 3 and its relatie seed is related to the seed of, which is: R R, C( G ( 3 R C ( G C L refers to the elocity ector of in the reference system and C ( 3 L refers to the seed of, 3 relatie to. resectiely refer to the angle seeds of and R refers to the osition while R refers to the osi- ectors form to tion ectors from to 3. In order to obtain the seed of 3 which is relatie to the reference system: 3 C( G 3 G, the influence that the local motion of L and L has on should be first calculated. According to the theorem of ector, the following equation can be obtained: 3 G R R R, 3 G ( R R It can be simlified as: 3 G 3 G R R 3 G refers to the seed of generated by ; R refers to the seed of 3 generated by ; 3 G refers to the osition ector of 3 in the reference system. In order to exress the seed relation among, and 3 more secifically, the relationshi between the angles of and with the osition of 3 in the model shown in Figure 3 can be written as: x y z R R R cos R sin R cos R cos( sin( sin( Conduct differential oeration to the angles of and. he relationshi between the angles of and with the osition of 3 can be obtained from the equation aboe: X (, X (, dx d d Y (, Y (, dy d Z (, Z (, dz d Conerse the equation aboe into matrix form as: X (, dx Y (, dy dz Z(, X (, Y (, d d Z(, According to the nature of the matrix and the ector roduct method, the equation aboe can be written as: d 3 G Y d, among which Y is X X Y Y Y Z Z Y refers to the differential relationshi between the angular dislacement of the node in the current structure and the infinitesimal dislacement of 3. he following equation can be obtained by bringing the matrix relation equation into the equation aboe: 0504-.4
ICEA 05 d 3 G d Y or 3 Y[, ] G he following equation can be obtained by bringing the equation aboe into the calculating equation for the relatie seed of 3 : X X Y Y OG [, ] R Z Z According to the rotational inertia rincile, the oerall rotational inertia of the throwing athlete should be: P M H i i Among which, M i refers to the quality of each article of a human body and H refers to the distance from the athlete s each article to the axis. As a human body is a rigid body with continuous distribution, the following equation can be obtained: P H dm H dv refers to human density. he rotational tensor Y c of the arm that the throwing athlete uses while throwing is as follows: Y c ( H E H H dv he exression of the ector quantity on the arbitrary oint of the throwing athlete s body is H H E H E H 3 E 3. H H refers to the roduct of two ectors. he unit tensor is: E he unit orthogonal cure frame is ( C ; E, E, E 3. he resultant moment of the arm that the throwing athlete uses while throwing is k c. refers to the athlete s acceleration ector in the inertia moing system while refers to angular seed. herefore, the rotational tensor moment equation of the athlete s arm while throwing is as follows: kc Yc Yc he moment equation aboe of the athlete s arm on each coordinate orientation is the rojection of the original moment equation on the three-osition coordinate system. Hence, the resultant external moment generated by the athlete s arm rotating while throwing is as follows: J refers to the angular accelerated seed of the arm for throwing while J refers to the rotational inertia of the arm: m j J j refers to the radius of the uer arm; m refers to the quality of the uer arm; and refers to the angular accelerated seed of the uer arm: dw d hen, the angular seed of the forearm should be: dw dw d d Establish a restricted article dynamics equation according to the Lagrange equation. he d Lagrange functionu is the difference alue between the system kinetic energy J and the otential energy Q : U J Q he system dynamics equation should be: d U U F i i,,, n q q i i Among which, q i refers to the corresonding seed of article; qi refers to the kinetic energy of article and the coordinate of otential energy; and F i refers to the force laced on the No. i coordinate. he included angles between the uer arm and the coordinate axis and between the forearm and the coordinate axis are, resectiely while the lengths are L, L resectiely., resectiely refer to the distance from the centre-of-graity ositions of the uer arm and the forearm to the center of and the distance from the centre-of-graity ositions of the uer arm and the forearm to. hus, the barycentric coordinates of the uer arm X,Y should be: X sin Y X L sin sin cos Y L cos cos 0504-.5
MAEC Web of Conferences In a similar way, the barycentric coordinates of the forearm X,Y can also be calculated. he exressions of the system kinetic energy Ek and the system otential energy E are as follows: Ek Ek Ek, Ek m Ek ml m ml 0 cos E E E, E m g cos E mg cos mgl cos he moment M h at and the moment M k at obtained by the Lagrange system kinetic equation are as follows: he B ijk in the equation aboe is: B 0 B 0 B 0 B m B m m ml ml cos B m ml g sin m g sin B m ml cos B m ml cos B ml sin B ml sin B ml sin B B B B m g sin According to the analysis, it can be concluded that the momentum of throwing deends on the momentum of wrist while throwing. herefore, while throwing, the athletes must enhance their arm swing dynamics. When, accord with 38 95 and 0, the seed of 3 can reach the maximum alue on the sagittal surface. Furthermore, with the increasing of and, the change rate of the dissection angles at L and L in unit time will reach the maximum alues during the athlete s throwing. In this eriod, the change rate of the dissection angle at L is greater than that of L. he rincile is that the included angle of L and L at the moment of batting can be almost 80, and the force will ass along the axis of L to L. Howeer, as L and L are connected with each other, there s a certain loss of the force during the rocess of assing. As a result, the angle seed at L is greater than that of L which is more beneficial for the acceleration at. According to the kinetic analysis results of the athlete s arm while throwing, it can be concluded that during throwing, the throwing athletes should firstly adjust the angles of their shoulder joints to the minimum alue; and then adjust the angles of elbow joints and wrist joints to the minimum alues. Greater crook degree of arm can be more helful to accelerate the seed of wrist joint and make the angle seed of forearm become greater than the angle seed of uer arm, so as to increase the mechanical imulse generated by batting. 3 CONCLUSION his aer first obtains the main influence factors affecting the throwing distance by the mutual combination of motion equation and geometrical analysis. And then, it gies the acting force equation that the athletes hae to bear during throwing. his aer also takes the influence that the air friction has on the throwing distance and the shot height into consideration. It establishes the kinetic differential equation of the weight throwing while flying in the air; and obtains the best angle of release. Moreoer, this aer also builds the seed relationshi between each arthrosis during throwing and batting based on the kinetic analysis of the throwing athletes arms while throwing. It obtains the momentum relationshi of the athletes each arthrosis by means of rotational inertia analysis; and then establishes a restricted article dynamics equation from the Lagrange equation. he obtained result shows that the momentum of throwing deends on the momentum of the athletes wrist joints while batting. Besides, while throwing, the athletes should first adjust the angles of their shoulder joints to the minimum alue; and then adjust the angles of elbow joints and wrist joints to the minimum alues. Greater crook degree of arm can be more helful to accelerate the seed of wrist joint and make the angle seed of forearm become greater than the angle seed of uer arm, so as to increase the mechanical imulse generated by batting. he results show that the best angle of release should be 44. When an athlete s final shot seed reaches 6~30m/s, the acting force he/she bears is between KN and 3KN. Besides, final shot seed can bring better erformance. In rofessional games, the athletes will hae the same aerage height and will be in the basically same enironment. As a result, the influence that the shot height and the air friction hae on the final erformance is minor and can be neglected. REFERENCES [] heoretical Mechanics eaching and Research Office of Harbin Institute of echnology. 00. heoretical Mechanics. Beijing: Higher Education Press. [] Pranl L, Auswatiki K & Vigerhart K. 98. Introduction to Hydromechanics. ranslated by Guo Y.H. & Lu S.J. Beijing: Science Press. [3] Li Y.G. 003. Biomechanics Foundation of Exercise raining. Wuhan: Hubei Science and echnology Press, : 0. [4] Vladimir. 004. ranslated by Lu A.Y. Sorts Biomechanics. Beijing: Peole s Sorts Publishing House of China, : 377-379. [5] Drafting Grou of Sorts Biomechanics. 000, Sorts Biomechanics. Beijing: Higher Education Press, : 54. [6] Wang Q. 004. Alication of sorts biomechanics methods in analysis of motion. Journal of Shenyang Sort Uniersity,. [7] Yan H.G. 0. Sorts Biomechanics. Beijing: Beijing Normal Uniersity Press. 0504-.6
ICEA 05 [8] Zhou Y. B. 008. heoretical Mechanics Course. Beijing: Higher Education Press, : 64-65. 0504-.7