Intersegmental dynamics of the lower limb in vertical jumps

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1 Journal of echancal Scence and Technology 5 (7) (11) 1817~18 DOI 1.17/s y Intersegmental dynamcs of the lower lmb n vertcal jumps Young-Kwan Km 1 and Yoon Hyuk Km 1,,* 1 Department of echancal Engneerng, Kyung Hee Unversty, Yongn, -71, Korea e-spne Center, Industral Lason Research Insttute, Kyung Hee Unversty, Yongn, -71, Korea (anuscrpt Receved February 15, 11; Revsed Aprl 5, 11; Accepted Aprl, 11) Abstract The purpose of ths study was to nvestgate changes n ntersegmental dynamcs of the lower lmb at the nstant of push-off n vertcal jumps. Usng a mathematcal model ncludng dynamc equatons, the net jont moment (NET) was decomposed nto a muscle moment (US), gravtatonal moment, and nteracton moment (INT) n terms of jont acceleraton and velocty. Ten subjects performed two submaxmal jumps (% and 8% of maxmal heght) and one maxmal jump. Results showed that the hp and ankle jonts manly utlzed US to generate NET at the push-off nstant, whle the knee jont prmarly used INT at the nstant of push-off. The hp US ncreased wth ncreasng jump heght because the deep countermovement (larger flexon angle of hp and knee jont at the push-off nstant) n maxmal jump was a dsadvantage from ntersegmental dynamcs, but may be neurophysologcally advantageous. Keywords: Bomechancs; Vertcal jump; Inverse dynamcs; Human movement, Human jont moment, Intersegmental dynamcs Introducton Ths paper was recommended for publcaton n revsed form by Assocate Edtor aenghyo Cho * Correspondng author. Tel.: , Fax.: E-mal address: yoonhkm@khu.ac.kr KSE & Sprnger 11 The vertcal jump s very mportant n sports. A hgh vertcal jump contrbutes to successful athletc performance, partcularly n sports such as basketball, volleyball, and football. It s a crucal motor task of all human bengs and requres the coordnaton and synchronzaton of multple jonts and muscles. Prevous studes have emphaszed the mportance of the coordnaton of segmental actons [1-] and the functon of bartcular muscles [-5] for enhanced jump performance. In a vertcal jump, there are two ways to propel the body s center of mass (C) upward: a countermovement jump (CJ) and a so-called squat jump (SJ). In a CJ, people start from an uprght poston and ntate downward movement before startng to move upward, whle n a SJ they start from a squatted (or semsquatted) poston wthout a preparatory countermovement. It s well known that CJs are generally - cm hgher than SJs as a result of the stored elastc energy [], stretch reflexes [7], and the actve states of the muscles [8]. The ntal nstant of push-off durng a CJ (.e., the onset of the ascent moton mmedately after the descent moton) has been consdered an mportant moment n a vertcal jump because greater jont moments [8] and greater countermovement ampltudes [9] at ths nstant are closely assocated wth greater jump heghts. Although these results have been prmarly explaned usng neuromuscular characterstcs such as stored elastc energy and stretch reflexes [7, 1, 11], they could be also accounted for usng mechancal characterstcs (e.g., ntersegmental dynamcs), as reported n studes of other fundamental motor sklls [1-1]. echancally ntersegmental dynamcs are nevtable, snce the human body s confgured as a knematc chan. Normally, the acceleraton and velocty of one segment are not only assocated wth that segment tself but also nfluence the motons of other segments due to jont forces between the segments. Thus, n addton to jont moments, moton-dependent moments are mportant n generatng segmental rotatons. These moton-dependent moments are consdered to be nteracton moments, whch can be ether assstve or resstve to the goal-drected movement, dependng on the chan confguraton and the drecton of jont acceleraton [1-1]. For ths reason, understandng the characterstcs of ntersegmental dynamcs and effcently utlzng nteracton moments are very mportant n the control and mprovement of jump performance [15]. In ths study, we used a mathematcal model of a foursegment lnkage wth respect to a local coordnate system. The net jont moment (the product of nerta and acceleraton) was decomposed nto a muscle moment (computed from the equatons of nverse dynamcs), a gravtatonal moment (due to gravty), and an nteracton moment (caused by other jonts acceleratons and veloctes; e.g., the couplng nerta or Corols force effects) [1, 17]. The purpose of ths study was to nvestgate changes n the ntersegmental dynamcs of the

2 1818 Y.-K. Km and Y. H. Km / Journal of echancal Scence and Technology 5 (7) (11) 1817~18 lower lmb at the nstant of push-off accordng to jump heght. Jont knematcs and the knetcs of submaxmal and maxmal jumps were examned wth the four-segment lnkage mathematcal model. It s hypotheszed that INT ncreases at all three jonts wth ncreasng jumpng heghts because people would effcently utlze INT created by other segments rotatons n maxmal jump.. ethods.1 Subjects Ten male adults (age, 5. ±.; heght, 17.9 ±.1 cm; body weght, 7.8 ± 9. N) partcpated n ths study. All subjects had been njury-free for three months pror to the study and had no problems assocated wth repeated maxmal jumps. Pror to partcpaton, all partcpants sgned the nformed consent form that had been approved by the nsttutonal revew board of our unversty.. Expermental procedures Pror to the tests, the subjects performed a standard warmup routne, consstng of stretchng and moderate jumpng. After suffcent warm-up, the subjects performed fve CJs from an uprght standng poston (akmbo posture) at maxmal ntensty. Durng the maxmal vertcal jumps, the subjects were asked to remember ther knesthetc feelng of maxmal ntensty. Then, they were asked perform submaxmal jumps at the dfferent levels of 5%, 5%, and 75% of the maxmal heght accordng to ther knesthetc feelngs of submaxmal ntenstes. The order of the levels of submaxmal jumps was randomly selected and fve trals for each submaxmal condton were executed. There was no external feedback or external focus that would allow the subjects to guess or determne the jump heght. The actual heghts of submaxmal jumps were sgnfcantly hgher than the stated goals: 59.% (SD = 7.7) nstead of 5%, 78.1% (SD = 5.) nstead of 5%, and 87.5% (SD =.) nstead of 75%. We selected the trals closest to % (.9%, SD =.) and 8% (8.%, SD = 1.) of the maxmal heght for further analyses.. Data collecton We used a four-segment lnkage model n two-dmensonal space. The four segments were as follows: head-arm-trunk (HAT), thgh, shank, and foot. To construct the model, reflectve markers were placed on the acromon process, greater trochanter, lateral condyle, lateral malleolus, calcaneus, and the ffth metatarsophalangeal jont. Durng the countermovement and propulsve phases, marker poston data were obtaned by a hgh-speed moton capture system (Hawk Dgtal Real Tme System, oton Analyss System, Santa Rosa, CA, USA) at a samplng rate of Hz. In addton, the ground reacton force (GRF) and center of pressure were collected by a forceplate (P, Bertec Corporaton, Columbus, OH, USA) wth a samplng rate of, Hz. (a) Fg. 1. (a) Anatomcal landmarks and angle defntons; (b) Free body dagrams for nverse dynamcs. Note: HAT: head-arm-trunk, θ : segment angle relatve to the postve horzontal, and q : jont angle relatve to the dstal segment (q =θ - θ -1, >1).. odel of ntersegmental dynamcs of the lower lmb..1 Knematc varables Pror to any data analyss, the three-dmensonal trajectores of the sx reflectve markers were fltered wth a dual-pass nd order Butterworth flter (cutoff frequency of Hz) and the GRF were fltered wth a same flter (cutoff frequency of Hz). Jump heghts were calculated usng the arborne tme obtaned from a forceplate [18]. For the jont knematcs and knetcs, two dfferent angles such as segment angle and jont angle were used. The absolute vector angle wth respect to the postve horzontal was calculated as the segment angle. The jont angle was calculated by the proxmal segment angle wth respect to the dstal segment (Fg. 1(a)). Tme dervatves of jont angles (.e., angular veloctes and angular acceleratons) were numercally obtaned. Accordng to Kreghbaum & Barthel s notaton [19], the extenson of jont moton and plantar flexon of the ankle were expressed n postve values n reportng jont knematc and knetc results... Knetc equatons In order to observe the jont moment at each jont, conventonal nverse dynamcs [], presented n terms of Newton- Euler equatons wth respect to the global reference frame, were performed wth measured knematc data and body segment parameters [1]. For the foot, shank, and thgh ( = 1,, and ): F F+ 1 + mg = ma + [ r F] + [ r ( F )] = Iα. (1) + 1 d p + 1 For the HAT ( = ): (b)

3 Y.-K. Km and Y. H. Km / Journal of echancal Scence and Technology 5 (7) (11) 1817~ F + mg = ma + [ r F ] = I α. () d These equatons can be rewrtten n matrx form by elmnatng jont forces as follows [-] (where ˆ 1 = 1 k1, ˆ = k, ˆ = k, and ˆ = k): m m m m θ G m1 m m m G θ = + m1 m m m θ G m m m m θ G 1 N1 N1 N1 θ 1 N1 N N θ N1 N N θ N1 N N θ where θ 1 (foot angle) = q 1, θ (shank angle) = q 1 + q, θ (shank angle) = q 1 + q + q, and θ (HAT angle)= q 1 + q + q + q. The dynamc equatons of the four-segment lnkage were rephrased wth respect to local coordnate system (.e., jont angle) and the net jont torque was parttoned as follows n order to determne the physcal meanngs of the varous sources contrbutng to net jont moments: NET = US + GRA + INT () where NET s the net jont moment, US s the muscle moment, GRA s the gravtatonal moment, and INT s the nteracton moment. Then, = ( jj + j j) j= j= + 1 j= + NET m m m q US () (5) = () GRA = g r cos( q ) (7) j j j= and INT s the other terms consstng of q j, q j (j=1 to except ), and qq j at each jont..5 Statstcal analyss One-way repeated measures analyss of varance (ANOVA) was performed to assess the effects of jump heght on NET, US, INT, GRA, and knematc data. The measured jump levels were %, 8%, and 1% of the maxmal heght. A famlywse statstcal sgnfcance level was set at.5. When sphercty assumpton was volated, the Huynh-Feldt adjustment for degrees of freedom was appled. When a sgnfcant man effect was detected, the post hoc test (Bonferron s multple comparsons) was used to dentfy the cause of sgnfcance.. Results Knee oment [Nm/kg] Hp oment [Nm/kg] Ankle oment [Nm/kg] * ** ** * ** ** ** % 8% 1% NET US GRA INT NET US GRA INT NET US GRA INT Fg.. Intersegmental dynamcs of the lower lmb at the push-off nstant n vertcal jumps and ther changes wth ncreases n jump heght. Error bar ndcates a standard devaton.* ndcates a man effect of jump heght (p<.5). ** ndcates sgnfcant mean dfference between two levels (p<.17). Postve values are extenson moments and negatve ones are flexon moments..1 Intersegmental dynamcs of the lower lmb at the pushoff nstant Fg. presents changes n ntersegmental dynamcs of the lower lmb at the push-off nstant across three dfferent jump heghts. Postve values were extenson moments and negatve ones were flexon moments. The patterns n generatng NET were dfferent at each jont. The hp NET was prmarly created by US, whle the knee NET was manly generated by INT. All GRAs worked as flexon moment. In addton, ncreased jump heght changed the decomposton. The hp US ncreased wth ncreasng jump heght (p<.5). Post hoc test revealed that the mean hp US at maxmal jump was sgnfcantly hgher than the other two submaxmal jumps. Also, the hp flexon GRA contnuously ncreased flexon moments wth ncreasng jump heght (p<.5). The detaled changes wthn INT are presented n the followng secton.. The contrbuton of couplng nerta to INT at the pushoff nstant Snce the angular veloctes ( q ) were close to zero at the push-off nstant, centrfugal force-drven ( q ) and Corols force-drven ( qq j ) INTs were near zero. Therefore, couplng nerta (the off-dagonal element n an nerta coeffcent matrx) was a domnant source of the INT at each jont. *

4 18 Y.-K. Km and Y. H. Km / Journal of echancal Scence and Technology 5 (7) (11) 1817~18 Knee oment [Nm/kg] Hp oment [Nm/kg] Ankle oment [Nm/kg] INT INT % 8% 1% INT by knee INT by ankle INT by toe INT by hp INT by ankle INT by toe INT INT by hp INT by knee INT by toe Fg.. Contrbuton of couplng nerta effect to INT at the push-off nstant and ther varatons accordng to jump heght. Error bar ndcates a standard devaton. Postve values are extenson moments and negatve ones are flexon moments. Fg. shows the contrbuton of couplng nerta effect to INT at the push-off nstant and ts varatons wth jump heght. The hp INT was domnantly attrbuted to the couplng nerta effect of the knee jont (INT by knee). The ankle INT was asssted by the couplng nerta effect of the knee jont (INT by knee) but manly cancelled out by the couplng nerta effect of the hp jont (INT by hp). At the knee jont, the couplng nerta effects of both the hp and ankle jonts contrbuted to knee INT postvely. Thus, the results demonstrated that INT caused by the couplng nerta effect of the adjacent jont was assstve, whle INT nduced by the couplng nerta effect of the non-contactng jont was resstve at each jont. The couplng nerta effect of the toe jont (INT by toe) was trval to each jont. There was no sgnfcant effect of jump heght on the contrbuton of couplng nerta to INT.. Flexon angles at the push-off nstant Table 1 shows the mean values of the flexon angles at the push-off nstant. Flexon angles sgnfcantly ncreased wth ncreased jump heght, except for the ankle jont (p<.5). The flexon angle of the ankle jont dd not vary wth jump heght.. Dscusson In order to nvestgate the ntersegmental dynamcs of vertcal jumpng at the push-off nstant, ths study decomposed NET nto three contrbutng sources usng a mathematcal model. The three sources were US computed wth nverse Table 1. Changes n flexon angles at the push-off nstant (unt: degrees) [mean (SD)]. Hp Knee Ankle % 9.9 (18.) 8. (11.9) 111. (5.) 8% 8.8 (17.) 8. (1.9) 111. (.7) 1% 115 (.8) 98.8 (1.) (.) F P.1*.1*.59 * ndcate a sgnfcant man effect of jump heght (p<.5). dynamcs, GRA due to a gravty, and INT caused by the acceleraton and veloctes of other jonts. The push-off nstant n a CJ s very mportant n jump performance because an explosve GRF, created by the contrbutons of three jont motons, s necessary for maxmal jump heght and controlled GRF are also requred for submaxmal jumps. The current study ndrectly ndcated that the most postve contrbuton to the ground reacton force n response to ncreased jump heght was hp US, because only hp US sgnfcantly ncreased wth ncreasng jump heght. Ths fndng s n good accordance wth the fndng of Vanrenterghem et al. [9], who showed that the ampltude of CJ s closely related to ncreases n submaxmal jump heghts. Ths was prmarly attrbuted to the sgnfcant contrbuton of the most proxmal jont (.e., the hp jont). At the push-off nstant, the contrbutons of the decomposed moments to NET were dfferent by jont. The hp and ankle manly generated NET wth the help of US, whle the knee predomnantly used INT. Ths dfference mght be attrbuted to the locaton of each jont n a multjont system. The hp jont s the most proxmal jont and must overcome the largest nerta (HAT) n order to lft the body C upward, requrng the actve contrbuton of US (Fg. ). The knee jont, as a mddle jont, may work as a subordnate jont because the hp jont s the leadng jont and provdes the dynamc foundaton of the system at the push-off nstant. However, the knee jont mght work as a leadng jont n the mddle of the propulsve phase when the leadng role of the hp jont subsdes [5]. Then, the optmal soluton of a proxmal-to-dstal sequence of segmental rotaton would be naturally acheved [1, ]. The ntersegmental dynamcs of the lower lmb changed accordng to jump heght. The hp jont showed sgnfcantly ncreased US n order to overcome the ncreased flexon GRA. The knee and ankle INTs changed but showed no sgnfcant change due to large standard devatons. These large standard devatons mght be partally attrbuted to ndvdual dfferences and partally attrbuted to data processng (e.g., fluctuated angular acceleraton due to second tme dervatves at knee and ankle jonts). The INT at each jont was manly attrbuted to the couplng nerta effect of the next adjacent jont (Fg. ). Snce no effect of jump heght on INT was detected, our hypothess was not supported. These results were partally explaned by the chan confguraton of a multjont system.

5 Y.-K. Km and Y. H. Km / Journal of echancal Scence and Technology 5 (7) (11) 1817~ moment, gravtatonal moment, and nteracton moment usng closed forms of dynamc equatons. We nvestgated ntersegmental dynamcs of the lower lmb at the push-off nstant n vertcal jumps. Each jont showed dfferent NET generatng patterns. As the jump heght ncreased, deeper countermovement was detected. The ncreased ampltude of the countermovement was not advantageous from the perspectve of ntersegmental dynamcs. Rather ths change mght trgger ncreased extenson US actvtes, resultng n neurophysologcal advantages. (a) (b) Acknowledgment Ths work was supported by a grant from the Kyung Hee Unversty Post-Doctoral fellowshp n 9 (KHU- 9). Fg.. Illustraton on the relatonshp wth the chan confguraton and the couplng nerta effect of the knee jont moton at the push-off nstant: (a) Confguraton of a segment chan n submaxmal jump; (b) and n maxmal jump. Note: a t = tangental acceleraton actng on the adjacent segment. Fg. shows the relatonshp between chan confguraton and the couplng nerta effect at the push-off nstant. Normally the INT at each jont s affected by couplng nerta effects (angular acceleraton of the other jonts), centrfugal force effects (squared angular velocty of the other jonts), and Corols force effects (the product of two dfferent jont angular veloctes). However, the couplng nerta effects mght be the unque source of INT at the push-off nstant. Because all angular velocty at ths moment s near zero, only tangental force-drve INT s effectve. In submaxmal jumps, the subjects tended to have small ampltudes of flexon angles (less than 9 for the hp and knee) at the push-off nstant (Table 1 and Fg. (a)). The tangental acceleraton created by knee extenson asssted the other segment motons (.e., the hp extenson and ankle plantar flexon). However, when the subjects flexed deeply at the push-off nstant (more than 9 for the hp and knee) to maxmze ther jump heghts, the tangental acceleratons created by knee extenson tended to produce reverse effects on the other segment motons (.e., the hp flexon and ankle dorsflexon) (Fg. (b)). Therefore, the hp INT and ankle INT created by couplng nerta effects of the knee were reduced wth ncreases n jump heght. Ths reduced hp INT mght trgger more actvaton of hp US because the reduced INT hnders the upward body C moton. The larger countermovement at the push-off nstant does not provde people wth advantages from the perspectve of ntersegmental dynamcs. However, these confguraton may trgger ncreased extenson US contrbutons as a result of ncreased stored elastc energy or/and stretch reflexes [-8, 1, 11]. 5. Conclusons Ths study decomposed net jont moments nto a muscle Nomenclature The number of subscrpts s used n such a manner that a segment and ts dstal jont have the same numbers (=1: foot or toe, : shank or ankle, : thgh or knee, : HAT or hp), where HAT means head, arms, and trunk segments together. ˆ, ˆ j, k ˆ : Unt vector of local coordnate system affxed to a segment q, q, q : Jont angle, angular velocty, angular acceleraton wth respect to the dstal segment θ, θ, θ : Segment angle, angular velocty, and angular acceleraton wth respect to the postve horzontal l, ρ : Length of a segment and the dstance from the dstal jont to the center of mass of a segment g : Gravtatonal constant m, I : ass of a segment and moment of nerta at the center of mass of a segment a, α : Lnear and angualar acceleraton at the center of mass of a segment, F : Resultant jont moment and resultant jont force r p, r d : Vector from the center of a segment to the proxmal jont and the dstal jont m j, N j : Element of nerta coeffcent matrx and element of coeffcent of nteracton moment matrx. These are formed usng ndces j = 1,,, h = 1,,, and k = 1,,,, Ih + mhρh μ j = lj m, μ =, δh = μh +, γ h = μh + mhρh, l = j+ 1 hh = lhδ h, hk = lhγ kchk, kh = hk, N hh =, Nhk = lhγ kshk, Nkh = Nhk, where chk cos( qh qk ) and s sn( q q ) for the element (k > h). hk h k References [1]. F. Bobbert and G. J. van Ingen Schenau, Coordnaton n vertcal jumpng, Journal of Bomechancs, 1 () (1988) 9-. [] J. L. Hudson, Coordnaton of segments n the vertcal jump, h

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