Available online a www.sciencedirec.com ScienceDirec Procedia Engineering 72 ( 20 ) 8 7 The 20 conference of he Inernaional Spors Engineering Associaion Cycling Power Opimizaion Sysem Using ink Models of ower imbs wih Clea-Shaped Biaxial oad Cells Akihiro Masuda a*, Keno Yamashia a,keisuke Ishikura a, Hideki Takagi a a Universiy of Tsukuba, -- Tennodai, Tsukuba, Ibaraki 05-857, Japan Absrac A new opimizaion sysem of cycling power was invesigaed in his paper. The developed sysem consised of a newly designed biaxial load cells and analyical sysem using mechanical model of lower limb. The new biaxial load cells which were made by sainless seel (SUS0) were aached o he boom of cycling-shoes insead of he plasic cleas. Cycliss are able o connec heir cycling-shoes o pedals by he developed load cells. The sizes of load cells were almos same as plasic cleas (Shimano Corp) and measure he magniude and direcion of righ and lef pedal force using -srain gages, respecively. The analyical sysem solves he link model of human limbs o idenify he posiions and angles of each segmen of lower limbs. The lower limbs model consised of segmens, high, shank and foo. All posiion of every lower limb segmens, join orques and forces were calculaed by his sysem. Addiionally, he relaionships beween ankle angle and crank angle were also modelled by image-analysis sofware (TEMA D) wih he high-speed camera (Phoron FASTCAM SA). This cycling power opimizaion sysem were applied o he amaeur and exper cycliss o invesigae applicabiliy of our sysem. 20 20 The Published Auhors. by Published Elsevier d. by Elsevier Open access d. under CC BY-NC-ND license. Selecion Selecion and and peer-review peer-review under under responsibiliy responsibiliy of of he he Cenre Cenre for for Spors Spors Engineering Engineering Research, Research, Sheffield Sheffield Hallam Hallam Universiy. Universiy Keywords: Visualizaion, Pedaling-effeciveness, Biaxial load cell, Clea-size load cell. Inroducion Thomas e al. (2007) and Guillaume e al. (200) developed he pedal power sensor wih piezoelecric force sensors in order o evaluae he relaionship using cycle ergomeer. Also, Umbero e al. (20) repored ha he change of upper body posiion influenced a power oupu and muscle acivaion paern. Hanaki e al. (202) invesigae effecs of sea pos angle on he power oupu. * Akihiro Masuda. Tel.: +8-29-85-50 ; fax: +8-29-85-5207. E-mail address: a_masuda@kz.sukuba.ac.jp 877-7058 20 Published by Elsevier d. Open access under CC BY-NC-ND license. Selecion and peer-review under responsibiliy of he Cenre for Spors Engineering Research, Sheffield Hallam Universiy doi: 0.0/j.proeng.20.0.0
Akihiro Masuda e al. / Procedia Engineering 72 (20) 8 7 In addiion, some cycling power meers have been available commercially such like he SRM power meer. Commercial power meers oupu he average power calculaed by he crank orques which were communicaed by he wireless daa ransmission sysem. This paper invesigaes a newly developed power opimizaion sysem for compeiive cycliss. This sysem consised of wo echnical issues which were developmen of clea sized load cells and visualizaion sysem. The firs echnical issue was ha we developed original clea shaped load cells which measure horizonal and verical load independenly (Fig. ). The load cells were possible o insall o sole of cycling shoes by wo seel bols wihou special jigs or special processing. The shape and size of load cells are almos same as commercial plasic cleas which were manufacured by he Shimano Corporaion. Thermo-mechanical reamen process are applied o he SUS0 body of he load cell afer machining process. Developmen of clea shaped biaxial load cells permi paricipans o apply heir own bicycle and shoes o he performance es. I would be very imporan issues for serious compeior o use heir own maerials wihou change of body posiion. Also he wired load cells provide us accurae informaion abou pedaling forces. The second echnical issues was ha we developed a visualizaion sysem of performance es resuls which works on general lapop PC (Fig. 2(a) and Fig. 2(b)). This sysem analyzed he posiion and angle of crank, pedal, oe, heel, knee and greaer rochaner during pedaling by a link mechanism and a free body diagram of cyclis s lower limb. The pedaling forces and join orque were calculaed and visualized on he lapop PC jus afer he performance ess. We applied his sysem o amaeur cycliss o invesigae endency of he force and orques during pedaling and key-poin for beer and sronger pedaling. Fig.. Clea sized biaxial load cell (a)direcion of verical and horizonal forces, (b) Overview of he loadcell Fig.2 (a) Visualized resuls of developed sysem working on PC, (b) Paricipan of performance ess 9
70 Akihiro Masuda e al. / Procedia Engineering 72 ( 20 ) 8 7 2. Consrucion of visualizaion sysem 2. Clea-Sized Biaxial oad Cells The load cells were designed o aach o he boom of cycling shoes in place of plasic cleas. 2-se of wired 8- srain gages bridge circuis were inroduced o each load-cell, respecively. The load cells could be conneced o he bicycle pedals o measure verical and horizonal force from he boom of he shoes. oad capaciy was ±,000 N in he verical direcion and ±500 N in he horizonal direcion. The load cells were calibraed using weighs and he nonlineariy of load cells were under %.Cycliss were able o use heir own bicycles for performance ess and o measure he pedaling force of each leg independenly. 2.2 Pedaling Visualizaion Sysem In he pedaling visualizaion sysem, posiion and angle of crank, pedal, oe, heel, knee and greaer rochaner are calculaed by lower limb model which is shown in Fig. (a). The posiions of greaer rochaner, knee, heel, oe and ankle were defined as vecor X, X 2, X, X and X, respecively. The lengh of high, shank, foo and crank were defined as, 2, and. Moreover, was he lengh beween ankle and heel and 8 9 was he lengh beween oe and heel.,,,, 2 8 and were supposed consans and were measured before performance ess. 9 The posiions of he boom bracke and he greaer rochaner were supposed o fixed poins. The acceleraion of ankle angle was approximaed wih he following funcion using image analysis sofware TEMA D (Phoron Corp., Japan). a b c a sinb c a sinb c a sinb sin c 2 2 2, () where a i, b i and c i (i=,2,,)are consan parameers for each paricipans. 7, 2 and vecor X were calculaed using ankle angle. 2 2 + 2 cos, 7 2 2 - cos sin sin, 2 X 7 (2) sin 5, and in Fig. were calculaed as follows: 2 2 2 2 x x y 2 -, sin, 5 7 cos,. () 25 5 y Thus, knee posiion X, X and ankle posiion X 2 5 were calculaed as follows: 2 x a x 5 X x, n x ( 5 cos ) X x 2 x x2 cos2 y2 y sin2 7 2 y a y 5, X y n ( cos ) 5 y 5 () 2 y2 y y2 cos2 x x2 sin2 7 Here, X was emporary posiion for compuaional calculaion, 5 n is uni vecor of X X and a is he orhogonal vecor of n. in Fig.(a) was consan and heel posiion X were given as follows: 2 2 2-8 9 cos, X 28 x x 8 8 cos cos 8 x x y y 8 sin y y x x sin (5)
Akihiro Masuda e al. / Procedia Engineering 72 ( 20 ) 8 7 7 From he above equaions, all join posiions of he lower limbs relaive o crank angle were deermined and pedal angle was calculaed. x x cos () From pedal angle, he verical and horizonal pedaling force componens from he ground were calculaed wih conversion of measured forces. f x'= f z sin + f x cos, f z ' = f z cos + f x sin (7) where fx and fz were verical and horizonal pedaling force componens from he cycling shoes, respecively. The angenial pedaling force f and normal pedaling force f n were calculaed by crank angle, as follows; f = f x' cos + f z' sin, fn = fx' sin + fz' cos (8) Here, only he angenial pedaling force f was convered o bicycle driving force and he normal pedaling force f n was used o adjusing balance of pedaling. Fig (a)ower-limbs model wih link mechanism, (b) Free body diagram of lower limbs 2. Join Torque Calculaion by Free Body Diagram To calculae join orque, he free body diagram (in Fig.(b)) of lower limbs were applied. The free body diagram was supposed o separae o segmens (high, shank and foo). Equaions of moion for ranslaion were defined as follows: m x = f f + m g (9) k k k,p k,d k Here, g is graviy vecor, m k are mass of each segmens and f is force. k is segmen number. k= means he foo segmen, k=2 means he shank segmen, and k= means he high segmen, respecively. Equaion of moion for roaion were defined as follows: I = P f k k k,cgp k,p P f k,cgd k,d T +T k,p k,d (0)
72 Akihiro Masuda e al. / Procedia Engineering 72 ( 20 ) 8 7 Here, were he angular velociy, I k k were he momens of ineria and T k were he join momens. The body segmen ineria parameers which was deermined by Ae e al. (992) were applied o calculae cener of graviy and he mass of segmens m k.. Performance Tes. Paricipans and es condiion Pedaling performance ess were carried ou and es resuls were analyzed o evaluae he applicabiliy of developed sysem. Paricipan was an amaeur male cyclis. In performance ess, a road bike (Via Nirone 7-AU, Bianchi Corp.) and a room raining machine (V270, Minoura Corp.) were applied. Also, he paricipan was ordered o keep cadence as 00rpm during pedaling performance es. Horizonal and verical loads of righ and lef legs were recorded in 0 seconds by he high-speed digial recorder (EDX-00A by Kyowa Corp.). Cadence and pedal angle were also recorded by he digial recorder using magneic sensor. Recording frequency of digial recorder was 500 Hz. Wired ransmission was applied o he connecion beween he load cells and digial recorder. Small racking markers were aped o he join of ankle, knee and oe o invesigae relaionships beween ankle angle and crank angle. The posiions of markers were recorded by he high-speed camera (Phoron FASTCAM SA). The relaionships beween ankle angle and crank angle given as equaion () were modelled by imageanalysis sofware (TEMA D). Modeling of he relaionships beween ankle angle and crank angle were conduced before he performance es. The experimen was approved by he ehical commiee of he Universiy of Tsukuba..2 Resuls and discussion Original recorded resuls of lef pedaling force was shown in Fig. (a). The lengh of he arrows corresponds o he magniude of human leg power. Also, he direcion of he arrows represens he direcion of human leg power. From his figure, i can be seen ha he cyclis applied leg power in he lower direcion a he boom, dead cener posiion. Thus, much of he power was no convered ino driving force and pedaling force was almos downward force. The effecive pedaling force f is possible o separae o wo componens () f and () f. () f is a componen in () () () he posiive direcion. f is in he negaive direcion. f works effecively as a driving force, and f disurbs crank roaion. In addiion, he radial componen f n was a non-effecive force, which does no influence driving force. Thus, pedaling effeciveness E is defined wih he following equaion as a funcion of crank angle : ( ) f () E 00(%) 2 2 f f n From Fig., i could be confirmed ha adjusmen of he direcion of pedaling force was one of imporan keypoin of pedaling echniques. To clarify his key-poin, virual improvemen of pedaling force direcion were supposed. Here we suppose improvemen rae of pedaling force angle as I.R. and i was defined as he percenage of linear projecion o he angenial direcion. As examples, I.R.=00% means ha all pedaling force were produced o angenial direcion and I.R.=0% means ha all pedaling force were produced o radial direcion. In Fig (b) (c), (d), (e), improved resuls (I.R. were 0%, 20%, 50% and 00%) were shown. From hese resuls, pedaling effeciveness E was calculaed using equaion () and relaionships beween I.R. and pedaling effeciveness E were ploed in Fig. 5(a). In Fig. 5(b), relaionships beween join orques and I.R. was shown. Relaionships beween I.R. and pedaling effeciveness E showed linear endency from 0% o 0% of I.R. From hese resuls, effeciveness of adjusmen of pedaling force direcion shows imporance for compeiive cycliss. On he oher hand, srongly adjusmen of pedaling force migh be a cause of knee injury.
Akihiro Masuda e al. / Procedia Engineering 72 ( 20 ) 8 7 7. Conclusion In his research, a new visualizaion raining sysem for cycling pedaling echnique was developed. Clea-sized biaxial load cells were developed o measure he direcion and magniude of pedaling forces. The measured force was convered ino effecive and non-effecive forces using a lower-limb model and join orques were calculaed free body diagrams of lower limbs. Effec of adjusmen of pedaling force direcion and risk of join injury were possible o be invesigaed using his sysem. Effec of informaion abou power oupu and pedaling effeciveness on he cyclis s performance would be discussed in fuure works. Original I.R.=0% I.R.=20% I.R.=50% I.R.=00% Fig. Original and virual pedaling force (a) Original resul, (b) I.R.=0%, (c) I.R.=20%,(d) I.R.=50%,(e) I.R.=00% a) b) Fig. 5 (a) Average of pedaling effeciveness, (b) Exension and flexion orque of lower limb Reference Ae, Y., Tang, H., Yokoi, T., 992, Esimaion of ineria properies of he body segmens in Japanese ahlees, Biomechanism, No., Sociey of Biomechanisms Japan, pp.22-2. Guillaume, M., Karim, Z., Elodie, M., Régis, B., Alain, B., 200, A cycle ergomeer mouned on a sandard force plaform for hreedimensional pedal forces measuremen during cycling, Journal of Biomechanics, Vol.9, pp. 29-0 Hanaki, S.,Rober, S., 202, Richard, R., The effecs of sea pos angle in cycling performance, Universiy of Kenucky, UKnowledge. Science, pp. 59-50. Thomas, K., ee, M., Ian, M., James, C., 2007, Effec of Pedaling Technique on Mechanical Effeciveness and Efficiency in Cycliss, Medicine Science. Spors Exercise, Vol.9, pp.99-995. Umbero, E., Tamara, H., Jachen, D., 20, Influence of racing posiion on cycling paerns, Poruguese Journal of Spor Sciences, Vol., pp. 2-2.