RIDGWAY, M.

English

ISBS (International Society of Biomechanics in Sports): Conference Proceedings Archive

A BIOMECHANICAL ANALYSIS OF CONVENTIONAL AND NON-CONVENTIONAL BICYCLE PEDALING MECHANISMS RIDGWAY, M. university of Texas-Arlington Arlington ABELBECK, K .  I Design Engineer Kaiser Sport Health Equipment Prasno USA The use of tbe bicycle erterds far beyond mdm recreation and sports racing events. Bicycle ergometers are videly used as testing devices to d e t e h  aerobic fitness levels and cardiac function. Over the past several years, pedal-povered vehicles and statiomry bikes have increased in popularity. This has cow about as a result of an increased public awareness of the bealth benefits of cardiovascular conditioning, as well as providing an alternative forn of transportation. The latter deals with the development of the human powered vehicle (BW) vhere efficiency of locorntion i s  of chief iiportance. The ppurpose of this paper i s  to study the efficiency of a conventional circular pedal mtion (6W) bicycle cyclist. Patello-femoral force i s  a contributirq factor to chondromlacia-patella (Dicksan, 1985) ard is a concern in both locomotion and exercisefrehabilitation. Research investigating the forces applied uinq conventio~l CPH systens is extensive (Cregor et  al., 1985: Davis and Bull, 1981; Bull and Davis, 1981: Men and Meyefa, 1979: Bull and Jorge, 1985; and )levmiller et al. ,  1968). Reported wvement patterns and applied forces at specific pedal positions are relatively consistent betwen studies. The less popular and less available NCPn system has not been studied extensively by the research community. The CPH system bike vas made by Dnivega vith toe clips, me bike n s  munted on a stationary trainer to aliov video taping of simulited ridinq. The EPH system was the Uenax Tramsbar Power bycicle. This ;ys:em has tvo ratchet* sprockets, one on each side of the rear tire. One end of each of Wo &ins i s  attached tc one end of a pair of levers vim pedals on the op~osite ends of the levers. The levers reciprccate via a cable connecting the free ends of the chain. Because tk chain canat tolerate a coapression along i ts  long axis, no tension can te created by pulling the pedals up. Ho tw c l i p  wre needed because vhen one pedal is woed dovn the other mves up. The HCPH system bicycle bas munted on a mtor driven treadmill to provide a ridinq simulation, and a shuttered video camera vas used to f i la  the subject completing ten stroke cycles on each system. Video prints wre made at  approximately 0.45 rad intervals of crank rotation. A theoretical Dodel n s  developed and applied to both systems. Joint m m t  a m  vere determined for the right ankle, knee and hip by analyzing x-rays of the subject's thigh, shank and foot segments. Instant centers of rotation vere detemined by the use of Mire frirqes s (Gertlbein, e t  al. ,  1985) and respective mment arms were neasqred from tbe x-ray film. These ~easurements are necessary to deternine the vork done by antagonistic muscle qroups spanning more than one joint. This condition is referred to as Lombard's paradox (Lombard, 1903; Gregor, et.al., 1985). Ibe muscles involved are the gastrocnemius, responsible for knee flexion and plantar flexion; biceps femris, semimabranosus, and , semiterdinosu contributing to to knee flexion and hip extension; and the rectus femoris which i s  a hee extensor and hip flexor. The contribution of each of these sscules a s  determined by estimating each nuscle's marim length of shortening art the amount of tcqdon displacement alocq the long axis of tbe w c l e ,  as it mves from its resting length to i t s  shortened length. Koloent arms of the tendon wre plotted against joint angle. The sum of the htegrlls of the equations fittinq those curves bas detanined, from resting ( 0  rad) to the tw respective joint angies. An assuption was made that a x l e  will shorten 213 of i ts  restiq length. The only lauscle vhere tension was nit exerted by the contractirq muscle vas the qastrwnenius at the 6' past top  dead center (TCC) cnnk VIII Symposium ISBS - 153 - Prague 1990 pmltioa In Mu ePIl s y s t a  bicycle. Cms rct ia~l  rrrar of tbr two-joint mcl- relative to tbr total aou vctioarl uw of the ebrl  a)or mxla  wws at ttn hip,  lncr and ankle e r r  d e t e d .  %a follwinq -ions vcn made: (1) The gutroauritm t4ndoo ca thr prrtuior faur w urignd a trarica of MI of tho total fonr utNd by th =)or plaahr f luon .  ( 2 )  lb br temrfs provldrd 1st of tfm tensim rtutd by tbr bm atenmm. (3) tb m a  of th g l a t m  luLr pd Lbr porterlor p3rtianr of ttm glutmm r d i a c  Md glutam rlnkur rxut h .  ~ u r r b f a m u ~ r o d t b r l o n p b u d o f t b r b i a p r f m r b ,  dtadinmaandsdu&mw. Tb br u t i l i d  for b l  f o m  aplllcltim for tbc CPI( syatu k r h i l u  to an Pud by Sc&n ud -fa (1979). rtwir 'idur ard l t im did not r l lw for tbr rbrrr tonu rnrbd by thr foot m r e l  quip vitb tor c l i p .  !q tht this form uu not siqnifiunt ud cruld be aittd. kuPr t rn t  trcbnlqua d by 0 t h  fmufiqaton [Bull ud Jaw, 1985: Davis ud M l ,  1981; m11 ud hvis, 1981 Md kn i l l e r ,  et al.,l9M) ldiah otbuviu. A man $ak m l u  of tbr rbslr forcu nlrtioc to m m l  pdai toms w drturind to br 1:l r u p c t i ~ l y .  dbuPd crank an tqa wruxiutes Ibr lallouing nuvr (Q 11 bere Y h tbr vutiul tom ud I is th displacement cl&iu brgirdrq at EC.  r - Y s i n  9 (1) lb brrk dm In w brlf padal revolution uas Ctanind us& w arbitrary mit of lor-. Ibr c r d  an bas 18a laq  but standardued to 1 leqtb mit to siqli!y tfm calculation. Total wrk don is detemhd by sclviq Un inteqral: /.Yn e d e  (2 )  u* = 0 ur I. 2au ( 3 1  bcboril~trl h l u t r  va!u of a broken down into tfm coqonnt is tbe char force appllcd to Uw w!. The fo.m/ p o r ; t i ~  m e  vas th a i m  cum of lil th aql iMe of tb pat vert:cal !am. l5c total uort don can k follwinq r u t ~ u l  and boriuntal coqennts: (0  U. = 2 L', - I sin 9 d e  - 2/3 I cos 8 d e  0 0.3217 ?;pun 1 sIbm tbr t o ~ l p a i t r o n  cam !or tb mrt ia l  ud b r i m t a l  caqocmt~. R* u nirtmsb:? u s  wd to btmh tfm -1 tom on tb, *P1I sptm, minq tfm oQvnd l e w  m liars. An us-. u s  .sdr tbrt tbur u m C l r  t om,  ud thr m n t  t om bd 4 r r r t iu l  cqmatt t h t  utu*~n W1 VIIf Symposium XSIZE - 154  - Pragw 1990 follouing equation: r = Z sin 8 (6)  The work done in one pedal stroke of each respective pedalling system was deterrined by solving the integral: "BJ UI - jl sin e - 2.u (7) 8; . Lirq tbe limits of the crank stroke for ard $2 as 1.431 and 2.758 respectively, the constant Z (peak tow) ms solved. 2.758 z ( - cos 8) ) = 2au I (8) 1.431 (9) In both systems the wrk done i n  lifting tbe wight of the leg vas outted because that potential energy is released on the nert stroke. Vertical travel of tbe leg's bas considered not significantly different betnen U e  CPK and HCPK system Forces Ere solved conforming to tbe Ddcl described. Absolute pedal angle via respect to the horizontal fl vas used i n  detedng forces. Because the WCPn system had no toa cl ip ,  the assumption vas mde tbat a l l  forces applied vere noml to  the p b l ,  and a frictiollal force was exerted to b l d  the foot on tbe pedal hen swll absolute angles existed. Equation 11 was substituted for Py (vertical force) in equation 10. P (force normal to the pedal) vas solved for using equation 12. Pipre 2 shows tbe NCPK forces. Note that d is 1 . h  times the one length unit used in the CPN systea ($ 1). r = 1.875 sin 8 = D F, sin 8 (10) P. cos 8 = F, (11) F, 1.875/1.757 cos q F, - 1.067/cos 9 (12) Figure 2: WCA Pedal Forces. V I I I  Symposium ISBS Prague 1990 'Lbe CF% syssyster force coqownts are solved for in a shilar fashion except that nw both shear aad mmal forces exist. $Patio11 13 ws used to solve for the vertical force applied b generate the torque w e s a q  at thecrankan Fgure 3 details thenormal and shear components of the vertical forces Fy. Figure 3: CPK Pedal Forces. Pipations 14 and 15 WlpPnsate for the absolute pedal angle. Equations 16 and 17 are equations 13 combined vith 14 and 13 corbincd vith 15 respectively; used to solve for m m l  vertical FWu' and sbedr vertical Fsv forces: For: O < 8 < U  P. = F. cos v P. = F. s i n  v l / d  - 1/3d t a n  8 1 F, c o s  v l / d  - 1/3d t a n  8 = P, c o s  v F,= cos v/d - cos v/3d t a n  0 (18  p,n sin v/d - s i n  v/3d t a n  8 (19  1 Ihe horizontal force Fg and cGllpDnentt FM and F wre determined in  the same nanner vith the exception tbat the direction of the force c b k q ~ ~  at 0 = r/2. ~ o f o v i n ~  tbe convention established: VIIf Symposium 1- - 156 - Prague 1990 b Since: r = 1/3 cos 8 = P, d cos 8 F- = F. sin Q, and PI - P. cos Q Therefore: s i n  v/3d = P, f o r  : 0 5 8 ,  r/2, ( 20a I - s i n  v/3d = P, f o r  : r/2 < 8 S n, (2Ob) cos 9/3d = P, f o r  : 0  d 8 < n/2, ( 2 l a )  - cps Q/3d = P, f o r  : r/2 < 8 S r (21b) and Table 1 presents tbe algebraic sum of a l l  shear and m m l  form. Yoml and shear forces were calculated for tbe CPI( and )ICPII systaa. Lines w e  dram normal to tbe pedal and parallel to the surface of the pedal tirouqh its u i s  of rotation. Erternal m w t s  were reasured fro6 th perpendicular distance from the line t o  the center of rotation for kch of the three joints. A positive counterclockwise mverent convention v t j  estblished. TABU 1 b m l  and shear forces for CPI systen bicycle a t  various cranl angles. (Nomlited for crank length of I unit). VIII Symposium ISBS for 8: P, = pmE Prague 1990 0 S 8 c 0.3217 sin v cos (p 0.3217 3 e < r/2 sin9 -(sinv/3tane) + cOsrp/3 cosq -(coso/3tane) + sin93 r/2 < e < 2.820, sinq -(sin~/3tane) - cos cp/3 coso -(cosv/3tane) - sin 1p/3 2.820 S a -sin Q cos v T S ~ Q J ?  ankle =mi!: r? ; ~:ii?lLI by Q e  lever cr; c:' tAe C.Z?!:~,IP~, t? a!,~n an4 nuitipiizd h.i ::.60 b . . .  y : t ~ c  cj:;trcc~sr>s. tension. i'.i1.3 r:il;i~;n ~ii!t.ii~:itd bi it: i a w r  sat \t ?rigrr, a t  t,kt he angle, V' .i,A,ri.c; L P .t.i I n s m ?  &.e %~i'i~;ii ?be .s:ecru; h;;; xxiiti Ltsr 3s U? $ 4 ~  of 3.75 t i ~ s  th:' Y~C:?![S w : z t ~  i9,re.r ara ard 0.25 T i ; ,  * .  :ic+ f ~ : i s ,  sedte%l:r.aixs i;\l -irim&rmcsus iwer  ara. ~'31.5: 311. atensics " ~ s : o n  was d e t m h i 3  mi ait t (p~:d Ly 0 , 2 5  t~ &bm!.rie :.kt cersion in bls cc.qlex at tjz si.te o f  ti!!ial insertion. Tht hs~rtinil~% m a t  am, :t thtt jai.:~t arg,e: m s  maswd a d  tkg p-dpro yigieidec! c a ~ c t n d  intern1 ltw mmt. h o 3  "& em of a l l  ROW&!, .:d~tk+ c:t ?a?",et, force5 i:: t% p t e l . 1 ~  higax~nt: znd rrndrieps t ~ d o i ~  rere detfrninahi said '1.25 t i ~ s  tb ic  esliic, ti.=.: th mmt ark recta I;m~Liplq at; the i l ~ e t a h ! ~ ,  produces an32pjler * internal w m t .  Yk m9trerilution of k i s  >ev resclL~it nwc extsr/~i,n tor?es vds remlca!i.ted mtil tiX dis:re~x~ fi.911 *& FLCI~OOS -I?:!'.?: 621s 1s: *Ail S f .  Ii~.:.4 4 b s  1 free k.2;~ diagran depistiy a l l  forces, o'&r th q a v i t y ,  acimq c?: the ief; FRh Reacton Force (Normal) FRS = Rcaaran Fo.ie 'She A!) FR, = Fwce Rertus Femor~s Fw - Farce HanEtnrgs (at o , ~ ~ n )  F,, - Force 14arnstrcngi :at insrn~o~i) Fa, = Force Ouadrceps Tendon F-.! Fc = Form Sasifocnermus Fc =  FOR^ Calcaneal Tendon FGU = FOICO Gluleus M ~ c ~ r n u s  Fiyx? 4 :  Forces appiied and r ip  chnver,:ion sf s D c n r j  ah';: the h i p ,  knes and :exc]cding wj. ve:7?:. Ths resultant mwnt abol:t sack joint vcs ierrxined d! the selected joint a:g:es. T k i e  rti-e,; w:e piotted against joint angle and intqntrd over the Inilia: to f i s i  juint ayle  vai2xs,  w i n g  into accQG2r 3:; chznges i n  direction encountered bj c!e joints ;  otse:virq ecceni::; c:ntra~tions E j  aeli. !aatelii;"ew::c; '?a>: e r e  calculated based on the tension v3iu.s jn the cpadrice~s telido? ird :he pte!lar liq3;e::t. Tkj; :or:e IS t$e aloebraic suo of the prdxts o i  tendon dnd ligament twsicns l id t5e cosine of tf.2 angles e z c h o i  these vectors ~ k e  vitb a line thdt passes though :?A plnt of contac: o f  the ptei la  and feaur and t ' e  ja!e:~?~';j:fi s of the tbi3 force vectors. [Ellis, e t  a l . ,  1980). The sin o these t i o  vector cornymencs +TI; !:.if.-. 3s t?,eresultant compression patel1o:'emral for-e. These values wre piotted and fit.tpd v;:h a smo:!: 3:::ve 5:: integrated along the range of wtion cf t4e joint. l?!e total work done bg WE msi!es of each jcint is listed i n  Table 2. Piyurs 5 iliustratsr, the j t r s i t i ~  sequences i n  CPY and NCR. F'se totdl  work prcdxed wit. the d nou eqllal to 13 cm put jnta tte 31 ;,::::: s:". eqnaticns 2 and 3 yielded a vork product 0: 16 au  (cs) for each 112 revol~~tion. The data shnvr a 7 t  l . * ~ : d d ~ i !  :n the amount of vork done in the con.rentiona1 CPX system bicycle as coioputed t o  the NB!! systea. ?he con~fntisnal vIII Symposium ISBS - 1 5 8  - Pragu-. 1990 CPH systea attribatas 39,4\ of the wrk pmducrd by the BISC~~S is dw to talbard's Paradox as eonpared to 26.9\ in the sB11 ryster. T A U 3  2 lbrrcular work required to do 36 au Q ot work for 611 aad llCPlI s y s m .  Joint CPM (Work Done) NCPM (Work Done) (a .ar) (au.cm) Value %Total Value %Total s HIP 34.82 58.60 23.47 47.00 Knee Ext 14.38 24.30 15.32 31.10 Knee Flex 2.63 4.40 00.00 00.00 Ankle 7.55 12.70 10.46 21.20 NCPM Figure 5: Stroking Sequences in CPH and WCPN. Figure 6 shows the range of mtion at the hip, Lnee and ankle for each type of pedal motion. This decrease in the joints use of acilable ranqe of motion partially explains the smaller a n t  of antagonistic musc:? action. a 60 W Y (D I " .  HIP KNEE ANKLE JOINT Figure 6: Joint Ranges of Notion for CPN and NCPH Peealling System. VIII Symposium ISBS - 159 - NCPM Fl Prague 1990 Awqwimwr ma3obatveentbcrrtvobi~leryrtm basadontheanntofvork &norelativetothe cmactioaal uca of tbs mjor msclcs wves involved. Plagabwfls data (1987) w e  I#d to d c k d a e  total aossectioaal area of th mjor uscle rmzo for tbe joints analyzed. Tbe data are rwrdcd in Table 3. Joint Actbn CroU.c1lWPt % ot %Work K Work ~ r e a  (cm? Total Done A CPM NCPM A HIpExtension 109.70 37.00 58.60 21.60 47.70 10.70 Knee Fiexlon 69.50 23.40 4.40 19.00 00.00 23.40 Knee Extension 71.10 24.00 24.30 0.30 31.30 7.10 Ankleplantar FI.4.62 15.60 12.70 2.90 21.20 5.60 z 43.80 46.80 Patellofemral forces vere analyzed for w stroke cycle for both CPW: and llCPK. The area under the curve for one stroke cycle was 2.486 total units with the KIDII systm and 2.191 total units i n  the 81 syster. lbis represents a 11.9\ difference ktveen the CPH and 1ICnl systcrcr. Mote that this force is applied through 0.87 nd. angular displacuent on tbe BCPll systea or 2.857 units fom/rad. knee displaarnt and throqh 0.56 rad (3.91 units fom/rad knee displacement) tor the CPU system. There is a 27.0l decrease in patellofemoral forces p r  unit of area contacted in  the WCPH in comprison to the CPK systes. The priaary findings of this study suggest that a mre e!ficient systen of producing work my exist with a e  NCPI systei? as coqdred t o  a conventional C ? I  systea. At very high pedal velocities this increased efficiency in the I1CPZl systen my be lost becaw rotational kinetic eneryy is stored i n  the crank, pedals and lowr extrenities i n  a circular pedaling mtion. In the WCPK systen the mss w t  be accelerated and decelerated in order to change direction at the beqi~inq and end of each stroke. If the forces required to cause these decelerations comes from rrscle pover, tben efficiency is lost. I t  is possible that this energy could be transferred to the locorntion rchanism of the bicycle without exerting uscular force to change the direction of the mvewt. To alleviate this potential problem, very high pedal velocities should be avoided. As the pedal force is increased, th absolute ptellofemral force per pedal stroke also increases. If the power oufqut required can be achieved by a low pedal force ard velocity, tbe increased efficiency, found i n  this rodel, my bold true. With respect to a PdC of exercise, ubere proloqed high powr outputs are not the issue the WCPn systu my offer a practical altemtive. For prsons vith a lhited h ip  or knee range of ation, chondrolaalacia patella, or other lhiting conditions, this pedalling system my prove advantageous. It is cweivable that a low mss lever driven system could be developed in order to satisfy both populations. Ihen using r bicycle for transportation and exercise, tba elhination of d e t r h t a l  stressed is of obvious benefit. The data sqgest that a 26.9l decrease in form par unit of mssectional area exists at the patellofemoral joint i n  the )ICPU in cowrison to the CPI( systu. The larger mre sporadic patellofemral forces calculated in tbe BW as colpared to the NCPH s y s b  my also cattribute to improper patellar tracking and excessive patellofemral force. btb  of these my contribute to chondmalacia ptellae. The data also suggest that both systms could psdbly be laproved by repitioning tbe pedal a n  or crank to a m  equally use the body's natural strengtb potrptial. The advantage of a push-pull lever WCR( cyst- offers a plausible altemtive to conventional pedalling system. VIII Symposium ISSS - 160 - Prague 1990 chvrs, R.R. and BILL, H.L.(198l),~urenent of pedal loading in bicycling: I1 analysis and r&ults, 3. Bioaecbanics, 14, 857-872. DICP;SOU, J.B. Jr. (1985) Preventing o v e n w  cycling injuries, The Physician and Sports Micine, 13,(10), 116-123. ELLIS,K.I.; SeEDBOW,B.B.; YKIGB1, V. and BlEON,D.(1980), &I evaluation of tbe ratio between the tensions a l q  the quadriceps t d m  ard tbe patellar ligament. Rqineerbq in Iledicine, 9,189-194. s .  GmTWIB, S.D.; W, K.B.;TaB, 11.; SELICMW, J. and KAPASWBI,A. (1985), lbire patterns: an accurate technique for deterahtion of the locus of the centers of rotation x, 3. Biomximics, 18, 501-509. (XmR, R.J., CAWIGj, P.P. and WPORIPWB,11., (1985), Xnee . flexor wmts &ring propulsion in cycling - a creative solution to Lolbard's Paradox, J. Biorecbanics, 18, 307-316. ~JLL, H.L. and JORGE, 1. (1985), A letbod for bicmechical analysis of bicycle pedalling. J. BioleChani~~,l8,631-61(. RILL, M.L. abi MVIS, B.R. (1981), lleasurmt of pedal loading in bicycling: I Inrtruwtation,14,843-856. IDIIBABD,Y.P.(1903), The action of two-joint mscles,A I. Pbys Ed. Res.,l),l41-145. WEnaLLFX,J: FJLL,I(.L. and ZAIJ.C,P.E. (1988), A lechanical decoupled tvo force component bicycle @a1 dynamometer. J.Bioaechanics,Zl, 375-386. PLACWAOE?', S. (1987), Anatomy for Rehabilitation, Bennet R y ~ a i c  Labs, Largo, FL, 76-80. SODM, P.D. and ABEYETA, B.A. (1979), P o r w  a ~ l i e d  to a bicycle during m m l  cycliy. J.Biomechanics,12,527-541. VIII Symposium ISBS Prague 1990 

A BIOMECHANICAL ANALYSIS OF CONVENTIONAL AND NON-CONVENTIONAL BICYCLE PEDALING MECHANISMS

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A BIOMECHANICAL ANALYSIS OF CONVENTIONAL AND NON-CONVENTIONAL BICYCLE PEDALING MECHANISMS

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