Locating Joint Axes of the Whole Human Body

Transcription

1 The 4th IFToMM World Cogress, Tape, Tawa, October 5-3, 5 DOI Number:.6567/IFToMM.4TH.WC.OS. Locatg Jot Axes of the Whole Huma Body M.J. Tsa, J.H. Chao, Y. R. Hwag 3 Professor, Dept. Mechacal Egeerg, Natoal Cheg-Kug Uversty, emal: mjtsa@mal.cku.edu.tw Seor Lecturer, Dept. Electroc Egeerg, Mg Chua Uversty, emal: chahog@mal.mcu.edu.tw 3 Graduated studet, Dept. Mechacal Egeerg, NCKU, emal: @mal.cku.edu.tw Abstract: I ths paper, a dual-mode 3D optcal measuremet system wth body scag ad moto capturg capabltes s used to fd the body jot axes. At frst, a perso should be scaed to costruct a body geometrc model. It s a wellstructured meshed body model that s the segmeted to 3 body lks. A body kematc model s created whch 48 jot axes have assged betwee the lks. The pattered markers are placed o the body for moto capturg. The equvalet jot screw (EJS) s obtaed by movg sgle degree of freedom of each jot dvdually. Ths study proposes four methods for fdg the body jot axes usg screw moto cocept. Evaluato of the four methods are also performed based o the error aalyss betwee captured data ad theoretcal path pots geerated by the EJS ther full moto rages. The results show that the deal jot method performs better tha others. It ca be justfed that, the covetoal assumpto of rotatoal jot for the body s vald for moto aalyss. For the purpose of applyg the EJS to aother huma model, ths study proposes a odmesoal process to regster the EJS dfferet huma models. Keywords: Dual quatero, Screw axs, Huma model, Jot axs fdg. Itroducto Recetly, the techque of 3D dgtal huma modellg for computer amato ad bo-mechac aalyss has bee mproved tremedously. The study of body moto requres two models. Oe s the body geometry model (BGM) that descrbes the persoalzed body shape; the other s the body kematc model (BKM) that defes the jot degrees of freedoms (JDOF) ad jot locatos of that perso. Two types of equpmet are eeded to costruct the BGM ad capture the moto data for BKM. These are the 3D body scaer ad body moto capturg (mocap) system. Ufortuately, the covetoal 3D body scaer caot capture body moto, whereas o mocap system ca buld a BGM. As a result, for body moto aalyss, the huma models were, fact, costructed by skeleto; ad artfcal fgures were created for moto amato. May kds of sesor have bee used the mocap systems to fd jot locato, such as electro-magetc sesor [], ertal measuremet ut (IMU) [, 3], ad optcal type [4, 5]. The IMU cossts a accelerometer ad a gyroscope whose measured data eed a base frame for tegrato, the result would subject to drftg ad accumulato errors. The optcal markers are mostly sphercal shape, a pot ca be computed by oe marker, so that at least 3 markers should be placed o a body lk to costruct a coordate frame. Besdes, they are dffcult to label the markers that causes matchg problem stereo computato whe the amout of marker s large. To avod ths problem, some mocap systems are marker-less, Gavrla ad Davs [6] ad Horaud et al. [7] usg mage cotour to fd body moto. Lucas ad Kaade [8] ad Sh ad Tomas [9] tracked some feature pots the body moto mage. Lu et al. [] used ths method to track face moto. Ths method does ot put ay sesor o to the body that makes the subject moves more freely. However, t requres a more sophstcated software algorthm, ad ts accuracy stll eeds mprovemet. Due to complexty of cotact geometrc betwee body boes, the relatve motos betwee pared boes do ot accordg to a fxed axs, rather, the axes would shft due to the cotact geometry of the par surface s ot uform. As a result, the overall moto screws of a body jot comprse a axode, whch s a collecto of all the ftesmal screw axes. For computer smulato, a JDOF s commoly represeted by oly a fxed screw. Ths s the so-called EJS. I ths paper, four methods are employed to fd the EJS. Comparsos of the correctess of the EJS from dfferet methods are made. Every EJS s the attached to ts correspodg lk geometrcal model, such as three axes may attach to the eck lk so that the head lk ca move wth respect to the chest model. I ths way, a BKM ca also be costructed. Combg the BGM ad BKM, the authetc body moto ca oly be realzed by the realstc persoalzed huma model. Some of the body jot movemets are ot provded by oly two par surfaces. Istead, the jot motos are compled by relatve movemets of several boes, such as the scapular, wrst, palm, ad foot, etc. They are all mult DOF jot. The movemet of scapular s provded by the relatve motos of the clavcle, the blade boe ad the humerus (called the shoulder complex) [-3]. Yag et al. [4] bult a eght DOF scapular model ad used Euler agle to descrbe the scapular movemets. Bottlag, et al. [] desged a akle jot fxture ad aalyzed the moto characterstcs due to the chage of jot axes locato ad oretato. Tujthof et al. [5] foud the axs of the akle jot from the CT scaed mage of the akle s extreme postos. Kloopcar ad Learcc[6] compared the rage of moto of a jured upper lmb wth that of a ormal arms usg actve markers mocap expermets. Ehrg et al. [7] made a survey of formal methods for determg the cetre of rotato of ball jots. For kematc ad dyamc

2 aalyss, researchers smplfed the body jots ad modelled the mult-freedom jot by a umber of sgle DOF jot; each jot has a fxed jot axs located relatve to the body structure. Although may methods to locate huma jot axes, ether -vvo or -vtro, have bee publshed, most of them worked merely o a specfc JDOF. For whole body moto aalyss, fdg all body jots to create a whole BKM s ecessary. Furthermore, oce the jot axs was located o-ste durg a expermet, the locato of jot axs wth respect to the huma body would be lost wheever the regstrato fxture s removed. Therefore, the located jot axes are applcable durg the expermet, let aloe to be used for aother huma models. To solve these problems, a stadardzed ad persoalzed body model s eeded ad accurate jot locatos should be obtaed to regster oto the ormalzed body model. As for the descrpto of rgd body moto, there are may data types used [8]. Amog them, Chasles moto, Rodrgues parameters ad Study s dual agle have bee used frequetly. Page et al. [9] expermetally aalyzed rgd body moto to determe fte ad ftesmal dsplacemets from pot coordates. Baroo ad Rava provded a over-determe (ODS) [] method that ca be used to compute the screw axes from fte motos of the lks. I ths paper, a persoalzed body geometrc model s costructed from 3D scaed data of huma body. The body model preserves the aatomcal features of the body so that a stadardzed dgtal BGM s bult []. The specal data structure of BGM ca be easly segmeted to 3 body lks for the purpose of moto aalyss. It s the ecessary to add jot costrats that descrbe the relatve moto freedoms of adjacet lks. Ths s to costruct a BKM. The BKM cotas the essetal kematc parameters that are requred to aalyze the moto characterstc of the perso. If the BKM has ot bee properly buld accordg to the persoalzed jot locatos, the body model could t replcate the accurate moto of that perso. Wthout accurate jot locato, the body kematc ad dyamc propertes caot be accurately computed, ad the bo-mechac aalyss would yeld erroeous results. The am of ths study s to fd all the jot axes of huma body to costruct a rgorous BKM for whole body moto aalyss ad amato. The mocap capablty of the same apparatus s used to fd the jot axes by capturg the markers attached o the body. The mocap expermet should be coducted o each dvdual JDOF. Ad the locato of the jot axes are regstered oto BGM to create a BKM for subsequet usages.. Dual-mode 3D Optcal Locator. Hardware Archtecture Tsa et al. [] costructed a dual-mode 3D optcal locatg system whch has body scag/mocap capablty. It s coveet to use because the regstrato betwee the scaed huma model ad the body moto data ca be doe automatcally. I ths study, the dual-mode system s used to costruct a body model as well as capturg the body moto of that perso. As show Fg., the system cossts of 4 modules of optcal 3D optcal locator, each module has CCD cameras wth 6x pxel resoluto. The mocap capturg rage of the whole system s about 5x5x (LxWxH) meters. Four Camera-Lk mage grabber cards are stalled to a PC wth 4 cores Itel processors. A trgger box s used to provde a 3Hz sychroous sgal to the all cameras for mage capturg. The system s developed uder Mcrosoft Vsual Studo.Net 8 developmet evromet. Fg.. The dual-mode 3D optcal locatg system. System Calbrato ad Regstrato The 3D optcal locators s calbrated by a D chess board that provdes x pot patter. After recogzg the corer pots o the chess board, the trsc ad extrsc camera parameters are obtaed usg a optmzato method. The the 3D system calbrato error ca be computed usg those CCD parameters ad the pot patter mages. Table shows the 3D system calbrato errors for the optcal modules. The average error are all uder.7 mm ad the stadard devato s about.5 mm. The precso of the system s adequate for measurg the locato of body jot. I ths paper, all the dmesos are measured mm. Table. 3D calbrato error of the four modules. Module I II III IV Average STDEV Max M Ut: mm Sce the optcal sesors are subjected to lght occluso problem, the 3D locatg system has four modules put aroud the huma body. Every module has ts ow coordate system after calbrato. A regstrato process s ecessary to brg the mocap data to a predefed world coordate system..3 Cubcal Markers There are two types of optcal markers commoly used by commercal mocap systems: the passve type ad actve type. The actve type emts lght by tself ad IrLed s mostly used. The passve type s made of reflectve materal, ad t s commoly sphercal shape. Sce the actve type markers eed a power source, the battery ad wrg may affect the body moto. To avod the matchg problem computato, each marker should have ts ow ID umber. Cubcal markers wth patters made of retro-reflectg materal were desged. As show Fg., each cubcal marker has oe face attached to the huma body, the other 5 faces have dfferet patters. Each patter represets a uque code so that t ca be recogzed by the computer algorthm. The marker wth matchg ID umber ay two cameras are used to compute ts spatal locato, ad

3 wll be output as a coordate frame. coordates: ˆ o [ LM,, N ; PQR,, ] S s s (3) (a) Fg.. Cubcal coded markers (b) 3. Jot Axes Fdg Methods Durg moto capturg, the marker locatos wth respect to the world coordate, MO, are recorded. To fd the jot axs betwee two adjacet lks, the marker frames of the two lks ca be used. After fdg the jot axs, t ca be subsequetly regstered oto the lk model. However, t s almost mpossble for the perso to move oe lk whle keepg all the other lks fxed. Sce most of the body jot have multple freedoms, t s also dffcult for the perso to move about oly oe sgle freedom of the jot,.e. let the moto geerated by a decoupled jot freedom. Therefore, relatve moto cocept s used. All the marker frames are trasferred relatve to ts prevous lk, called MP. The trasfer all the MP dfferet tme frames to the locato of tal tme frame; so that the moto ca be regarded as relatve to a fxed frame. Accordg to Chasles theory, every two locatos of a rgd body have a fte screw to represet the moto. As stated above, the body motos are complcate, the jot axes computed by successve motos would ot cocde. I ths secto, four methods to obta EJS are preseted. Fve types of error are also aalyzed for the evaluato of the four methods. 3. Fdg the Jot Axes I ths paper, dual quatero (DQ) [3] s used for calculatg twst screws stead of usg trasformato matrx. DQ represetato of relatve moto has the advatages of more effcet computer codg ad occupes less storage space. It also has lear property that ca be used for terpolatg ulke usg the matrx represetato. A rotato ca be represeted by a ut quatero: Q c c cjc3k cos s ( sxsy jszk) Where s the rotato agle ad s ( sx, sy, sz) s the rotato axs (ut vector). The relatoshp betwee two les ca be represeted by a dual agle: o cc d () Where s the agle betwee the two les, ad d s the dstace betwee the commo ormal of the two les. The spatal trasformato of a rgd body ca be represeted by a geerally screw moto. A screw ca be wrtte Plücker () Where s [ L, M, N] s the drecto cose of the screw axs, ad s o [ P, QR, ] s the resultg momet of the screw about the org. The a DQ ca be obtaed by combg () ad (3) to get: o Qˆ QQ o o ( cs) ( c s ) o ( d) ( ss ) S The screw dsplacemet from ˆr to ˆr ca be acheved by a geeral screw operator (half-agle operator): rˆ ˆ ˆ ˆ ˆ ˆ ˆ q( r) q q( r)kq (5) Where qˆ cos sˆ s s a ut DQ, ad Kq ˆ s the cojugate of ˆq, (K qˆ S), whch s equal to the verse of ˆq. Therefore, screw motos of a body ca be represeted by operatos of ut DQ. We wll use dual quatero to compute the body jot axes. DQ s rather abstractve ad s ot easly uderstadable. The dual agle axs, (, S) was used for presetato, sce t has more geometrcal meags ad s easly vsually coceved. The coverso from DQ to DAA s gve by: (4) q s = (6) s( ) o o d s s( ) cos( ) q q (7) s ( ) q ta ( ) c d c q c q c o o c From (8) ad (9), the ptch of the screw s: q d h () Let q ad q descrbg the trasformatos of two objects wth respect to the some coordate system, the relatoshp betwee the two objects s obtaed as: (8) (9) q q q () Referrg to Fg. 3, two lks ped by a jot move from tme frames t to t. MO s the trasformato (DQ) of a marker fxed o lk wth respect to the org tme frame. The trasformato [MP] betwee lk ad - ca be obtaed as: MP [MO ] MO ()

4 Some jot axes dslocate qute a lot at both eds of moto rage, whereas they vary lttle the mddle of travellg. Ths method takes the rato of travelg dstace as weghtg factors to all of the DQ. As show Fg. 5, f two postos spaed by a screw has bgger path, ths screw axs takes larger weghtg, whch s defed as: $ $ + Fg. 3 Relatve moto betwee two adjacet lks. Where MP s the DQ of a marker frame wth respect to ts prevous oe. Usg a left superscrpt to deote the referece tme frame, we brought all moto data of lk - to cocde wth ts tal tme frame MI: MI MO MO (3) Now t s possble to fd the movg axs betwee lk ad -. From Fg. 4, lk (-) at the tal posto ca be regarded as a base about whch lk s movg aroud by the costrat of a jot assumed betwee. The the moto screw of lk movg aroud the base, MB, cosecutve tme frame, ca be obtaed by: MB [ MP ] MP (4) t= + d + d P r Fg. 5 Path weghtg method. t=+ t=+ P w,,,, (7) P Where P ( r ) ( d ),,,, (8) The multply the weghtgs to (5) ad (6): qˆ w q ˆ (9) cˆ w wcˆ () w Fg. 4 Relatve moto of lk wth respect to ts prevous lk. 3. Fdg Equvalet Jot Axes A cotuous moto of a body jot s geerated by dfferet axes, the jot axes obtaed from dfferet tme frames comple a axode whch each screw has dfferet ptch. Ths fact, causes dffculty to aalyss the body moto. If the scatterg of jot axe s lttle, t s coveet to fd a uque EJS to represet a sgle JDOF. Fd the EJS, three methods were used: Method : averagg method Ths method drectly averages the real part ad dual part of all DQ: qˆ ˆ avg q (5) cˆ avg cˆ (6) Where s the total umber of screw axes. Please otce that the DQ parameters should be ormalzed to a ut DQ after ay computato, or else they caot represet a rgd body trasformato or a screw. Method : weghted averagg method Method 3: Mult-Over-Determe Method Charles theorem states that there s always a uque screw ca be computed from two locatos of a object. However, f the locatos are measured data, the data wll cota measurg errors. The screw computed by dfferet le segmet would yeld dfferet screw,.e. o uque screw ca be obtaed. Baroo ad Rava [] used Lagraga multpler to fd a optmal screw axs for multple le segmets that move betwee two measured locatos. Ths s the Over-Determe System (ODS) method. Sce the body moto data are captured cotuously, there are a sequece of screw axes computed. The ODS method should be modfed to accommodate successve screw locatos. To solve ths problem, Tsa, et al. [4] modfed the ODS to MODS (Mult-Over- Determe System) method so that a uque optmal screw axs ca be obtaed from multple locatos of screws. I ths paper, we used the method to fd the EJS ad called ths the Method 3 wthout gve the detals. The process of expadg the ODS method to MODS method s gve by [4]. 3.3 Fdg Ideal Jot Axs (Method 4) The EJS stll has fte ptch that s ot coveet for practcal usage. For easer smulato ad aalyss, body jots are geerally modelled as a revolute jot, whch s a screw of zero ptch. The the screw s regarded as a le. Ths s the so-called a deal jot because the pure rotato

5 has bee assumed. The deal jot assumpto has the advatages for smplfyg moto aalyss ad for makg/cotrollg humaod robots to mtate the body moto. The moto produced by the jot s a pure rotato, ad the moto trajectory of ay pot o the body s a crcular arc. The locus of a pot o the movg body les o a plae. Uder ths crcumstace, the org of lk wll move wth respect to lk -, [MB] Eq. (4), a crcular arc. Frst we fd the plae or rotato by fttg all the orgs of the movg frame. The ft a crcle by projectg those orgs o to the plae. The le that passes through the ceter of the ftted crcle ad s perpedcular to the ftted plae s the rotatoal axs. Fally costruct the le (rotato axs) usg DAA otato. The overall process s gve by the followg steps:. The equato of a plae s gve by: x by cz d () Applyg Pseudo Iverse method to fd the coeffcets of the plae from the path pots of movg frame. y z x b y z x T T c, NX S, X N N N S d y z x () Normalze the coeffcets of the plae equato to get the ormal drecto (s) of the deal jot axs.. Costruct a ew coordate system usg the pla ormal as the z-drecto. The trasfer all the moto data to the ew coordate system usg Equatos (3) ad (4). Ux Vx Wx Cx Uy Vy Wy C y M (3) Uz Vz Wz Cz D 3D P M P (4) Where P 3D s the orgal 3D path pot; P D s the pots after trasferrg to the plae. 3. Projectg the path pots oto the plae, ft a crcle for these pots. The equato of a crcle s gve by: x y dxey f (5) Put the projected pots to (5), ad fd the crcle coeffcets usg pseudo verse process aga. x y x y d x y x y T T e, NX S, X N N N S f x y x y (6) The ceter ad radus of the ft crcle ca be obtaed as: d e C,, (7) r d e 4 f (8) 4. Fally trasfer the ceter C o the D plae to 3D, ths s the pot that the rotatoal axs passes through. C M C (9) The drecto of deal jot axs s parallel to s ad passes through pot C, the jot axs ca be wrtte DAA format as: ˆ ( ) ( o Q S d ss ) (3) s OC s (3) Sce ptch of the deal jot s zero, we ca coveetly put = ad d =,.e. oly dual part (pure dual vector) of the DQ s of sgfcat. 3.4 Deftos of EJS Error Sce actually there s o such a fxed jot axs exst betwee two adjacet lks. The computed EJS (cludg deal jot axs) are subjected to error. Besdes, dfferet methods to fd the EJS may have dfferet level of errors. If the error s too bg, the EJS caot be used for moto aalyss. To verfy the valdty of the four jot fdg methods, crtera should be defed. I ths paper, we omate fve methods to evaluate the errors, whch are descrbed as follows: Error : Ceter error After gettg the EJS, set a plae wth plaar ormal parallel to EJS ad passg through the frst data pot. The follow the same steps the prevous secto to fd a crcle by fttg the projected data pots o the plae. As show Fg. 6, the dstace from the ceter C(x c, y c, z c ) of fttg crcle to the pot P E (x E, y E, z E ) at whch the EJS tersects the plae s defed as the ceter error. Plae E E C E C E C E P C x x y y z z (3) EJS Fttg crcle Error Error 5 Error 4 Error Error 3 Fg. 6 Defto of errors Orgal pot Projected pot Teortcal pot Ceter pot of fttg crcle Traslato correspodg to the ptch Error : Crcular error The averaged dstace from the projected data pots to the fttg crcle s called the crcular error, gve by: E c c c x x y y z z r (33) Error 3: Plaar error The averaged dstace of the data pots to the fttg plae. Ths s to measure the off-plae error f the jot axs s a pure rotato. E3 ax by cz d (34) Error 4: Ptch error If the EJS has o-zero fte ptch, plaar error (Error 3) s ot approprate to evaluate the accuracy to the jot.

6 The plaar error should mus the travel dstace alog the axal drecto at the correspodg rotato agle () due to o-zero ptch. E 4 ax by cz d h (35) Error 5: 3D error The total 3D error s defed as the dstace betwee data pots to ther theoretcal postos twsted by the EJS. Ths s obtaed by combg Error ad Error 4: 5 4 E E E (36) 4. Expermet o Auto Jot Axes Fdg 4. The Structure of Body Geometrcal Model (BGM) The 3D body scaed data s a uorgazed pot cloud. There s o correlato betwee the dscoected pots so that the scaed pot cloud caot be used as a body model. To fd the jot axes from the body model ad regsterg the jot axes o to the body, t s ecessary to orgaze the pot cloud to a well-structured body model. Frst of all, the aatomc features of body should be recogzed so that body lks are segmeted to establsh a meshed structure of body model, the BGM. By assgg the JDOFs oto the lks, jot fdg process ca be coducted to locate the jot axes. Ad fally, the jot axes should be regstered o to the BGM to obta a BKM for persoalzed moto aalyss ad replcato. Tsa [] preseted a method for costructg a wellorgazed BGM. The BGM s a mesh structure orderly accordg to body aatomc features. The vertexes of the body mesh are called the structure pots. The BGM s dvded by logtudal pots ad grth pots so that the whole body s deleated by body geodesc coordates (BGC) that smlar to those of the earth. The BGC are ormalzed ature that do ot subject to dmesos, geder, ad age of the perso. As depcted Fg. 7, the BGC s desgated as (g, h); e.g. (38, ) ad (38, 7) are located at the 38 grth of the torso o the th ad 7 th structure pots of the grth whch are the left ad rght bust pots respectvely. (a) Body scaed pots (b) Body feature curves the bust grth (38, ) Y (38,) (38,7) (38, ) X (38, 3) (38,4) (38, 5) (c) Structure pots of the 38th grth (38, 6) Fg. 7 The defto of body JDOFs. (d) Meshed body structure As show Fg. 8(a), the BGM s subsequetly segmeted to 3 lks for moto trackg. Therefore, f the jot axes are foud, they ca be regstered oto the BGM usg the BGC as referece. The jot axes ca be reused by the same perso for ext expermets or be used by dfferet perso sce the body shapes are commo ature after structural ormalzato. Rght scapula Chest Rght upper arm Rght lower arm Rght had Rght fgers Hp Rght thgh Rght lower leg Rght foot Rght toe Head (a) Neck Left scapula Left upper arm Wast Left lower arm Left had Left fgers Left thgh Left lower leg Left foot Left toe (b) Fg. 8 The defto of body JDOFs. DOF DOF 3 DOF 4 DOF 4. Expermets The BKM bult by ths paper has totally 48 degrees of freedom (DOF). As show Fg. 8(b), four DOFs are assged to the eck, wast, left ad rght scapulae, whch oe sldg freedom s gve to smulate the stretchg freedom ad three are used to smulate the rotatoal freedoms of sple ad scapula; Three rotatg DOFs are assged to the shoulder ad hp jots; Two revolute DOFs are assged to the elbow, wrst, kee, ad akle jots. Oe DOF s assged to the grp ad toe, although there are a lot of moto freedoms provded by the fgers ad toes. Ths s due to the characterstc of ths optcal locator does ot sut for small movemet. I fact, a realstc had model had bee costructed by [4] usg smlar cocept. I order to acqure better moto data, the actor wears a lght color leotard. As show Fg. (b), every lk of the body s affxed at least oe cubcal marker. After a prescag, the markers are recogzed, ad ther spatal locatos are regstered to the BGM to get tal postos of MO (marker to the org). The automatc jot axs fdg process should be coduct for each JDOF dvdually. For mult-freedom jot, a jg may be eeded to costra the moto be geerated by oly sgle freedom. For example, to fd the yaw rotatoal axs of the shoulder jot, be careful the moto does ot couple wth ptch or roll movemets. I each jot moto, at least pctures are take at 3Hz. Cotue the expermet utl all 48 jots fsh capturg. The four jot fdg methods Sectos 3. ad 3.3 are used to compute the EJS. Errors are also estmated accordg to Secto 3.4. The results show that, for the jots havg larger moto rage (such as the yaw freedom of wast, ptch freedom of elbow, ad kee), the resultg axes locatos are close by ad the errors are small comparg to other jots wth small moto rage. Fg. 9 llustrates the jot axes of wast yaw ad elbow ptch freedoms foud by the four methods. I the fgures, the EJS obtaed from Method s deoted by $. Smlarly $ s for Method ; so does $ 3 for MODS method ad $ 4 for deal axs method. The blue porto of the screw axs dcates the legth of the ptch. The axode s draw as a ruled surface usg fve fte moto screws as geerators (show loger les o the surface), whch the legth

7 of gree le dcates the ptch of the correspodg screw. The Plücker coordates ad fttg errors of the EJS for left elbow ptch freedom are gve Tables ad 3, respectvely $ - $ $3 5 (a)wast Yaw $4 Axode Ut: mm $ $ - - (b)elbow Ptch $3 $ Fg. : Comparso of akle roll jot axs locatos: (a)(b) from deal jot method, (c)(d) from Referece [5] Fg. 9: Wast yaw ad elbow ptch EJS obtaed by 4 methods. Table EJS for left elbow ptch freedom. Method L M N P Q R Ptch I II MODS Ideal Ut: mm Table 3 Errors of left elbow ptch EJS. Method I II MODS Ideal Error AVE STD AVE STD AVE STD AVE STD E E E E E Ut: mm For the scapular jot, the EJSs obtaed by the four methods are rather scattered. Ths s due to the moto s produced by mult-boe cotact, ad the movg rage of each JDOF s relatvely small. The captured data heretly has system error so that t has bgger error comparso to the jot havg larger moto rage. Besdes, all JDOFs of scapula are coupled together by terlockg of boes ad tedos. It s dffcult to cotrol the scapular to move by sgle decoupled freedom. For the akle jot, the resultg EJSs of akle jot by four methods are also close together, as show Fg.. It shows the axs locato of akle roll freedom (Subtalar Jot Axs) comparg to that obtaed by Refereces [7] ad [8]. The results are closed by ad are all reasoable. Z 3 - Y $4-5 $3 $ Axode -4 - $ 4 X 6 mm Fg. : EJS of akle roll. Fg. dsplays all the body jot axes foud by the four methods. From the fgure, t ca be observed that some of the jot axes do ot le sde the body. Those EJSs belog to the jots that havg small moto rage, especally o the roll freedom of mult-freedom jots. Ths may due to the multple types of errors, e.g. error from the moto ot geerated by sgle JDOF, or error from the mocap system. However, t s terested to kow whch method s the better oe to locate the jot axes. Ths s evaluated by ther fttg errors. Error 5 s the total 3D error, t s chose as a crtero. For each JDOF the whole body, we fd the bggest Error 5 amog the 4 methods. The dvde the bggest error to 5 levels, ad gve a grade pot to 5 for all methods. The best oe get 5 pots, ad the worst oe get pot. Table 4 lsts the fal grades for the 4 methods by averagg all the 48 EJSs. (a) Method ($) (b) Method ($) (c) MODS ($3) (d) Ideal jot ($4) Fg. : The whole body EJS obtaed from: (a) Method, (b) Method, (c) MODS, ad (d) Ideal jot method Table 4 Evaluato for the 4 methods. Method I II MODS Ideal Score As expected, Method got hgher score tha Method. Sce Method takes the travel legth to accout, t yelds better result tha Method wthout weghtg. As expected, Method 3 (the MODS) has eve better result comparg to the other two prevous methods. The MODS fd the mmum error by cosderg the screw moto characterstcs. It should perform better tha the frst two methods that smply mapulates the DQ parameters. It s surprsg that the Method 4 (deal jot assumpto) got the hghest score. 4.3 Regstrato of EJS oto Body Lk Frame The EJS obtaed ths paper are refereced to ts prevous lk. Actually, the computed EJS s refer to the

8 marker attached o the surface of ts prevous lk, as show Fg. 4. Durg mocap, oly the markers ca be traced. The locato of each marker s computed from the stereo vso system, ad a marker frame [M ] s obtaed. For each body lk, we ca buld a coordate system from the structured pots of the frst grth. The costructo of lk frame s show Fg. 3. The frst grth of lower arm (the elbow grth) has structure pots. The org of the lk s puttg o the cetrod of the elbow secto. The x- axs les alog the loger prcple axs whereas the y-axs le alog the short prcple axs. The z-axs s defed by the rght had rule. Ths s the lk frame [L ]. Usg Eq. (37), we ca get the trasformato from [M ] to [L ], ths s ML. As llustrated Fg. 4, to regster the EJS oto the lk frame, all the EJS should be multpled by ML. ML [L ] M (a) Mesh structure of huma had (37) grths of lower arm 9 87 Body scaed pots (b) Grth of body lk (upper arm) W 3 9 (c) Structure pots of a grth Y Cetrod Structure pots Fg. 3: No-dmesoal regstrato of EJS o to the lk frame. Frst grth of the lk Structure pots of lk Frame ML Cubcal marker Global frame Fg. 4: Trasformato from marker frame to lk frame. Besdes, parameters EJS s subjected to the chage of body dmeso sce the dual part of screw ad DQ cota momet ad ptch whose dmeso s legth. Sce huma begs have smlar jot structure, the jot axes locatos obtaed ths study may be used for aother perso for o-rgorous applcatos. Ths s to avod the tedous ad troublesome of jot fdg process. No-dmesoal parameters are eeded f the EJS s to be used for dfferet people. We should ormalze the screw parameters term of the correspodg lk feature legth. The lk characterstc legth s takg as the wdth of the frst grth of the lk, as show Fg.3. Accordg to the 6 7 X defto of structure pot assgmet, pot umbers 6 ad 6 are the tersectos of the body grth wth the loger axs. The dstace (6, 6) s the wdth of the grth (W ). The real part of the screw coordates deotes the drecto cose that s o-dmesoal. Oly the dual part [P, Q, R] ad the ptch [h] eeds to be ormalzed, ad are gve by: ' P ' Q ' R ' h P, Q, R, h (38) W W W W Whe applyg the EJS to aother perso, we should compute the frst grth wdth of the lk. The multply the screw parameters by the wdth to get the relatve locato wth respect to the lk frame. 5. Cocluso I ths paper, the procedures of fd the locatos of jot axes based o a dual-mode 3D optcal locator s preseted. The purpose s to costruct a BKM for body moto aalyss. The BKM s based o the BGM that s created by the scag fucto of the dual-mode system. The the jot fdg processes are coducted by usg the mocap fucto of the same apparatus. Ths paper provdes four methods to fd the EJS. Evaluato of the four methods are also based o the error aalyss. As a result, Method 3 performs better tha Methods ad sce t cosder the geeral screw moto characterstc. However, t also take logest computatoal tme. Method drectly averagg the DQ parameters that s smplest ad yelds the fastest computato for t does ot requre matrx verso. Surprsgly, the deal jot assumpto outperforms all other three methods by cosderg whole body JDOFs. Based o the error aalyss, t s cocluded that ether the body jots are pure revolute, or are they movg by fx screws wth costat ptch. For f there s a twst () about a o-zero ptch (h ) screw, there would be a offset geerated by the moto (d=h). Actually, o such lk offset s observed after the body motos. Would ths suggest the body jots have eglgble ptches? Therefore, the covetoal assumpto of rotatoal jot for the body ca be justfed. The output of screw coordates s regstered oto the lk frame. It s the o-dmesoed by troducg the wdth of the frst grth of the lk. The the EJS foud for oe perso ca be used for aother people to elmate the tresome jot fdg processes. The accuracy of the EJS depedg o the persoal ablty of cotrollg the jot movemet. For example, the jot freedoms of the scapula help to crease the moto rage of upper lmbs. But ts moto drecto s ot uque. Sce ts moto rage s small, wth costat system accuracy, the captured marker posto have relatve large errors. Ths ca be mproved by the assst of gudg devces so that the more accurate jot locatos ca be foud by costrag the uwated moto drectos durg expermet. Ackowledgmet The authors wat to thak the facal support from Natoal Scece Coucl, Tawa. Cotract No: NSC - -E-6-5. Refereces [] Bottlag, M., Marsh, J.L., ad Brow, T.D. (999), "Artculated exteral fxato of the akle: mmzg

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