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joint center calculation in Dynamics of Human Gait (Vaughan etal.)

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  • joint center calculation in Dynamics of Human Gait (Vaughan etal.)

    Dear All,

    I have been trying to verify some equations from book Dynamics of Human Gait, by Christopher L Vaughan, et al.(second edition).
    For instance, to calculate uvw coordinate system from markers (external landmarks) of right foot according to equations B2, B3 and B4 (page 87&88) we have:

    u=(p1-p2)/norm(p1-p2); (Eg. B2)
    w=cross(p1-p3,p2-p3)/norm(cross(p1-p3,p2-p3)); (Eq. B3)
    v=cross(w,u); (Eq. B4)

    where p's are markers position obtained from Table 3.4 on page 24.
    p1=[0.157 0.142 0.057]; % R. Metatarsal head V
    p2=[-0.016 0.207 0.032]; % R. Heel
    p3=[0.033 0.155 0.067]; %R Lateral malleolus
    Then, the obtained values for unit vectors of uvw system are u=[0.9277 -0.3485 0.1341];w=[ 0.1280 0.6340 0.7627];v=[0.3508 0.6904 -0.6327];

    Now, when we proceed to equation B5 and B6 (page 88) to calculate position of the ankle joint and longest toe, we have;

    prankle=p3+0.016*A13*u + 0.392*A15*v+0.478*A17*w; (Eq. B5)
    prtoe =p3+0.742*A13*u + 1.074*A15*v-0.187*A19*w; (Eq. B6)

    where A's are anthropometric data for 'Normal male' data obtained from Table 3.2 page 19.
    A13=0.260; % R. Foot length
    A15=0.060; % R. Malleolus height
    A17=0.074; % R. Malleolus width
    A19=0.098; % R. Foot breadth
    Finally we obtain prankle=[0.0496 0.1922 0.0797]; prtoe=[0.2322 0.1206 0.0381];

    HOWEVER, these data differ from data authors reported for prediction of right ankle joint center (R. Ankle 0.059 0.204 0.090) and toe (R. Toe 0.261 0.232 0.133) in Table 3.5 . on page 28. Similar happens with the rest of joint centers data.

    To someone who is more familiar with book content these are my questions: What am I missing here? Tables captions said that parameters/markers positions etc. refer to the moment T=0.00s for Normal Male at , i.e. right heel strike, thus that should be same instance of time? Or perhaps not all data shown are taken from the same trial? The reason for that suspicion comes from fact that markers p2 and p9 which are supposed to be right and left heel respectively (Table 3.4 page 24) suddenly change to different values in Table 3.5. page 28 (although tables captions refer to same instance of time T=0)!? In case data do come from different trials I do not see much point of showing them in tables after subsequent equation derivations since one cannot then verify those with values in tables? Did some kind of filtering took place?

    Thank you. Best, Tomislav.

    Tomislav Pribanic, M.Sc., EE
    Department for Electronic Systems and Information Processing
    Faculty of Electrical Engineering and Computing
    3 Unska, 10000 Zagreb, Croatia
    tel. ..385 1 612 98 67, fax. ..385 1 612 96 52
    E-mail :

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