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  • Calculation of ankle joint forces and moments

    Hi all,
    I have a question regarding calculation of ankle joint forces and moments which also has been explained by Prof.Winter (biomechanics and motor control of human movement,3ed,chapter 4).
    I cannot understand why the effect of muscle activity (muscle force vector) is not considered in linear equation of motion and it can just be seen in angular equations?
    Regards
    Zahra

  • #2
    Re: Calculation of ankle joint forces and moments

    Hi Zahra,

    By "linear equation of motion" I assume you're referring to the calculation of the resultant joint force.

    You can't make any strong inferences on muscle force from the resultant joint force because the resultant is the sum of all internal force in the joint, not just the muscle forces. For example you could have a small resultant joint force but a large muscle force if the joint contact force is also large.

    The resultant joint moment is similarly the sum of the moments from all of these internal forces, but because the muscle forces are usually the only internal forces that have both large magnitudes and large moment arms, it's often reasonable to assume that the resultant moment is generated primarily by muscles.

    Ross

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    • #3
      Re: Calculation of ankle joint forces and moments

      Hi Dr.Ross,
      I thank you for your answer, but I did not understand the whole concept yet. Do you mean muscle force is a part of joint reaction force therfore there are two unknowns in equation, so we can neglet muscle force in linear equation and compute it through sum of moments.
      I could find examples ,arm carring load , and muscle force as well JRF both are considerd in linear equation.
      Zahra

      Comment


      • #4
        Re: Calculation of ankle joint forces and moments

        Hi Zahra

        You can look at to these papers, may be you can find your answer on them.
        Best regards,
        Ali

        1_ Arampatzis, A., Morey-Klapsing, G., Karamanidis, K., DeMonte, G., Stafilidis, S., & Brüggemann, G.-P. (2005). Differences between measured and resultant joint moments during isometric contractions at the ankle joint. Journal of biomechanics, 38(4), 885–892. doi:10.1016/j.jbiomech.2004.04.027

        2_ Arampatzis, A., Karamanidis, K., De Monte, G., Stafilidis, S., Morey-Klapsing, G., & Brüggemann, G.-P. (2004). Differences between measured and resultant joint moments during voluntary and artificially elicited isometric knee extension contractions. Clinical biomechanics (Bristol, Avon), 19(3), 277–283. doi:10.1016/j.clinbiomech.2003.11.011

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        • #5
          Re: Calculation of ankle joint forces and moments

          Originally posted by safaee View Post
          Hi Dr.Ross,
          I thank you for your answer, but I did not understand the whole concept yet. Do you mean muscle force is a part of joint reaction force therfore there are two unknowns in equation, so we can neglet muscle force in linear equation and compute it through sum of moments.
          I could find examples ,arm carring load , and muscle force as well JRF both are considerd in linear equation.
          Zahra
          Yes, it comes down to having more unknowns than knowns in the equations. Here's an example. When we calculate the resultant joint force (Fres) and moment (Mres) from inverse dynamics, these vectors are balanced out internally by the vector sums of the forces and moments from all force-carrying structures in the joint. Suppose these forces consist of muscle (Fm), joint contact (Fc), and ligament (Fl) forces:

          (1) Fres = Fm + Fc + Fl
          (2) Mres = Rm*Fm + Rc*Fc + Rl*Fl

          where Rm, Rc, and Rl are the moment arms to the joint rotational center. Even if you know the moment arm for every force in the joint, or a "net" moment arm for a "net force" (e.g. the total muscle force), there are still too many unknowns. We can make some assumptions to simplify the problem. For example it can sometimes be assumed that ligament forces are small (Fl << Fm and Fl << Fc). Then the equations become:

          (1) Fres ~= Fm + Fc
          (2) Mres ~= Rm*Fm + Rc*Fc

          Muscle forces are tensile and often compress the joint surfaces together, so Fm and Fc can be similar in magnitude and dissimilar in direction. Therefore you often can't drop Fm or Fc from (1). However, muscle moment arms are typically much longer than contact force moment arms (Rm >> Rc), in which case you can reduce the equations to:

          (1) Fres ~= Fm + Fc
          (2) Mres ~= Rm*Fm

          So now we can say that the resultant moment is due mostly to Fm, but the resultant force is still indeterminate in Fm and Fc. This is why you often see inferences on muscle force drawn from Mres but not from Fres. There are a number of approaches you can take to get around the problem of having more unknowns than knowns when calculating the internal forces. Static optimization is a popular one.

          There are certainly examples in the literature where conclusions on Fm or Fc have been made purely from Fres, and there may be particular situations where this is appropriate, but as a general guideline I think it is a risky step to take.
          Last edited by Ross Miller; April 16, 2012, 10:11 AM.

          Comment


          • #6
            Re: Calculation of ankle joint forces and moments

            Thank you for clear answer.Would you please possibly let me know if I explain the mentioned Winter'e example right.

            F(JRF)= muscles forces+ contact forces + ligament,... which already has solved by static optimization.

            So according to the book:
            Net moment around ankle= muscle moment + JRF moment + GRF moment

            Now here is my question: if JRF already has the effect of muscle force in it, arenot we considered the muscle moment twice?
            Soulden't we compute muscle force and subtract it from FJRF and then calculate JRF moment?
            Thank you again

            Comment


            • #7
              Re: Calculation of ankle joint forces and moments

              If you sum the moments about the ankle joint center, the JRF has no moment arm, so it's not counted twice in the calculation of the muscle moment. If you sum the moments about the center of mass, then the JRF has a non-zero moment arm, but then gravity has no moment arm, the moment of inertia changes, and other moment arms change, so that everything stays in dynamic equilibrium.

              What you're referring to as the muscle moment is what I was referring to as the resultant moment (Mres). The "net moment about the ankle joint" is the inertial term (I*alpha). In 2D you should get the same Mres regardless of what point you sum the moments about, which is a good check to do.

              Ross

              Comment


              • #8
                Re: Calculation of ankle joint forces and moments

                I think the answer is that the joint is being modelled as a frictionless pin-joint (in 2D), and the muscle as a "torque motor". So, it is assumed to generate a pure moment about the joint. It's just one of the many assumptions needed for inverse dynamics.

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                • #9
                  Re: Calculation of ankle joint forces and moments

                  Thank you Ross, I've been really learning from each of your invaluable comments.
                  I am sorry , I forgot to mention the equilibrium point . As you well explained , and according to Prof.Winter explanation , it is around COM.
                  I checked moments around ankle joint and the answer was the same.

                  Regards
                  Zahra
                  Last edited by Zahra Safaeepour; April 21, 2012, 03:22 AM.

                  Comment


                  • #10
                    Re: Calculation of ankle joint forces and moments

                    Thank you Ali,
                    I downloaded two articles and I will read them preciesly.
                    Regrads
                    Zahra

                    Comment


                    • #11
                      Re: Calculation of ankle joint forces and moments

                      Dr. Kirtley,
                      Hi,
                      It's my pleasure to hear from you as I 've found your book really useful especially for teaching gait biomechanics to medical students.
                      I also found the mentioned example in your book too (1th ed, chapter7, page122). There is again joint reaction force assumed in stationary position but I cannot distinguish if it contains the effect of muscle force and the other forces ? On the other word, what do you mean here by joint reaction force?
                      About the simplification and the assumption of ‘‘frictionless joint'' I do agree with you but what do you mean by pure moment?
                      Regards
                      Zahra

                      Comment

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