Announcement

Collapse
No announcement yet.

Vertical and leg stiffness

Collapse
X
 
  • Filter
  • Time
  • Show
Clear All
new posts

  • Vertical and leg stiffness

    Hi,


    Iam new here and in Biomechanics So I hope that you can help me a little bit.

    Iam trying to calculate CoM position by double integration of acceleration during hopping.


    I know that:

    Fv – P = m . a

    And velocity:

    Integral (Fv – P ) = m.V + constant according to [1]

    [1] Cavagna G.A., J. Appl. Physiol., 1975. 39(1): p. 174-179.

    The value of constant is zero when a subject begins to move on the platform
    from the resting condition (V = 0). This means that after the first hop on the force plate the initial velocity (the velocity that we touch on the force place) is no longer zero. I just have one force plane available (60 cm X 40 cm). How can I calculate this velocity (this constant) ?

    Another question is this:
    To calculate leg spring stiffness I need to calculate the Length spring change that is calculated by

    CoM vertical length change + standing CoM position * (1-cos alpha)


    How can I determine the standing CoM position?? Most of the papers don’t mentioned how this is done and some use the distance from (greater trochanter to floor). There is another way to determine the standing CoM position ? Or I need to use the distance from greater trochanter to floor?


    Kind regards,
    Armindo

  • #2
    Re: Vertical and leg stiffness

    Hi Armindo,

    I don't think I understand your first question. If the subject started at rest then the integration constant for calculating velocity is just V = 0 like you said. Are you splitting the acceleration up into individual hops? Why not just integrate the entire time series at once? If this is problematic, you could also assume V = 0 midway through the flight phase. This assumption can be faulty if the take-off and landing heights differ substantially but it should be pretty close.

    To calculate leg stiffness, I think the initial "spring length" is often defined as the distance between the hip and the center of pressure at initial ground contact (e.g. http://jeb.biologists.org/content/185/1/71.long).

    Hope this helps,
    Ross

    Comment


    • #3
      Re: Vertical and leg stiffness

      Armindo,

      The initial velocity is determined using the impulse-momentum relationship. The procedures are outlined in McMahon et al. (1987). Groucho Running. J. Appl. Physiol. 62(6): 2326-2337.

      Brent

      Comment


      • #4
        Re: Vertical and leg stiffness

        Thank you for the help.

        The first part of the question is solved (in relation to velocity).

        However i still have some doubts about how to determine Length spring change.

        Many papers only mentioned that they used a force plate (without video) so how they were able to assess Length spring change ?

        According to several papers like [1,2], L0 is the distance measured from CoM (or greater trochanter to floor) to the floor (center of pressure I suppose) at initial ground contact (so the CoM is not on top of the foot). However if they just use a force plate and the subjects are running how they measure this distance?

        Some papers mentioned that this distance is the standing leg length? What this means? That they measured the distance (let say from greater trochanter to floor) when subjects were standing in an upright position and they measured this distance in this way?

        Any help would be appreciated...

        kind regards



        [1]Farley C., et al., The Journal of Experimental Biology, 1993. 185(1): p. 71-86.
        [1]Butler R.J., et al., Clin Biomech, 2003. 18(6): p. 511-517.

        Comment


        • #5
          Re: Vertical and leg stiffness

          If kinematic data are not measured/mentioned, I would suspect they measured the leg length manually and used that as L0. Farley et al. (1993) has a table with leg length data.

          In any case for stiffness I think the change in length (which you get from processing the acceleration data), not the absolute length, is the important variable. Any stiffness in general is (change in force) / (change in length), i.e. you should get the same stiffness regardless of the value of the initial length.

          For example in the mass-spring model that these analyses are based on, the stiffness is parameter of the model. You can specify any initial position arbitrarily, but it does not change the stiffness.

          Ross
          Last edited by Ross Miller; July 18, 2011, 02:34 PM.

          Comment


          • #6
            Re: Vertical and leg stiffness

            As Ross stated, change in length is the key point and comes from either kinematic data or acceleration data. L0 is standing leg length so distance from greater trochanter to floor when weight bearing.

            Comment


            • #7
              Re: Vertical and leg stiffness

              Thank you for all the help.

              I agree with Ross in the situation where we are measuring the vertical stiffness (and we just need the Delta y). However in leg stiffness We have kleg = Fmax/Delta L

              Delta L = Delta Y + L0* (1-cos alpha)

              Delta Y = CoM vertical length change
              L0 = standing CoM position

              The variation of Delta Y is usually only a few centimeters so if we dont measure well the L0 I think that we can get big errors.

              Nevertheless this is probably one limitation of the methods.

              I still have one doubt that I have not been able so solve. The doubt is how to determine in leg stiffness (not in verical stiffness) the delta Y. Accordint to [1]

              [1] Cavagna G.A., J. Appl. Physiol., 1975. 39(1): p. 174-179.

              Ther is a procedure that can be used however Cavagna used a 4 meters force plate and was able to get a comple stride and calculate velocity as explained in the above paper. But how can we calculate the Delta y if we just have one force plate (60 x 40 cm)? Several studies used this type of force plate but dont explain how they get CoM vertical length change (delta y).

              Can some one help me on this please.


              kind regards
              Armindo,
              Last edited by Armindo Marques; July 19, 2011, 01:55 PM.

              Comment


              • #8
                Re: Vertical and leg stiffness

                Hi Armindo,

                With only one footstep, you lack the complete information that would enable you to integrate acceleration (a = Force/mass) and use periodicity constraints to determine constants of integration.

                Nevertheless, if you are willing to assume that the body is structurally and functionally symmetrical, you can make an estimate by applying your measured forces to both feet.

                You will need EITHER (A) a "good" measurement of the subject's mass, preferably by having the subject stand on the force plate, while wearing all the experimental apparatus, or (B) a "good" measurement of ground contact timing (heel strike and toe off) of the foot that does Not step on the force plate.

                Then, you take two copies of the forces measured from one foot, and shift them in time by exactly 1 step period.
                You can determine the step period using either (A) or (B) from above:
                (A) if using a good measurement of mass and assuming symmetry, the time shift you are adjusting between left and right heel strikes, combined with the duration of the GRF you measured, defines the Stride time. You can solve for the time shift from equilibrium between gravitational force (M*g*Tstride) and integrated ground reaction forces for the two legs (INTEGRAL(Fz*dt), from 0 to Tstride).
                or
                (B) using measurements for heel strike and/or toe off of the opposite foot, you just shift a copy of the forces to match the measured timing.

                Once you shift the forces, you have an estimated full-stride force record. Then you can use Cavagna's methods with no problem.

                Remember also to reverse the sign of Medio-Lateral forces in the copied version.
                And please note that there are various ways this can go badly: any "bad" estimate of mass for method A will mess up the timing shift; any subject that is not really walking symmetrically will lead to nonsense data; etc.


                As an alternative, you can do independent measurements of the forces on the two feet on successive trials. Then you align them in time using a Mass or Timing measurement, and you don't have the weakness in cases of asymmetrical human subjects. But then you have the converse problem, of using measurements from two feet that never actually happened together in real-time.

                But, if you are doing an experiment with a strong main effect, these techniques will likely be sufficient for what you are hoping to observe.

                -Peter Adamczyk

                Comment


                • #9
                  Re: Vertical and leg stiffness

                  Hi Peter,

                  Thank you for the help. I understand the process (B) but dont understand very well the process (A) can you elaborate a little more or do you have any exemple that I can see?

                  kind regards
                  Armindo
                  Last edited by Armindo Marques; July 21, 2011, 05:47 PM.

                  Comment


                  • #10
                    Re: Vertical and leg stiffness

                    The first question was already solved. I can get velocity = 0 if the subject started at rest.

                    However the other question related with leg stiffness (not vertical stiffness) during running is not completely enlightened.


                    The doubt is how to determine in leg stiffness (not in vertical stiffness) the delta Y. Accordint to [1]. There is a procedure that can be used however Cavagna used a 4 meters force plate and was able to get a complete stride and calculate velocity as explained in the paper. But how can we calculate the Delta y if we just have one force plate (60 x 40 cm)? Several studies used this type of force plate but don’t explain how they calculate delta y.
                    Most of the articles mentioned that they measure the delta y (the displacement of CoM) but how they determine this during running (in hopping is easy because we can get v0 = 0, but this is not true when running) without using motion analysis system or force plates smaller than 4 meters like Cavagna used?

                    Furthermore, most of the papers don’t tell how they identify CoM position to determine Length spring change. How can I identify the CoM position without using motion analysis system to determine Length spring change (L)?



                    In summary:

                    1) How to determine delta y during running using just one force plate (60 cm X 40cm)?

                    2) How to determine CoM position to calculate Length spring change during running?
                    Last edited by Armindo Marques; August 1, 2011, 12:00 PM.

                    Comment

                    Working...
                    X