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A question of lever arms

Discussion in 'Biomechanics, Sports and Foot orthoses' started by mike weber, Jul 19, 2010.

  1. Members do not see these Ads. Sign Up.
    Hi Folks this question has been bugging me for the last few days...........

    Kerrie started a thread about one of her patients.


    The focus of her question is, Her patient a personal trainer had a 3cm leg length discrepency, the shorter leg has more muscle bulk than the longer and she asked if it possible to have muscle symmetry and the same force produced by the muscle group, the Quads in this case.

    I wrote this.

    Since my post Dennis and David have been having discussions about functional and structural leg length and the use of heel lifts.

    The thing that I´m getting stuck on is if we add a heel lift, won´t the Quads have to work harder due the increase in the distance of the lever arm from the knee down ? I´ve draw a basic diagram to show what I mean.

    If we take the basic function of the quads to be extension moment at the knee, by causing this moment the pull on the tibia at the insertion of the patella tendon will most likely lead to movement of the tibia and posterior leg. Again only thinking basicially about the quad function, if our persianl trainer patient of Kerries gets fitted with a heel lift and then goes to the gym and length of the lever arm at which the quads contraction will effect has got longer, while the femur length has not, so the muscle contraction must be greater the before the left was fitted. (?)

    So over time there will be the training effect Ive discribed above and the quads will increase in bulk.

    Hope that makes sense.

    Ps I hope that this will stay a discussion about lever arms not the use of the lift in this patient or not, that has been discussed in Kerries thread.

    Also as an aside question, mainly to Simon Spooner if he reads this.

    Do you think the lenght of the spring segments when we discuss leg stiffness (Kleg) effect the abilty for the body to maintain Zones of optimal leg stiffness ( ZOOLS)

    So again if we take the above patient and we say his Femur length is the cause of the LLD, will the shorter spring segement (Knee to Hip), with greater muscle bulk effect the bodies abilty to maintain ZOOLS compaired to the longer side.

    I´m thinking that it will and that people with longer legs may have the ability to adjust kleg during gait better than shorter leg people,due the relative lenght of the spring segments.

    ok I´ll stop now before I confuse myself some more.

    Attached Files:

  2. Griff

    Griff Moderator


    I'm not 100% sure what you are asking, so forgive me if I have misunderstood.

    What you are doing essentially modelling the quadriceps/knee joint/leg+heel raise as a class 1 lever as below, where:

    EFFORT = Quadricep contraction, FULCRUM = knee joint, and LOAD = weight of leg.

    As we know the greater the distance of the fulcrum from the load then the greater effort required. So is your question that the addition of a heel raise would effectively introduce this situation and require increased quadricep contraction?

    Attached Files:

  3. Hi Ian, Ive been going around and around this in my head, so it maybe clear to me but " as clear as mud" for others sorry.

    The sentance in bold, is much better than my ramblings.

    So , thats what I got, the longer the distance from the knee the load the greater the effort ( work ) required by the quads ( using simple extension of knee as the motion).

    So the addition of the heel raise in the situation of asymmentric muscles (Quads in this case) would lead to more work required by the muscles when underload, due the increased distance from the fulcrum ( the knee). The greater the work required by Quads the more "training effect" the greater the cross sectional area of muscle.

    So if my randon ramblings and thoughts are correct, then Kerrie adding a heel lift to patient, to deal with the LLD will effectivly overtime lead to the short side having more muscle and look larger compaired to the longer side.
  4. Mike, this is a Hookes' law problem. If we have 2 springs indentical in every respect except the resting length of one spring is twice the length of the other, for a given load the longer spring will extend (or compress) twice as much as the shorter one.

    The implication being that even with a leg length difference the body should be able to maintain a smooth centre of mass path by modulating leg stiffness.
  5. Thanks Simon,

    Here´s where I´m heading with this one. which maybe up **** creek in a barbed wire caneo.

    Forefoot strinking and rearfoot striking in running. The distance from ground impact to the knee ( Fulcrum) will be longer in FF striking. ie the distance from knee to plantarflexed forefoot will be longer than the distance from knee to plantar heel

    As the quads are very important as anti gravity muscle group ie the ability of the COM to stay upright. This change in the distance from the fulcrum will mean

    more work from the quads to produce an extension moment at the knee

    a change in the relationship of spring length - tibia section to femur section

    a greater abilty of the hamstrings to create a flexion moment at the knee, from the fact that the quads must work harder to maintain COM upright postion.

    Due to the fact of QUADS work to maintain upright postion of COM, and the relationship of lever arms of femur to Pelvis- hip flexion moment.

    increased knee flexion, increased hip flexion = reduced Kleg

    again I hope this makes sense,
  6. Kerrie

    Kerrie Active Member

    Hi Everyone,
    WOW, this is all so helpful!! Thank you to everyone who is taking an interest in this and contributing, really means alot.
    Good thing is also I managed to get my hands on a bit of an older book on sports biomechanics which looks at lever arms too so that is helping alot.
    Really cannot thank everyone enough for all the help, he is coming back in soon so I will be armed with knowledge to the eye balls :)
  7. But to shoot myself down the increased GRF vector to the Forefoot should cause an extenal extension moment at the knee :confused:

    someone pass the caneo paddle, I´m off....
  8. Griff

    Griff Moderator


    Sorry for the delay in response - a busy morning.

    I don't think this theory works here. The actions you mention are more of a class 3 lever (below), as the LOAD (leg/foot/heel raise/shoe etc) is distal to both the FULCRUM (knee joint) and the EFFORT (quadricpes pull via tibial tuberosity). To my mind the lever arm does not change here with the addition of a heel raise. (The lever arm effectively being the distance between the knee and the tibial tuberosity).

    You could argue that an increased LOAD may alter quadriceps function, but this would probably be neglible in this example given the average mass of a heel raise?


    Attached Files:

  9. Hi Ian, Ok I see what you are saying here, to be honest pretty much self read in the line of physics.

    If we say that the class 3 lever that you have drawn describes the lever.

    I´m notsure if you have read Kerrie thread, but the patient in question is a personal trainer, and claims that the quads produce the same force, but one has more muscle bulk than the other.

    So the guys want to know if symmetry is possible, the heel lift may work against this symmetry. But being a personal trainer I´m assuming he weight trains. So by adding the load at a greater distance from the fulcrum due to the lift, greater work will be required by the muscle group.

    I´ve than exercise where you sit down an extend your knees to push the weight up the incline in my head.

    I agree the heel lift has no real mass, but the change in would in my mind lead to greater work not less of the quads.

    maybe ?
  10. Griff

    Griff Moderator

    Hi Mike,

    I think Kevin summed it up best in that thread. If the guy wants the muscles to look identical, (and there is indeed a true structural discrepancy) then they will not have the same strength. One or t'other...

    I must confess I'm still struggling to grasp your point mate. How does introducing a heel raise change the lever arm of the quadriceps?
  11. I´ve been going around and around this in my head for the last 2 weeks so thought I´d put it out there. I may just be talking crap so just need to be told.

    The heel lift may not/ does not change the lever arm of the quads, but it does mean the load is further away from the fulcrum, which in my thinking must effect the work of the quads.

    But again I might be hitting a speed bump in the journey, and should be told to let it go.
  12. Conradm

    Conradm Member

    I am bad at explaning things so I won't try.....but in following what Ian has said above --> Wouldn't it help to come to a clearer understanding of the levers and fulcurms involved and what they have to do??
    - Conrad
  13. efuller

    efuller MVP

    Mike the concept you are missing is line of action of force. A moment created by the force is the perpendicular distance from the line of action of the force to the axis in question. The line of action of force is a line that is in the direction of the force extending from the point of application of the force. This is what makes center of pressure useful. The center of pressure can be considered to be the point of application of force.

    So if we look at running at the instant of ground reaction force contact (We also have to assume a solid (non mobile) ankle.). The line of action of force is mostly upward with some posterior to anterior component. Sagittal view draw the vector and the knee axis. Now add a lift under the heel. The distance from the line of action of force to the knee axis may change a little bit. Probably, not enough to worry about.

    However, the point is made moot by the requirement of the ankle being solid. The reason why you cannot calculate ground reaction force moment at the knee is that the moments at the ankle effect the moments at the knee. Mid stance in gait: a plantar flexion moment at the ankle will tend plantar flex the foot while simultaneously attempting to rotate the top of the tibia backwards. (Real life example: genu recruvatum with an equinous) So, a plantar flexion moment at the ankle will (with the inertia of the body) tend to extend the knee.


  14. Mike:

    I have attached a nice lecture on lever systems I found on the web for you.

    As you will notice from the lecture, every lever has a force arm and a resistance arm. In your case of a heel lift, the resistance arm for the quadriceps will increase if ground reaction force (GRF) is acting on the plantar heel of the shoe and a heel lift is added to a shoe since the distance from the plantar shoe sole to the knee joint axis has increased. However, this does not also mean that adding a heel lift will make an individual's quadriceps muscle stronger or weaker for a given exercise or will be better at promoting, over time, increased or decreased cross-sectional area of the quadriceps.

    Increases in muscle mass are dependent on many factors, not just resistance arm length. Factors that are also very important include angular velocity of contraction, number of repetitions, duration of exercise regimen, diet, hormonal activity and other types of exercise activity of the muscle, to name a few factors.

    I know from my own past experiences when confronted by similar problems, that doing drawings (e.g. free body diagrams or other basic mechanical model illustrations) that model the quadriceps force and resistance arm length will shed further light on this issue for you. You will be able to see more clearly how the velocity of the foot would change with different resistance arm length for a given contractile velocity of the quadriceps muscle. In addition, you could also model how changes in resistance arm length of the quadriceps would change the amount of external knee flexion moment and therefore also affect the internal knee joint extension moment from quadriceps contractile force that would be necessary to maintain static equilibrium (i.e. rotational equilibrium) at the knee joint during certain isometric exercise.

    By performing these modelling exercises I think you will be able to come to much better answers regarding your questions on quadriceps muscle function.

    By the way, in the animal kingdom, the lever arms of muscles relative to their resitance arms and their joint axes is quite different in different animals depending on their unique habits and their specialized physical activities. For example, between the cheetah and the mole, how would you design the forearm of each animal in to optimize the speed of limb movement in one for running speed and optimize the strength of limb movement in the other for digging ability?

    Attached Files:

  15. Ian, Eric and Kevin.

    Thanks for working through it all with me. Lots to consider and think about. I´ll go read the link that Kevin has posted, see where we get to from there.

    Again thanks

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