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Free body diagrams and biomechanical foot models

Discussion in 'Biomechanics, Sports and Foot orthoses' started by Petcu Daniel, Jun 9, 2016.

  1. Petcu Daniel

    Petcu Daniel Well-Known Member

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    As many of you I believe the free body diagrams and biomechanical foot models are the main "instruments" to be used to understand and practice in the frame of tissue stress theory. To me some articles are hard or even impossible to be understood but I think it could be somehow useful ! So, I'm thinking to put in this thread what I found on this subject hoping there will be other more useful contributions in this sense !
    To me the main resources are :

    -Eric Fuller and Kevin Kirby, Subtalar Joint Equilibrium and Tissue Stress Approach to Biomechanical Therapy of the Foot and Lower Extremity, in Lower Extremity Biomechanics: Theory and Practice, Volume 1, edited by Stephen F. Albert and Sarah A. Curran, Bipedmed, LLC, Denver, Colorado, 2013, p.260

    -Fuller, E A. ?The Windlass Mechanism of the Foot. A Mechanical Model to Explain Pathology.? Journal of the American Podiatric Medical Association 90, no. 1 (January 2000): 35?46. http://www.ncbi.nlm.nih.gov/pubmed/10659531

    -Kevin Kirby's "- Foot and Lower Extremity Biomechanics I-IV: Precision Intricast Newsletters

    Other examples:
    -Yarnitzky G, Yizhar Z, Gefen A. Real-time subject-specific monitoring of internal deformations and stresses in the soft tissues of the foot: a new approach in gait analysis, J Biomech. 2006;39(14):2673-89 http://www.ncbi.nlm.nih.gov/pubmed/16212969
    -Heung-Youl Kim, Shinji Sakurai, and Jae-Han Ahn. ?Errors in the Measurement of Center of Pressure (CoP) Computed with Force Plate Affect on 3D Lower Limb Joint Moment During Gait.? Int. J. Sport Health Sci. 5 (2007): 71?82. https://www.jstage.jst.go.jp/article/ijshs/5/0/5_0_71/_article

    Hope these helps !
  2. efuller

    efuller MVP

    This article looked at more and less complex models. Depending on the accuracy that you need, simple models can suffice.

    Theoretical considerations and practical results on the influence of the representation of the foot for the estimation of internal forces with models.
    Morlock M, Nigg BM.
    Clin Biomech (Bristol, Avon). 1991 Feb;6(1):3-13. doi:
  3. Petcu Daniel

    Petcu Daniel Well-Known Member

    An excellent explanation of the free-body diagrams comes from Sheri D. Sheppard, Benson H. Tongue, "Statics: Analysis and Design of Systems in Equilibrium", Wiley 2007 ( http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471947210.html )

    Two quotes from Chapter 6:
    "The free-body diagram is the most important tool in this book. It is a drawing of a system and the loads acting on it. Creating a free-body diagram involves mentally separating the system (the portion of the world you?re interested in) from its surroundings (the rest of the world), and then drawing a simplified representation of the system. Next you identify all the loads (forces and moments) acting on the system and add them to the drawing."(page 215)

    "...the general rule that describes a boundary?s restriction of motion can be used to identify the loads at the support. This rule states:If a support prevents the translation of the system in a given direction, then a force acts on the system at the location of the support in the opposite direction. Furthermore, if rotation is prevented, a moment opposite the rotation acts on the system at the location of the support." (page 267: steps to create a free-body diagram)

    More useful information in chapter 6: "Drawing a free-body diagram" which is free to download from: http://www.wiley.com/college/sc/sheppard/free.html

    Also, you can find some "free-body diagrams self tests" at: https://www.physics.uoguelph.ca/tutorials/fbd/Qmenu.htm

  4. Petcu Daniel

    Petcu Daniel Well-Known Member

    Thank you! Excellent article !

    Quote from conclusions: "...However, forces in internal structures of the foot are of interest to all researchers who investigate the influence of therapeutic measures (such as insoles or special shoes) on internal loading, the influence of different shoes or floor surfaces on internal loading, or injury mechanisms in general. At this point in time, models comprise the only possibility to estimate these forces. It has been shown in this study that the absolute magnitude of internal force estimates depends on the representation of the foot (the model) and that a comparative approach can eliminate systematic errors, such as systematic overestimation of forces, and, therefore, yields similar results with different (but still appropriate) models...."

  5. Petcu Daniel

    Petcu Daniel Well-Known Member

    Even if not directly related with foot biomechanics the next one is in the same line with the article indicated by Eric. The approach is similar with Tissue stress theory (but with an emphasis on the use of free-body diagrams) as it can be seen from this quote:

    "...the professionals involved should ideally provide answers to one or more of the following questions:
    1.-Which structures in the low back are supposed to be overloaded (intervertebral disc, vertebra, muscle, or ligament) and under which types of load, e.g. compression force, shear force, or axial torque (i.e.the load criteria)?
    2.-What is the actual load value for each load criterion in a working situation?
    3.-What is the maximum acceptable load value for each load criterion (i.e. the norm)?" (ZOOS ?)

    Clin Biomech (Bristol, Avon). 1992 Aug;7(3):138-48. doi: 10.1016/0268-0033(92)90028-3.

    Value of biomechanical macromodels as suitable tools for the prevention of work-related low back problems.

    Delleman NJ, Drost MR, Huson A.


    Biomechanical macromodels are evaluated with respect to their possible usefulness for health professionals and ergonomists, as well as for applied research on the prevention of low back problems. It is concluded that in the context stated geometrically simple models, in particular the model by Schultz and co-workers, are to be favoured over more complex models. However, load predictions in extreme trunk postures should be dealt with carefully. It is recommended that the model load predictions should be used only in the comparison of work situations and not for an assessment of the absolute acceptability of a work situation. Low back problems are related to mechanical (over)load at work. This study shows the pros and cons of various biomechanical macromodels as tools for health professionals and ergonomists, as well as for applied research on the prevention of work-related low back problems.


  6. Petcu Daniel

    Petcu Daniel Well-Known Member

    Prosthet Orthot Int. 1977 Dec;1(3):161-72.

    Graphic analysis of forces acting upon a simplified model of the foot.

    Veres G.


    Application of a graphical technique to analyse internal forces on a simplified model of the foot in various external loading patterns. The method is applied when the external load is acting purely upon the forefoot, the hindfoot and on both locations. The pes planus situation and the effect of the "rocker" and inlay sole are studied.
  7. Petcu Daniel

    Petcu Daniel Well-Known Member

  8. Petcu Daniel

    Petcu Daniel Well-Known Member

    A nice video regarding free body diagrams on hip joint:
  9. Petcu Daniel

    Petcu Daniel Well-Known Member

    Foot Ankle Clin. 2014 Dec;19(4):701-18. doi: 10.1016/j.fcl.2014.08.011. Epub 2014 Sep 26.
    The effect of the gastrocnemius on the plantar fascia.
    Pascual Huerta J.
    Although anatomic and functional relationship has been established between the gastrocnemius muscle, via the Achilles tendon, and the plantar fascia, the exact role of gastrocnemius tightness in foot and plantar fascia problems is not completely understood. This article summarizes past and current literature linking these 2 structures and gives a mechanical explanation based on functional models of the relationship between gastrocnemius tightness and plantar fascia. The effect of gastrocnemius tightness on the sagittal behavior of the foot is also discussed.
  10. efuller

    efuller MVP

    Hicks gave a pretty good demonstration of the interaction between Achilles tendon tension and tension in the plantar fascia back in 1954. Although it is good to see continued use of free body diagrams. I did not read the full text. I hope they referenced Hicks.
  11. Petcu Daniel

    Petcu Daniel Well-Known Member

    Yes, Hicks is cited but not with the 1954 paper (Hicks, J.H.,1954.The mechanics of the foot.II. The plantar aponeurosis and the arch.J. Anat.88,25–30.).
    An interesting article which is referencing and challenging the above mentioned Hicks' paper is: G. Fessel et. al. "Changes in length of the plantar aponeurosis during the stance phase of gait–An in vivo dynamic fluoroscopic study" which is concluding: "muscles contribute to support of the longitudinal arch of the foot and can possibly relax the PA (plantar aponeurosis) during gait. The‘windlass effect’ for support of the arch in this context is therefore questionable." https://www.researchgate.net/public...of_Gait_an_in_vivo_Dynamic_Fluoroscopic_Study

    One of the authors (Jacob HA) has an article where is using the free body diagrams: "Forces acting in the forefoot during normal gait an estimate" ( https://www.ncbi.nlm.nih.gov/pubmed/11714556 ). The conclusion is: "The high forces acting along the flexor tendons of the heavily loaded first ray support the so-called longitudinal arch of the foot. The second metatarsal bone is also heavily loaded, but more in bending. If the first ray with its powerful toe be deprived of its function, be it through muscular fatigue, disease, or trauma, the second metatarsal bone will probably also fail."

  12. Petcu Daniel

    Petcu Daniel Well-Known Member

    If foot orthoses are designed to alter the components of the ground reaction force vector then I think one of the next steps is to know how this will influence not only the COP but also the CM. This article brings into equation the velocity of CM as a necessary variable in the evaluating of the dynamic stability. Hard to understand it but doesn't mean it shouldn't be taken into consideration!

    Pai YC, Patton J. Center of mass velocity-position predictions for balance control. J Biomech. 1997 Apr;30(4):347-54.
    The purposes of this analysis were to predict the feasible movements during which balance can be maintained, based on environmental (contact force), anatomical (foot geometry), and physiological (muscle strength) constraints, and to identify the role of each constraint in limiting movement. An inverted pendulum model with a foot segment was used with an optimization algorithm to determine the set of feasible center of mass (CM) velocity-position combinations for movement termination. The upper boundary of the resulting feasible region ran from a velocity of 1.1 s-1 (normalized to body height) at 2.4 foot lengths behind the heel, to 0.45 s-1 over the heel, to zero over the toe, and the lower boundary from a velocity of 0.9 s-1 at 2.7 foot lengths behind the heel, to zero over the heel. Forward falls would be initiated if states exceeded the upper boundary, and backward falls would be initiated if the states fell below the lower boundary. Under normal conditions, the constraint on the size of the base of support (BOS) determined the upper and lower boundaries of the feasible region. However, friction and strength did limit the feasible region when friction levels were less than 0.82, when dorsiflexion was reduced more than 51%, or when plantar flexion strength was reduced more than 35%. These findings expand the long-held concept that balance is based on CM position limits (i.e. the horizontal CM position has to be confined within the BOS to guarantee stable standing) to a concept based on CM velocity-position limits.

  13. efuller

    efuller MVP

    I'd say that foot orthoses aren't really designed to alter the components of ground reactive force (ant-post, vert, med-lat). They are more designed to alter the point of application of that force.

    David Winter had a few papers that discussed static stance and postural sway, and then another paper on the initiation of gait. Starting gait is very similar to stopping in terms of physics. It is all related to the relationship of the center of mass to the location of center of pressure. Say the center of mass is anterior to the center of pressure. The down ward force of gravity and the upward force from the ground create a force couple that will tend to make the person fall forward. The person contracts their soleus muscle and this shifts the center of pressure anterior to the center of mass making the person accelerate backward (stopping the forward fall). This is postural sway. It is hard to keep your center of mass directly over your center of pressure. If you don't keep adjusting you will fall over.

    The above paper is stating the obvious that if you are falling forward so fast that maximum contraction of the soleus and the toe flexors, can't shift the center of pressure anterior enough (beyond the end of the foot) to create a large enough moment to stop the forward falling, then you will fall forward. There is a bit of additional complication in gait and that is forward momentum of the body. You still need the force couple of center of pressure of ground reactive force being anterior to the center of mass to slow and hopefully stop forward progression by creating a falling backward rotational moment. Winter showed, in gait, that velocity of the center of mass decreases when the center of mass is posterior to the stance leg and increases after the center of mass passes the stance leg up until the swing leg contacts. Gait is just a repetition of the process of using the body's momentum to vault over the stance leg. If you want to stop gait, you just place your swing leg a little farther anterior to create a bigger, and longer lasting, rearward rotational moment.

  14. Good one Eric. I was also going to respond with David Winter's research to answer Daniel's questions. Here is a great little book by David Winter that is an easy read and well worth reading and digesting to understand these basic biomechanical concepts of balance. https://www.amazon.ca/anatomy-biomechanics-control-balance-standing/dp/0969942001[​IMG]
  15. Petcu Daniel

    Petcu Daniel Well-Known Member

    Sorry Eric but I don't understand why do you consider more important to alter one component of a vector (point of application) than the others (magnitude and direction)?
    For example, here is a quote from a very interesting article: "Our results suggest trunk sway may need further investigation to understand how it functions to reduce KAM. Our results may also provide insight into how other current gait modifications alter KAM. Decreased walking speed has been shown to decrease KAM by 8%, which may be due to changes in the GRF [33]. Since our results show 20% of the KAM to be attributed to the vertical GRF, there may be other factors that interact and change during walking speed to affect KAM. Increased stance width can decrease KAM by up to 9% [7, 34], toe-out by 1% [35], and lateral-wedge insoles by 9% [36], all of which are thought to be a result of alterations in medial-lateral COP. However, our results showed medial-lateral COP to not be significantly related to KAM and superior-inferior COP an insignificant predictor (1% of the variance). Therefore, these modifications may be acting through other mechanisms (i.e. GRF, knee alignment) that could be investigated in future studies. " Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4268356/

    To me a definition is what is driving the way of thinking and I feel there is something missing in the definition of foot orthoses:, something between altering "the magnitudes and temporal patterns of the reaction forces" and "in order to allow more normal foot and lower extremity function and to decrease pathologic loading forces on the structural components of the foot and lower extremity during weightbearing activities". How exactly can I alter the GRF vector in order to allow more normal functioning? In the above referenced article we are believing that through altering the COP position but, complicated instrumented biomechanical devices and methodologies is showing in that specific case other variables are explaining ( "20%") the outcomes. I suppose that a better understanding of "dynamic balance" could provide an answer!

    Reference: "An in-shoe medical device which is designed to alter the magnitudes and temporal patterns of the reaction forces acting on the plantar aspect of the foot in order to allow more normal foot and lower extremity function and to decrease pathologic loading forces on the structural components of the foot and lower extremity during weightbearing activities" (Kirby KA: Foot and Lower Extremity Biomechanics II: Precision Intricast Newsletters, 1997–2002. Precision Intricast, Inc., Payson, AZ, 2002.)

  16. efuller

    efuller MVP

    What I was talking about was what you can design an orthotic to do. I was not talking about what was important. I understand how you can alter the point of application of force with an orthotic. I don't see how you can design a foot orthotic to alter the magnitude, or direction of ground reactive force. The vertical component of ground reaction force is determined by gravity and by vertical movement of the center of mass. The CNS an alter muscular activation to move the center of mass. An orthotic is not going vertically move the center of mass during a step. In the article trunk sway is talked about in altering Knee moments. Trunk sway is controlled by the CNS and cannot be "controlled" by an orthotic.
  17. Petcu Daniel

    Petcu Daniel Well-Known Member

    In this case should we change the definition of foot orthoses in "An in-shoe medical device which is designed to change the position of center of pressure in order to...." ?
  18. Petcu Daniel

    Petcu Daniel Well-Known Member

    I'm thinking that modifying the coefficient of friction at the foot-foot orthoses interface will modify the horizontal components of GRF (shear forces) and, probably, the direction of GRF vector. Important in the case of diabetic foot. I suppose the controlled instability induced by orthotic will determine a reaction from CNS in order to maintain the dynamic balance
  19. efuller

    efuller MVP

    One problem with using the outcome of center of pressure is that Center of Pressure location can also be altered by muscle activity. You may not see the change in center of pressure that your orthotic was designed to produce. Someone might say that you orthotic was ineffective because the center of pressure isn't where you said it was, but the patient might not want to give you back the orthotic because it feels better with it than without it.

  20. efuller

    efuller MVP

    Where on the orthotic are you thinking of doing this?

    A lot of the medial lateral and anterior posterior component of ground reaction force is needed for movement of the center of mass. If foot placement is to either side of the line of progression, then there has to be an acceleration toward where the opposite foot is going to land.

    In the ap direction, even without muscle contraction, as the body vaults over the stance leg, anterior posterior frictional forces will be generated.
  21. Petcu Daniel

    Petcu Daniel Well-Known Member

    This make me think at the paradox defined by Craig Payne: "What we do clinically works, but not by trying to do what we think we are doing" ( https://podiatryarena.com/index.php?threads/foot-orthoses-outcomes-and-kinematic-changes.214/ ) We can measure somehow why the patient might not want to give us back the orthotic, but we can't be sure that our orthotic's design objective was achieved. The problem could be with the next patient who will not feels better with our orthotic who was designed to change the COP's position. Is the "COP position" from tissue stress theory similar with "pronation" from STJN theory?.

    At the moment, it make sens to me to try to alter the coefficient of friction under the diabetic foot patient because, next to pressure, shear is one of the ulceration's risk factors. I think it could be of interest also in the case of tibial fractures risk in sport activities where we have a lot of researches about shoes' rotational traction properties. In this case the AP and ML components of GRF will not be enough to provide adequate information as they are related with translational friction. A measure of rotational friction will be useful and this seems to be the free moment especially because this measure could be related with dynamic stability
  22. efuller

    efuller MVP

    I should have made the following distinction more clear. There is what we try to do with center of pressure and then there is looking at center of pressure before and after an intervention. I can feel my posterior tibial muscle relax with a more inverted heel cup of my orthosis. If I add too much varus wedge effect in my orthosis I can feel my peroneal muscles contract at heel contact. So, the attempt to shift of pressure is doing something. However, I don't know if the change in muscle activity that I feel will allow a change in location of the measured center of pressure. If the goal was to reduce stress in the posterior tibial tendon, and the stress is reduced, we don't care if there was a change in the location of center of pressure. My point was that we may not want to use location of center of pressure as a measure of our success. I do believe that we should still attempt to shift the center of pressure more medially with pathology that is modeled to be from high pronation moments from the ground.

    It's hard to say if Cop is similar to pronation in STJN theory. In our discussions on the arena about STJ neutral theory there hasn't really been a consistent coherent explanation of the relationship between pronation and the orthosis. (There is disagreement within proponents of the theory on how an orthosis works.) In tissue stress the relationship between CoP and pathology is related to the cop affects moments and internal forces in the foot.
  23. Petcu Daniel

    Petcu Daniel Well-Known Member

    J Biomech. 1990;23(10):977-84.
    Joint reaction forces at the first MTP joint in a normal elderly population.
    Wyss UP, McBride I, Murphy L, Cooke TD, Olney SJ.

    The calculation of net ankle, knee, and hip joint reaction forces is an often applied procedure in the analysis of gait. Except for very few studies, joint reaction forces have not been measured in other joints such as the fingers, wrist, elbow, shoulder and toes. In this study the joint reaction forces between the metatarsal head and the proximal phalanx and the metatarsal head and the sesamoids are calculated for the push off phase during gait. The results of ten normal elderly subjects show that the maximum resultant loads of the two articulations lie close to the longitudinal axis of the metatarsal. The knowledge of the magnitude and direction of the joint reaction forces of a normal elderly population will be essential for the design of an optimal fixation of an artificial anatomical first MTP joint.
  24. Petcu Daniel

    Petcu Daniel Well-Known Member

    Wright DG, Rennels DC., A Study of the Elastic Properties of Plantar Fascia. J Bone Joint Surg Am. 1964 Apr;46:482-92. https://insights.ovid.com/pubmed?pmid=14131427
    Gefen A, The In Vivo Elastic Properties of the Plantar Fascia During the Contact Phase of Walking, Foot Ankle Int. 2003 Mar;24(3):238-44.
    The in vivo elastic properties of the plantar fascia during the contact phase of walking were determined experimentally by integrating a pressure-sensitive optical gait platform with a radiographic fluoroscopy system for recording skeletal motion. In order to calculate the fascia's tension-deformation relation, lateral images of the foot's skeleton that allowed evaluation of the fascia's transient length from the arch-contact to toe-off stages of walking were obtained simultaneously with the vertical foot-ground contact forces. The plantar fascia was shown to undergo continuous elongation from arch-contact to toe-off, reaching a deformation of 9 to 12% between these positions. Rapid elongation of the fascia, at a strain rate of about 0.9 +/- 0.1 Sec-1, was observed before and immediately after midstance, while a significantly slower elongation occurred at a strain rate of approximately 0.2 +/- 0.1 Sec-1 around push-off and toe-off. The average stiffness of the fascia at the slow-to-moderate walking velocities was 170 +/- 45 N/mm, which is similar to reported stiffness values for cadaver fascia specimens. The present technique may be useful for validation of computational models of the soft tissues of the foot as well as for testing the effectiveness of orthoses and shoe types for relieving excessive strain of the fascia in the treatment of plantar fasciitis.
  25. Petcu Daniel

    Petcu Daniel Well-Known Member

    In "Are we losing the Art in the Science" I found referenced 'Occam's razor' and a possible empirical justification: " Occam's razor has gained strong empirical support in helping to converge on better theories (see "Applications" section below for some examples). In the related concept of overfitting, excessively complex models are affected by statistical noise (a problem also known as the bias-variance trade-off), whereas simpler models may capture the underlying structure better and may thus have better predictive performance. It is, however, often difficult to deduce which part of the data is noise (cf. model selection, test set, minimum description length, Bayesian inference, etc.)."
  26. Petcu Daniel

    Petcu Daniel Well-Known Member


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