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T.E. #7: External Forces on Objects: Problems with Only Motion Observation

Discussion in 'Biomechanics, Sports and Foot orthoses' started by Kevin Kirby, May 16, 2006.

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    In Thought Experiment #7, a tall object stands on a flat surface and is acted on by varying external forces, in an attempt to show how externally applied forces affect the ground reaction force (GRF) acting on its two supporting surfaces, A and B.

    The object has a mass of 204.1 kg, which, assuming a gravitational acceleration, g, of 9.8 m/sec/sec, means that the weight, W, of the object is 2,000 N. The object is 2.0 meters tall, and 0.4 meters wide, with concave top and bottom surfaces. Since the object is homogeneous, the center of mass (CoM) of the object is located exactly in the center of the object. The bottom edges of the object support the full weight of the object with the GRF at its left hand supporting edge, A, and the GRF at its right hand supporting edge, B, both being 1,000 N (Fig. A).

    A researcher, named Dr. Filmore Fudd, next walks up to the right side of the object and, with his hand, exerts a horizontal force, C, with a magnitude of 200 N directed toward the left, at a vertical distance of 1.7 meters from the ground, on the object (Fig. B). Dr. Fudd notices that no motion of the object has occurred with pressing on the object. However, since he has assumed that if an external force that is applied to an object has caused no change in motion of the object, that this also means that nothing mechanically significant has happened with the object, he is unaware of the change in GRF under the left (A) and right (B) edges of the object that has occurred.

    Dr. Fudd next presses even harder with his hand, with a force of C, at the same location on the object and still observes no motion of the object (Fig. C). He again assumes that his externally applied force has not affected the object since no motion of the object has occurred. However, unknown to Dr. Fudd, this harder push has resulted in the full weight of the object being applied to the left edge of the object (i.e. A = 2,000 N) and has resulted in the right edge of the object just touching the ground, with negligible GRF being exerted (i.e. B = 0 N).

    Now, you being a much more bright physics student than Dr. Fudd, inform him that he is incorrect in assuming that just because an object doesn't move when an external force is applied that there has also been no significant mechanical changes in that object. [You also know that the GRF acting under the object in B and C are not directed exactly vertically since they will be directed slightly toward the right due to the horizontal component of GRF being directed to the right. This horizontal component of GRF results from the frictional force that must occur between the object and the ground in order for the object to remain in equilibrium when Dr. Fudd is applying force C with his hand. Only the vertical component of GRF is shown for the object-ground interface to simplify the discussion.]

    As evidence of your mechanically coherent explanation, you show him how to calculate the forces being applied on the ground by the edges of the object when a certain external force is applied. Unfortunately, Dr. Fudd is frustrated since he just had a paper published in the Journal a few years ago which describes how the lack of motion of an object in response to an applied force means that nothing mechanically significant has occurred in the object. You smile and tell him to not be discouraged because you have seen other researchers make similar mistakes in designing their experiments. You tell him that this has happened numerous times in regard to foot orthosis research where a researcher has measured the wrong parameter in an foot orthosis experiment, only to find that he or she has not discovered the true mechanical effects of the externally applied forces of foot orthoses on the foot because only motion or position of the foot was measured.

    Here are the questions that you need to answer to improve Dr. Fudd's understanding of physics and mechanics of external forces acting on objects:

    1. In Figure B, what are the values for GRF A on the left edge of the object and for GRF B on the right edge of the object when Dr. Fudd pushes with 200 N?

    2. In Figure C, what is the magnitude of force that Dr. Fudd is pushing with in order for GRF A to be 2,000 N and GRF B to be 0 N (but still no object movement).

    3. What types of measurements should be made internally and externally to the object described above to help Dr. Fudd become more fully informed of the mechanical effects of external forces on objects?

    4. Ideally, what types of measurements should be made internally and externally to the foot if a researcher wants to know the true mechanical effects of foot orthoses on the foot and lower extremity?

    5. Why then is measuring only motion and position of a foot problematic in foot orthosis research?

    Attached Files:

  2. Donna

    Donna Active Member

    Hi Kevin,

    I have had a bit of a guess on this one - I'm sticking my neck out big time here! :eek:

    Please steer me in the right direction here...I think I've made a bit of a mess of it! :(

    1. GRF A = 1850N, GRF B = 150N
    2. C = 235N
    3. Could scales be used under A and B to measure how the GRF values change when a force is exerted on the side of the object? :confused:
    4. The response of the muscles could be measured, eg. to see how much work the posterior tibial muscle has to do to produce the same movement with and without orthoses. :confused:
    5. Just measuring motion and position of joints can't tell us how much stress or compression that the joints and soft tissues are placed under during gait. It is stress and compression that cause injury, so orthosis research should take this into account.


  3. Donna:

    Again you have demonstrated your superb biomechanics/physics skills. Good job!!

    1. Correct

    2. Correct

    3. Internal measurements that could be made on the object to detect how external force application affected it mechanically include the use of strain gauges embedded within the surfaces of the object to detect deformation of object in response to altered external force application. Internal stresses within the object could also be accurately predicted using finite element analysis techniques via computer modelling. External measurements could also include use of force plate, or "scales" for vertical only ground reaction force (GRF) vector only, at contact surface of the object with the ground.

    4. Basically the same measurements as described in question 3 could also be used in the foot. However, electromyography could also be used to estimate temporal patterns and magnitudes of muscular contractile activity. Strain gauges could be used in ligaments, tendons and bones to measure their deformation under load. Fiberoptic cables threaded into tendons/fascia/ligament could be used (in cadavers only) to measure tendon/fascia/ligament tensile forces. Finite element analysis could be used to estimate internal tissue loading forces and/or stresses. External measurements could include three dimensional (3D) motion analysis to measure 3D kinematics, force plates to measure the magnitude and direction of the GRF vector and center of pressure (CoP), and pressure mat/pressure insole systems to measure GRF under isolated segments/areas of foot and/or CoP.

    5. Correct. However, here is how I would slightly change your answer to make it a little more complete:

    Just measuring motion and position of joints will tell us very little regarding the magnitude, loading rate and type of force and/or stress that the structural components of the foot and lower extremity are subjected to during weightbearing activities. Without a knowledge of the magnitude, loading rate and type of force and/or stress that the structural components of the foot and lower extremity are subjected to, we are then ignorant of the biomechanical etiology of mechanically-based pathologies of the foot and lower extremity. It is for this reason that, if our goal is to design foot orthosis research to elucidate the true nature of their therapeutic mechanical actions, then we must design the orthosis research to either directly or indirectly measure these internal loading forces/stresses on the structural components of the foot and lower extremity that are the true causes of the injuries which the orthoses are designed to treat.
  4. Donna

    Donna Active Member

    Hi Kevin,

    Thanks for the positive feedback! And thanks for inventing the Thought Experiments, they're awesome! :D


    Donna :)
  5. Daniel Bagnall

    Daniel Bagnall Active Member

    Hi Kevin,

    My name is Daniel Bagnall and i am a registered podiatric practitioner, practicing in Australia.

    I must say that what you and other podiatrists have been presenting to the profession for over the last 20yrs, in regards to a more comprehensive and realistic approach to biomechanics is very enlightening. I have to admit that I was unfortunately schooled in the more traditional approaches.

    In accordance with your opinion about podiatrists needing to have a more sound understanding of physicis concepts, where would be a good place to start? I purchased the book you suggested a while ago, Fundamentals of Biomechanics: Equilibrium, Motion, and Deformation, however, there is a lot of content, and it is quite overwhelming.

    I ould greatly appreciate your help in regards to topics I should focus on, as I really want to grasp these concpets more thoroughly, and more importantly be able to apply them in a clinical setting.

    Kind Regards,

    Daniel Bagnall
  6. Daniel:

    Welcome to Podiatry Arena. You are unfortunately in a difficult situation trying to learn physics and biomechanics from books, instead of in a classroom situation where you can ask questions when you are stumped. However, I appreciate your enthusiasm for learning and would love to help you gain a better understanding of the mechanics behind the human locomotor apparatus.

    First of all, if you haven't already done so, you should read my two books. By going through a few newsletters every night you will be better able to understand many concepts since I use the foot and lower extremity as models to explain many difficult biomechanics concepts that may otherwise be hard to grasp (Kirby KA: Foot and Lower Extremity Biomechanics: A Ten Year Collection of Precision Intricast Newsletters. Precision Intricast, Inc., Payson, Arizona, 1997; Kirby KA: Foot and Lower Extremity Biomechanics II: Precision Intricast Newsletters, 1997-2002. Precision Intricast, Inc., Payson, AZ, 2002). I would bet that after you went through my two books and then went back to Ozkaya and Nordin (Ozkaya, Nihat and Margareta Nordin: Fundamentals of Biomechanics: Equilibrium, Motion and Deformation. 2nd Edition. Springer, New York, 1999) that you would much more appreciate their textbook. Another reference I like more each time I pick it up is the book by Whiting and Zernicke which is probably the best for understanding the concepts involved in Tissue Stress Theory (Whiting WC, Zernicke RF: Biomechanics of Musculoskeletal Injury. Human Kinetics, Champaign, IL, 1998).

    The way to learn is to ask questions.....lots of them (ask my biomechanics professors from CCPM....many of them tried to avoid me at times since I asked so many questions) Specifically if you, Daniel, or any other lurker on Podiatry Arena has a question regarding basic biomechanics terminology, you should not be afraid to ask on this forum since we have many very bright individuals who are always willing to answer questions.
  7. Daniel Bagnall

    Daniel Bagnall Active Member

    Hi again Kevin,

    I have been very eager to hear from you, and I thank you for your prompt reply.

    In relation to the references you have recommended, are these available through Amazon, or is there another specific source? In the meantime I will attempt to locate these references myself and get stuck into it.

    I’ve found it at times rather frustrating in the past, as I have spoken to senior colleagues that I have worked with about biomechanics and to be frank with you have had very discouraging responses. It’s a real shame, as it tarnishes the profession and more specifically the individuals who are trying to make an effort to better themselves academically and clinically.

    Well, I look forward to hearing from you again and enhancing my knowledge.

    Many thanks,
  8. Daniel Bagnall

    Daniel Bagnall Active Member

    Hi Kevin,

    Dont worry, I ordered your 2 books through Precision Intricast ;)


  9. Here are the links about the books I mentioned on Amazon.com.

    Fundamentals of Biomechanics

    Biomechanics of Musculoskeletal Injury

    You have been discouraged by talking with podiatrists about biomechanics?????....join the club! If you ever want to get confused about biomechanics, just talk to 95% of podiatrists about the subject. :eek: Biomechanics does not need to be complex, it can be made quite simple...as long as you have a good grounding in basic mechanics/physics principles and are willing to think and take the time to comprehend the mechanical phenomena embodied in Newtonian physics.
  10. Daniel Bagnall

    Daniel Bagnall Active Member


    Are you considering doing any workshops or conferences out here in Australia?

    I anticipate that your frantically busy, but I thought should ask as I would not want to miss out on the opportunity...

    I have always tried simplify the overall complexity of biomechanics, but as you said, I feel that I need a greater understanding in mechanical and physics principals.

    I am currently busy with your atricle that you published in 2001, Subtalar Joint Axis Location and Rotational Equilibrium Theory of foot function. This has been a great resource for me and has filled in some of the grey area.


    Is it possible to have a medially deviated STJ axis, even though the foot may not demonstrate the typical characteristics we would normally expect to see?

    For exmaple, a pt with Post Tib Dysfunction will normally present with abnormal medial convexity of the midfoot (posterior view) and abnormal medial and internally positioning of the talar neck. Logically, we assume medial deviation of the STJ axis, but what about pts who don't display this?

    I have had many patients before with foot complaints who have had relatively well maintained medial longitudinal arches and minimal convexity of the medial midfoot. However, during the supination resistance test, I found it very difficult to resupinate the foot. Is it sensible for me to assume a medially deviated STJ axis?


  11. I last lectured in Australia in Melbourne a few years ago and don't have another lecture scheduled in Oz currently.

    In the weightbearing setting, if the talar head and neck are medially positioned "pointing medial to the first MPJ" then the STJ axis is likely medially deviated. A supination resistance test that is high may occur without a medially deviated STJ axis if the patient is tonically contracting their peroneal muscles during the test since the STJ pronation moment arising from increased peroneal muscle activity will actively resist attempts at supinating the foot. I have never seen a patient with posterior tibial dysfunction without a medially deviated STJ axis and I have probably treated at least 1,000 patients with PT dysfunction.

    Here is a photo demonstrating talar head and neck position in a patient with PT dysfunction on her right foot. Both STJ axes are medially deviated but the right foot is more medially deviated than the left foot.

    Attached Files:

  12. Daniel Bagnall

    Daniel Bagnall Active Member

    Hi Kevin,

    Thnanks for your reply. Yes what you have illustrated makes sense to me now.

    I was speaking to one of my ex senior lecturers, who I highly respect, and also attended CCPM, and asked for his thoughts. He is very much in accordance with Sagittal plane theory, assisting first ray function, and “locking the calcaneo-cubiod joint” in flexible/pes-planus foot types.

    I am getting rather confused though as to, what do we mean by locking???? Does this concept hold true to some extent?? Is it the same as talking about the supposed locking mechanism of the mid-tarsal joint? I am aware there is some considerable debate over this topic, if I stand correct?

    Also, if you dont mind I would like to ask you, what are the key tests you do every time during a biomechnical assessment? Their may have been a previous thread re: this, however, I would like to know what you do currently in your practice?

    Many thanks,

  13. I really don't know what "locking of the midtarsal joint" is since the midtarsal joint is spring-like, does not "lock" and will dorsiflex more with increased joint loads and dorsiflex less with decreased joint loads [joint load = dorsiflexion force on forefoot]. Saying that the midtarsal joint locks would be equivalent to saying that "the leaf-springs on my truck lock when the tires accept the weight of the vehicle". Total mechanical nonsense!! We have had this discussion elsewhere om Podiatry Arena and I will be lecturing on midtarsal joint locking at the PFOLA meeting in November in San Diego. The midtarsal joint does not lock....it just temporarily stops dorsiflexing or plantarflexing until greater or lesser forefoot dorsiflexion loads are placed across it!

    I reviewed the points of my biomechanical examination in another thread recently. http://www.podiatry-arena.com/podia...e=1&pp=40&highlight=biomechanical examination

    Daniel, it would be most helpful to only ask one question per posting so I can take adequate time to anwer each of them. Multiple questions are very difficult for me to give adequate attention to given my current time constraints.
  14. Daniel Bagnall

    Daniel Bagnall Active Member

    Hi Kevin,

    My apologies for holding you up.

    I understand what you are bringing accorss re: your answer about the mid-tarsal joint. However, when my lecturer is talking about locking the calcaneo-cubiod joint is that somehting enirely different?


  15. Daniel:

    What your lecturer probably means when he/she says "locking of the CCJ" is that the CCJ has sufficient stability to dorsiflexion moments from the ground reaction forces that are acting plantar to the lateral column (i.e. 4th and 5th metatarsal heads). My problem with the descriptor "locking" is that it implies that the CCJ (or MTJ for that matter) will move no further once it moves into a stable position. This concept is simply not true as the MTJ or CCJ will dorsiflex further with increased dorsiflexion moments acting across it.

    My attention to these seemingly small details may seem overly picky to many podiatrists. However, I strongly believe that the joints of the foot, and especially the MTJ and CCJ, are mechanically more like a spring than like a locking-ratchet type mechanism. Describing these relationships with mechanically clear and precise terminology helps decrease the confusion and ambiguity that normally accompanies this complex subject during its written and oral communication.

    Thanks for only asking me one question this posting. I'll be away this weekend vacationing with the family so I'll be back in a few days if you have more questions.
  16. Daniel Bagnall

    Daniel Bagnall Active Member


    Well I'm glad you have cleared that up for me as it was getting rather confusing (no disrespect either, to my ex-lecturer).

    Well I hope you enjoy the vacation! I will await your 2 books that I have ordered and then by the time I start reading them I'm sure I will have many more questions. However, don't be surprised if I have bombarded you by the time you come from holiday.

    Thanks again,

  17. Asher

    Asher Well-Known Member

    Hi Donna / Kevin,

    The answers to the above questions are:

    1. GRF A = 1850N, GRF B = 150N

    2. C = 235N

    Would you mind showing me how to do these calculations? You can call me Dr Fudd. Thanks for your time, again!


  18. Rebecca:

    Here is how I solved the problems......Merry Christmas!
    Last edited: Dec 16, 2007
  19. Asher

    Asher Well-Known Member

    Hi Kevin,

    Thanks so much for your time and patience in showing me how to work out this equation. Can I go through this and you might be able to see where I am stuck:

    I understand that Fa + Fb = 2000N (Up forces equal down forces).

    Its the next bit I don't understand where you write:
    (1.7m x Fc) + (0.4 x Fb) = 0.2 x 2000N
    I thought at first you were doing anticlockwise forces = clockwise forces, the anticlockwise forces being Fc and Fb and teh clockwise forces are Fa. But you aren't.

    What are you doing? Why is (0.2m x 2000N), which is half of the width times the weight of the object coming in to it.

    Thanks in advance.


    PS: first pink plantar ligament ropes and now a santa clause picture. :santa:
  20. Rebecca:

    I am using the left side edge of the object (i.e. where Force A acts) as the axis about which I am calculating that the summation of the clockwise and counterclockwise moments should be equal to each other. The sideways pushing force, Force C, and the force under the right side of the object, Force B, both produce counterclockwise moments. The center of mass of the object (which is 0.2 m from each side of the object) pulling downward with 2000 N of force, 0.2 m to the right of the left side edge of the object, produces the clockwise moment on the object. Does this help??

    In solving problems of statics, as in this example, remember that the summation of the forces and moments acting on an object must be equal to zero, or the object would be accelerating. If the object is not moving, then it must be in both translational and rotational equilibrium so you can use the equations I set up in my last posting to solve for the unknowns.
    Last edited: Dec 17, 2007
  21. Asher

    Asher Well-Known Member

    Thanks Kevin for helping me through the Thought Experiments. And Merry Christmas to you and yours.



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