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    May 2013

    The transfer and storage of energy within the human body during ambulation

    Biomechanics appears to have adopted certain untested truths that relate to the determination of the flow and storage of energy around the human body. Essentially, the dot product of the reaction force at a joint is taken with its translational velocity, and then used to describe the flow and storage of energy to or from the segment in question. For example, the dot product of the reaction force at the ankle with its velocity, if positive is used to described energy flowing into the foot, and if negative used to described energy flowing out of the foot (Winter 1976; Gordon et al. 1980; Prince et al. 1994). While this is not altogether incorrect it is misunderstood.

    Using the foot again as an example during stance, when drawing the free body diagram (FBD) of the foot: the ground reaction force (GRF), the ankle centre reaction force and moment, and the unbalanced force (resultant) acting on the foot centre of mass (COM) should be considered. Using dynamic equilibrium, the applied force (F) acting on the foot COM can be determined. Taking the dot product of this applied force with the foot COM velocity (v), the mechanical power or mechanical work rate of the applied force acting on the foot COM can be evaluated. It should also be noted that the velocity of the body segment COM should be considered, not the velocity at the contact point of the ankle centre. The mechanical work rate of the moment (M) acting can also be resolved around to point of rotation. Therefore, the total instantaneous power developed by the applied force and moment is (Meriam et al. 2008):


    When the sense (direction) of the force or moment is in the same direction as the translational or angular velocity (ω), it can be described that work is done on the body (in the general sense). By the same account it is negative, if the sense of the force or moment is in opposition to the direction of travel (Meriam et al. 2008). However, these equations define the mechanical (energy) state of the body (in the general sense) in motion (Spiegel 1967; Meriam et al. 2008). They do not describe the intrinsic properties relating to energy storage and release, in musculature, or the structure of a prosthetic device.

    Consider the simple example of a vertically suspended spring on which a bob is attached; the spring will displace and find a new position of equilibrium. If the bob is now forced to oscillate like a pendulum, the radius of rotation will not remain constant, because the dynamic forces of motion cause the spring to shorter or lengthen. From the spring length and property of stiffness (defined be material and geometry) the stored energy of the spring can be evaluated or modelled most simply using a Lagrangian technique. The simple illustration demonstrates, while the applied forces of motion need to be know, the inherent properties of the pendulum system also need to be understood.

    At a point of rotation such as the ankle centre the muscles pull, and therefore, produced an applied moment. The forces at this contact point are equal and opposite so cancel. Hence, only the applied moment and relative angular velocity between the two segments need to be considered when evaluating the mechanical power developed, and mechanical work done by the muscles around this joint (Gordon et al. 2004). Cleary work can be done on or against the segment and this work changes the conservative energy state (kinetic and potential energy) of the body segment.

    A method to consider internal energy flow within a structure as complicated as the human body, is to use an explicit dynamic finite element technique that considers: geometric, material and boundary nonlinearities. Even for the prosthetic foot this will be considerable, although it is likely to show the transfer of strain energy along the foot to be minimal (Postema et al. 1997). For the biological limb the development of accurate model considering ligaments, tendons, bone and musculature would reveal the true internal energy transfers within the lower limb. However, these internal transfers of energy are very different from the work rates of the applied external forces acting on the boundaries of the FBD of the body segment considered. Therefore, the work rate alone of the force cannot be used as described by Prince et al. (1994) to take "into account the energy storage or dissipation and recovery within the compliant structure of the foot prosthesis", or the biological limb.

    In summary understanding the affect the dynamics of motion has on the system (body) being considered, will lead to the meaningful understanding of internal energy flow. This cannot be understood through looking at the energy state of motion alone.

    Gordon, D., E. Robertson, et al. (2004). Research Methods in Biomechanics. chapter 6

    Gordon, D., E. Robertson, et al. (1980). "Mechanical energy generation, absorption and transfer amoungst segments during walking." Journal of Biomechanics 13: 845-854.

    Meriam, J. L. and L. G. Kraige (2008). Engineering Mechanics Dynamics, John Wiley & Sons, Inc. Page 479

    Postema, K., H. J. Hemens, et al. (1997). "Energy storage and release of prosthetic feet Part 1: biomechanical analysis related to user benefits " Prosthetics and Orthotics International 21: 17-27.

    Prince, F. and D. A. Winter (1994). "A new technique for the calculation of the energy stored, dissipated, and recovered in different ankle-foot prostheses." IEEE 2(4): 247-255.

    Spiegel, M. R. (1967). Theoretical Mechanics, McGraw-Hill Inc. page 34

    Winter, D. A. (1976). "Analysis of the instantaneous energy of normal gait." Journal of Biomechanics 9: 253-257.
    Last edited by AnthonyCrimin; 05-16-2013 at 07:38 AM.

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