ELEC ENG 3BA3:

Structure of Biological Materials

Notes for Lecture #6 Tuesday, September 20, 2011

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3. BIOMECHANICS

Some areas of biomechanics research and application: – movement and locomotion mechanics – tissue mechanics – orthopaedic prostheses & implants – impact mechanics – neuromuscular control – functional electrical stimulation – cell mechanics and locomotion

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3.1 Locomotion

Quantifying the mechanics of human locomotion will be helpful in:

– developing mathematical models of biomechanical systems,

– understanding the effects of pathology or injury on locomotion, and

– determining the important properties required for orthopaedic prostheses & implants, functional electrical stimulation, etc. to restore near-normal locomotion

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Ground reaction force (GRF)

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Ground reaction force for walking & running:

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Determining kinematics from the GRF

Acceleration of the center of mass (C.O.M.):

where Fgz(t) and Fgy(t) are the vertical and horizontal components of the ground reaction force (N), m is body mass (kg), g is acceleration due to gravity (ms-2), and az(t) and ay(t) are the vertical and horizontal acceleration of the C.O.M. (ms-2).

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Velocity of the C.O.M.: where vz(t) and vy(t) are the vertical and horizontal velocity of the C.O.M. (ms-2).

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Vertical displacement of the C.O.M.: where dz(t) is the vertical displacement of the C.O.M. (m).

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Kinematics of walking & running:

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Total mechanical energy of the C.O.M.: where Ekin(t) is the kinetic energy of the C.O.M. (J):

and Egrav(t) is the potential gravitational energy of the C.O.M. (J):

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Mechanical energy for walking & running:

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Models for walking & running:

walking ¼ running ¼ inverted pendulum spring-mass system

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Models for walking & running: walking ¼ kinetic energy ) inverted pendulum gravitational potential energy ) kinetic energy running ¼ kinetic energy & spring-mass system gravitational potential energy ) elastic potential energy ) kinetic energy & gravitational potential energy

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Implications for orthopaedic prostheses & implants, functional electrical stimulation (FES), etc.

Walking: – optimal walking speed is »1.25 ms-1 for

adults, because the exchange of gravitational potential energy with kinetic energy is most efficient at this speed

– at walking speeds >1.5 ms-1, fluctuations in kinetic energy greater than fluctuations in gravitational potential energy

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Walking (cont.): – at walking speeds <1.0 ms-1, fluctuations in

kinetic energy less than fluctuations in gravitational potential energy

Consequently, to restore a near-normal walking motion with optimal efficiency, we need to obtain:

– a natural pendular motion, and

– a walking speed of between 1.0 and 1.5 ms-1.

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Running: – becomes more efficient than walking at

speeds >2.0 ms-1

– is dependent on normal elastic behaviour of the legs

Walking & running also depend on: – force-generating muscle contractions

– limb and joint stability

– neuromuscular control

– vestibular (balance) feedback