Post on 10-Dec-2015
Biomechanics Lab, Univ. of Ottawa 1
Measurement of Internal Workby Absolute Work Method
D. Gordon E. Robertson, PhD, FSCB
Biomechanics Laboratory,
School of Human Kinetics,
University of Ottawa, Ottawa, CANADA
Biomechanics Lab, Univ. of Ottawa 2
Mechanical Energy
Four forms– Gravitational potential (Egp)m g y
– Elastic potential (Eep) ½ k s2
– Translational kinetic (Etk) ½ m v2
– Rotational kinetic (Erk) ½ I 2
• Total mechanical energy is sum of all four
• Elastic potential energy is usually omitted because it cannot be measured accurately
Biomechanics Lab, Univ. of Ottawa 3
Total Body Mechanical Energy
• Sum of all segmental total mechanical energies (Es)
• Segmental total energy
Es = ms g ys + ½ ms vs2 + ½ Is s
2
• Total body energy (Etotal, sum over all segments)
Etotal = Es
Biomechanics Lab, Univ. of Ottawa 4
External Work
• External work = change () in total body mechanical energy
Wexternal = Etotal)• or simplified
Wexternal = Etotal (tfinal) – Etotal (tinitial)
Biomechanics Lab, Univ. of Ottawa 5
Zero-work Paradox
• If a body moves at constant velocity along a horizontal path no “external” mechanical work is done (work = 0)!
• Mechanical cost of moving body parts cancel out if motion is cyclic.
• Problem exists with all locomotor tasks but if body speeds up or rises (e.g., treadmill), some external work is done BUT additional costs of “cycling” the body parts are not included.
Biomechanics Lab, Univ. of Ottawa 6
Work Allowing No Transforms or Transfers of Energy
Work done that prevents both transfers and transforms of energy, i.e., from potential to kinetic and from segment to segment.
Wn = |ms g ys | + | ½ ms vs2 | +
| ½ Is s2|
• First summation is over all time intervals• Second summation is over all segments• Norman et al. (1976)
Biomechanics Lab, Univ. of Ottawa 7
Work Allowing within Segment Transforms
Work done that permits changes of forms of energy within a segment (kinetic to potential and vice versa) but no transfers from segment to segment.
Ww = |Es |• First summation is over all time intervals
• Second summation is over all segments
• Winter (1979)
Biomechanics Lab, Univ. of Ottawa 8
Energy Conservation by Transforming Energy within a Segment
• simple pendulum
pendulum
potential energy
potential energy
total energytotal
energy
kinetic energykinetic energy
Biomechanics Lab, Univ. of Ottawa 9
Internal Work
Internal work measures the mechanical costs of moving the limbs during a cyclic motion. The equation permits transfers of energy from segment to segment and transforms from one form (Egp, Etk) to another.
Winternal = |Etotal | − Wexternal
• Absolute values prevent decreases in mechanical energy from cancelling increases
Biomechanics Lab, Univ. of Ottawa 10
Energy Conservation by Transferring Energy between Segments
• compound pendulum
proximal segment proximal segment
total energytotal
energy
distal segment
distal segment
Biomechanics Lab, Univ. of Ottawa 11
Energy Saved by Transfers and Transforms
• Energy saved by permitting transfers of energy from segment to segment
Etransfers = Ww − Winternal
• Energy saved by permitting transforms of energy from one form to another (potential ot kinetic)
Etransforms = Wn − Ww
Biomechanics Lab, Univ. of Ottawa 12
Segment Energies during Walking
no conservation
in the leg (shank)
no conservation
in the leg (shank)
some conservation in the thigh
some conservation in the thigh
some conservation in the trunk
some conservation in the trunk
some transfer between left
and right sides
some transfer between left
and right sides
Biomechanics Lab, Univ. of Ottawa 13
Equation Summary
Etotal = ms g ys + ½ ms vs2 + ½ Is s
2
Wn = |ms g ys | + | ½ ms vs2 | + | ½ Is s
2|
Ww = |Es |
Wtotal = |Es | = Wwb
Wexternal = Etotal = Efinal − Einitial
Winternal = Wtotal − Wexternal
Problems & Errors
• assumes a loss of energy in one part of the body can be cancelled by a gain in another part
• therefore underestimates internal work
• some researchers (Williams & Cavanagh, 1983) have tried to remove this limitation by blocking such compensations but this also prevents energy being transferred from joint to joint (e.g., plantiflexing while standing upright does transfer energy from the ankle to the head and all parts in between).
Biomechanics Lab, Univ. of Ottawa 14