Biomechanics Lab, Univ. of Ottawa1 Measurement of Internal Work by Absolute Work Method D. Gordon E. Robertson, PhD, FSCB Biomechanics Laboratory, School of Human Kinetics, University of Ottawa, Ottawa, CANADA

Biomechanics Lab, Univ. of Ottawa2 Mechanical Energy Four forms –Gravitational potential (E gp )m g y –Elastic potential (E ep )½ k s 2 –Translational kinetic (E tk )½ m v 2 –Rotational kinetic (E rk ) 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 Ottawa3 Total Body Mechanical Energy Sum of all segmental total mechanical energies (E s ) Segmental total energy E s = m s g y s + ½ m s v s 2 + ½ I s s 2 Total body energy (E total, sum over all segments) E total = E s

Biomechanics Lab, Univ. of Ottawa4 External Work External work = change ( ) in total body mechanical energy W external = E total ) or simplified W external = E total (t final ) – E total (t initial )

Biomechanics Lab, Univ. of Ottawa5 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 Ottawa6 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. W n = | m s g y s | + | ½ m s v s 2 | + | ½ I s s 2 | First summation is over all time intervals Second summation is over all segments Norman et al. (1976)

Biomechanics Lab, Univ. of Ottawa7 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. W w = | E s | First summation is over all time intervals Second summation is over all segments Winter (1979)

Biomechanics Lab, Univ. of Ottawa8 Energy Conservation by Transforming Energy within a Segment simple pendulum pendulum potential energy total energy kinetic energy

Biomechanics Lab, Univ. of Ottawa9 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 (E gp, E tk ) to another. W internal = | E total | W external Absolute values prevent decreases in mechanical energy from cancelling increases

Biomechanics Lab, Univ. of Ottawa10 Energy Conservation by Transferring Energy between Segments compound pendulum proximal segment total energy distal segment

Biomechanics Lab, Univ. of Ottawa11 Energy Saved by Transfers and Transforms Energy saved by permitting transfers of energy from segment to segment E transfers = W w W internal Energy saved by permitting transforms of energy from one form to another (potential ot kinetic) E transforms = W n W w

Biomechanics Lab, Univ. of Ottawa12 Segment Energies during Walking no conservation in the leg (shank) some conservation in the thigh some conservation in the trunk some transfer between left and right sides

Biomechanics Lab, Univ. of Ottawa13 Equation Summary E total = m s g y s + ½ m s v s 2 + ½ I s s 2 W n = | m s g y s | + | ½ m s v s 2 | + | ½ I s s 2 | W w = | E s | W total = | E s | = W wb W external = E total = E final E initial W internal = W total W external

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 Ottawa14