Figure 1.
Musculoskeletal model used for simulations.
Note that because of space limitations in the figure, the moment arms of the muscle-tendon complexes at the joints (gray spacers at the joints) have not been drawn to scale; the actual moment arm values are presented elsewhere [18].
Figure 2.
Stick diagrams for maximum height jumps of models with isometric scale factors of 1 (L = 1) and 0.1 (L = 0.1).
Arrows pointing upward represent the ground reaction force vector and originate in the centre of pressure; arrows pointing downward represent the force of gravity and originate in the centre of mass (CM, open circles). Numbers below sticks indicate time in ms relative to takeoff. The leftmost stick diagrams represent the initial equilibrium posture, the other stick diagrams are spaced by one-tenth of the duration of the push-off. : vertical takeoff velocity of CM, h: jump height.
Figure 3.
Kinematic, energetic and work variables as function of time for models with isometric scale factors of 1 (L = 1) and 0.1 (L = 0.1).
is vertical acceleration of centre of mass (CM),
vertical velocity of CM, and
vertical displacement of CM.
is increase in effective energy during push-off relative to the start of the jump,
rate of change of
, and
work of muscle-tendon complexes, all expressed per kg body mass as indicated by caret over variables. Time (t) is expressed relative to takeoff (t = 0).
Figure 4.
Kinematic, energetic and work variables as function of isometric scale factor L.
is peak vertical acceleration of centre of mass (CM),
vertical velocity of CM at takeoff, and h (jump height) is vertical displacement of centre of mass (CM) in the airborne phase.
is kinetic energy due to
,
increase in potential energy during push-off,
increase in effective energy during push-off (sum of
and
),
peak rate of change of
during the push-off, and
work of muscle-tendon complexes, all expressed per kg body mass as indicated by caret over variables. IMP: Invariant Motion Pattern, i.e. values as they would be if segment angles over time were the same as in reference model (L = 1). BC: dependence of h on L predicted by Bennet-Clark [12] (equation 3).
Figure 5.
Explanation for reduced work output per kg of glutei (left panels) and vasti (right panels) with isometric downscaling.
Force, velocity and active state of contractile elements (CE) of glutei and vasti have been plotted as function of normalised CE-length () for models with isometric scale factor L equal to 1 (reference model) and 0.1.
is CE shortening velocity expressed in optimum CE-lengths (
) per second,
is CE force as fraction of maximum isometric force, and
is CE power output as fraction of its maximum according to the force-velocity relationship. Arrows indicate the direction of time. When L = 0.1, CE work per kg (proportional to surface under curves in A and D) is less because
is higher and active state is lower than when L = 1.