Sports Biomechanics by Roger Bartlett

Author:Roger Bartlett
Language: eng
Format: mobi
Tags: Social Sciences
Publisher: Taylor & Francis
Published: 2007-04-15T16:00:00+00:00

U(t)=E(Fmi/pcsai)3

(4.11)

reduces to a convex one for a one joint planar movement with two muscles. In this case:

Fm1=Fm2 (r1/r2) (pcsa1/pcsa2)3/2

(4.12)

The solution is shown in Figure 4.11. The reader interested in a mathematical consideration of the general inverse optimisation problem is referred to Herzog and Binding (1994).

The optimisation approaches discussed above are either static (and hence solved only once) or solved independently for each sample interval during a movement; these have been called, respectively, inverse static and inverse dynamic optimisation (Winters, 1995). They have not often been used for the fast movements that occur in sports activities (but see McLaughlin and Miller, 1980). An inverse dynamics integrated optimisation approach, where the cost function is defined over the time course of the activity (Winters, 1995), may prove more appropriate for such movements. Also, while non-linear optimisation can predict co-contraction of pairs of antagonist two-joint muscles, as in Figure 4.12 (Herzog and Binding, 1993), it does not account for co-contraction of antagonist pairs of single joint muscles. Such co-contractions have been measured using EMG, for example by Crowninshield (1978) in the brachialis and triceps brachii (medial head) in forced elbow extension. Furthermore, inverse optimisation has failed, to date, to predict the loops in muscle force curves that are frequently reported from force transducer studies (e.g. Prilutsky et al., 1994). For example, the predicted (lines 1–5) and measured (loops E) forces reported by Herzog and

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