## Multiple Muscle Involvement in Flexion of the Elbow

We have already seen that multiple muscles contribute to a certain task of movement or posture. Despite the presence of a number of muscle groups contributing to the same movement, it is common in biomechan-ics to consider one muscle group for the specified action, and compute the force (moment) that must be produced by this muscle to carry out the movement (against resistance). What is the magnitude of the errors involved in such back-of the-envelope type computations? We can address this question by assuming the following: (a) multiple muscles act on the joint and (b) the force generated by each muscle is proportional to the cross-sectional area at the midpoint at full activation. We illustrate this procedure by considering the flexion of the forearm against a resistance.

Example 6.7. Consider the flexion of the forearm considered in Example 6.6. Assume (as shown in Fig. 6.7c) that two muscle groups participate in the flexion, the biceps brachia and the brachioradialis. Assume further that the latter muscle originates at the humerus 4 cm away from the center of rotation of the elbow and inserts at the radius at 20 cm away from the center of rotation of the elbow. The cross-sectional areas of biceps and brachioradialis are, respectively, 12 cm2 (Ab) and 4 cm2 (Abr). Both muscles are maximally activated during flexion. Determine the contribution of each muscle group to the total joint moment.

Solution: The total joint moment is the moment created by the muscles to resist the clockwise moment created by the 10-kg weight. The joint moment was computed in Example 6.6 as a function of the joint angle 6. To determine the relative contribution of brachioradialis to the joint moment, we compute its moment arm with respect to the center of rotation of the elbow:

in which cbr and dbr represent, respectively, the length and the moment arm of the brachioradialis.

How do these two muscles share the load? We assume that the force produced by each muscle is proportional to their maximal cross-sectional area:

This assumption is equivalent to the statement that muscle fiber tension depends only weakly on the length of the fiber in physiological ranges of fiber length. Joint moment can be written as a summation of the moments contributed by the biceps and the brachioradialis:

As usual, the subscripts refer to the muscle groups involved in flexion. Equations 6.15 and 6.16 can now be used to compute muscle force as a function of the joint angle:

Comparing the biceps force computed in this example with that of Example 6.6, we find that biceps force was overestimated by 13% when the contribution of brachioradialis to the lifting of the weight was neglected. Inclusion of the triceps (which resists flexion) as opposed to brachioradi-alis in the analysis would show the evaluation of biceps force in Example 6.6 to be an underestimate.

## Getting Started With Dumbbells

The use of dumbbells gives you a much more comprehensive strengthening effect because the workout engages your stabilizer muscles, in addition to the muscle you may be pin-pointing. Without all of the belts and artificial stabilizers of a machine, you also engage your core muscles, which are your body's natural stabilizers.

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