The minimum intervention principle of optimal control relates the uncontrolled manifold to muscle synergies

The nervous system uses muscle activation patterns to perform successful motor tasks, and motor tasks inevitably satisfy the laws of mechanics. The number of muscles usually exceeds the degrees of freedom of the task such that multiple combinations of muscle activities satisfy mechanical demands. A low-dimensional space usually explains a large variance in the muscle activations, leading to the hypothesis that muscle redundancy is solved by neurally coordinated muscle synergies. In addition to synergies, motor task mechanics also enforce a structure on muscle activity. Muscles satisfy multiple non-negotiable mechanical demands of equilibrium, stability, force, and respect the constraints. The redundancy in the muscle architecture is the degree of freedom available after accounting for the necessary mechanics. In this study, I investigate how task mechanics structure muscle activities by using a biomechanical model of an index finger in contact and published measurements of seven muscle activities during a fingertip force production task. I derive a map from muscle activities to complete task mechanics with the necessary conditions of equilibrium, stability, and force. By invoking the uncontrolled manifold hypothesis, I show that the variability in muscle activities is channeled in the task-irrelevant directions, which is given by the null space of the map from muscle activations to task variables. Furthermore, I show that the principal component that explains maximum variance in muscle activations is oriented along the task-irrelevant direction with the highest projected variance, suggesting that the maximal principal directions correspond to the task-irrelevant subspace rather than the task-relevant directions. This study has consequences for understanding muscular redundancy and synergy, and also provides direct evidence that the simplified biomechanical models satisfy mechanical requirements.