One of the main goals of neuromuscular modeling is to establish the range of feasible muscle activations for a given mechanical output of the body. This is not a trivial problem because there are typically infinitely many combinations of muscle activations that will generate the same joint torques, as most joints are actuated by more muscles than rotational degrees of freedom. Here we show that well-established geometric methods easily provide a complete description of the set of muscle activations that generate a desired set of joint torques or endpoint forces. In contrast to iterative linear programming optimizations, geometric methods provide a set of solutions in muscle activation space simply by converting between the geometric representations of neural and mechanical constraints. As an example, we use geometric methods to find the feasible set of activations that produce fingertip forces in a set of directions. These results show that for a given set of fingertip forces, the range of feasible activation for each muscle can differ with the choice of mechanical constraints. Thus, the mechanical constraints of the task play an important role governing the options the nervous system has when controlling redundant muscles.

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