Neural control of movement has to overcome the problem of redundancy in the multidimensional musculoskeletal system. The problem can be solved by reducing the dimensionality of the control space of motor commands, i.e., through muscle synergies or motor primitives. Evidence for this solution exists, multiple studies have obtained muscle synergies using decomposition methods. These synergies vary across different workspaces and are present in both dominant and non-dominant limbs. Here we explore the dimensionality of control space by examining muscle activity patterns across reaching movements in different directions starting from different postures performed bilaterally by healthy individuals. We further explore the effect of biomechanical constraints on the dimensionality of control space. We are building on top of prior work showing that muscle activity profiles can be explained by applied moments about the limb joints that reflect the biomechanical constraints. These muscle torques derived from motion capture represent the combined actions of muscle contractions that are under the control of the nervous system. Here we test the generalizability of the relationship between muscle torques and muscle activity profiles across different starting positions and between limbs. We also test a hypothesis that the dimensionality of control space is shaped by biomechanical constraints. We used principal component analysis to evaluate the contribution of individual muscles to producing muscle torques across different workspaces and in both dominant and non-dominant limbs. Results generalize and support the hypothesis. We show that the muscle torques that support the limb against gravity are produced by more consistent combinations of muscle co-contraction than those that produce propulsion. This effect was the strongest in the non-dominant arm moving in the lateral workspace on one side of the body.