A novel muscle synergy extraction method to explain the equilibrium-point trajectory and endpoint stiffness during human upper-limb movements on a horizontal plane

Based on the idea of synergy to explore the building blocks of movements, this study focused on the muscle space for reaching movements by human upper limbs on a horizontal plane to estimate the relationship among muscle synergies, equilibrium-point (EP) trajectories, and endpoint stiffness in two ways: (1) a novel estimation method that analyzes electromyographic signals under the concept of agonist-antagonist (A-A) muscle pairs and (2) a conventional estimation method that uses mechanical perturbations. The experimental results suggest that (1) muscle activities of reaching movements by human upper limbs are represented by only three functional muscle synergies; (2) each muscle synergy balances the coacti-vations of A-A muscle pairs; (3) two of the muscle synergies are invariant bases that form an EP trajectory described in polar coordinates centered on a shoulder joint, where one is a composite unit for radial movement and the other is for angular movement; and (4) the third muscle synergy is the invariant basis for additional adjustment of the endpoint stiffness and has some influence on the direction and size of the endpoint stiffness ellipse.