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 agonistantagonist (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 coactivations 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.

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This paper proposes a novel method for assessment of muscle imbalance based on muscle synergy hypothesis and equilibrium point (EP) hypothesis of motor control. We explain in detail the method for extracting muscle synergies under the concept of agonist-antagonist (AA) muscle pairs and for estimating EP trajectories and endpoint stiffness of human upper limbs in a horizontal plane using an electromyogram. The results of applying this method to the reaching movement of one normal subject and one hemiplegic subject suggest that (1) muscle synergies (the balance among coactivation of AA muscle pairs), particularly the synergies that contributes to the angular directional kinematics of EP and the limb stiffness, are quite different between the normal subject and the hemiplegic subject; (2) the concomitant EP trajectory is also different between the normal and hemiplegic subjects, corresponding to the difference of muscle synergies; and (3) the endpoint (hand) stiffness ellipse of the hemiplegic subject becomes more elongated and orientation of the major axis rotates clockwise more than that of the normal subject. The level of motor impairment would be expected to be assessed from a comparison of these differences of muscle synergies, EP trajectories, and endpoint stiffness among normal and pathological subjects using the method.

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