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Background Soft wearable robots (exosuits), being lightweight, ergonomic and low power-demanding, are attractive for a variety of applications, ranging from strength augmentation in industrial scenarios, to medical assistance for people with motor impairments. Understanding how these devices affect the physiology and mechanics of human movements is fundamental for quantifying their benefits and drawbacks, assessing their suitability for different applications and guiding a continuous design refinement. Methods We present a novel wearable exosuit for assistance/augmentation of the elbow and introduce a controller that compensates for gravitational forces acting on the limb while allowing the suit to cooperatively move with its wearer. Eight healthy subjects wore the exosuit and performed elbow movements in two conditions: with assistance from the device (powered) and without assistance (unpowered). The test included a dynamic task, to evaluate the impact of the assistance on the kinematics and dynamics of human movement, and an isometric task, to assess its influence on the onset of muscular fatigue. Results Powered movements showed a low but significant degradation in accuracy and smoothness when compared to the unpowered ones. The degradation in kinematics was accompanied by an average reduction of 59.20±5.58% (mean ± standard error) of the biological torque and 64.8±7.66% drop in muscular effort when the exosuit assisted its wearer. Furthermore, an analysis of the electromyographic signals of the biceps brachii during the isometric task revealed that the exosuit delays the onset of muscular fatigue. Conclusions The study examined the effects of an exosuit on the characteristics of human movements. The suit supports most of the power needed to move and reduces the effort that the subject needs to exert to counteract gravity in a static posture, delaying the onset of muscular fatigue. We interpret the decline in kinematic performance as a technical limitation of the current device. This work suggests that a powered exosuit can be a good candidate for industrial and clinical applications, where task efficiency and hardware transparency are paramount. Electronic supplementary material The online version of this article (10.1186/s12984-019-0495-y) contains supplementary material, which is available to authorized users.