Current approaches do not allow robots to execute a task and simultaneously convey emotions to users using their body motions. This paper explores the capabilities of the Jacobian null space of a humanoid robot to convey emotions. A task priority formulation has been implemented in a Pepper robot which allows the specification of a primary task (waving gesture, transportation of an object, etc.) and exploits the kinematic redundancy of the robot to convey emotions to humans as a lower priority task. The emotions, defined by Mehrabian as points in the pleasure–arousal–dominance space, generate intermediate motion features (jerkiness, activity and gaze) that carry the emotional information. A map from this features to the joints of the robot is presented. A user study has been conducted in which emotional motions have been shown to 30 participants. The results show that happiness and sadness are very well conveyed to the user, calm is moderately well conveyed, and fear is not well conveyed. An analysis on the dependencies between the motion features and the emotions perceived by the participants shows that activity correlates positively with arousal, jerkiness is not perceived by the user, and gaze conveys dominance when activity is low. The results indicate a strong influence of the most energetic motions of the emotional task and point out new directions for further research. Overall, the results show that the null space approach can be regarded as a promising mean to convey emotions as a lower priority task.