Non-verbal social interaction between humans requires accurate understanding of the others’ actions. The cognitivist approach suggests that successful interaction depends on the creation of a shared representation of the task, where the pairing of perceptive and motor systems of partners allows inclusion of the other’s goal into the overarching representation. Activity of the Mirror Neurons System (MNS) is thought to be a crucial mechanism linking two individuals during a joint action through action observation. The construction of a shared representation of an interaction (i.e., joint action) depends upon sensorimotor cognitive processes that modulate the ability to adapt in time and space. We attempted to detect individuals’ behavioral/kinematic change resulting in a global amelioration of performance for both subjects when a common representation of the action is built using a repetitive joint action. We asked pairs of subjects to carry out a simple task where one puts a base in the middle of a table and the other places a parallelepiped fitting into the base, the crucial manipulation being that participants switched roles during the experiment. We aimed to show that a full comprehension of a joint action is not an automatic process. We found that, before switching the interactional role, the participant initially placing the base orientated it in a way that led to an uncomfortable action for participants placing the parallelepiped. However, after switching roles, the action’s kinematics by the participant who places the base changed in order to facilitate the action of the other. More precisely, our data shows significant modulation of the base angle in order to ease the completion of the joint action, highlighting the fact that a shared knowledge of the complete action facilitates the generation of a common representation. This evidence suggests the ability to establish an efficient shared representation of a joint action benefits from physically taking our partner’s perspective because simply observing the actions of others may not be enough.