The fundamental role of personality in shaping interactions is increasingly being exploited in robotics. A carefully designed robotic personality has been shown to improve several key aspects of Human-Robot Interaction (HRI). However, the fragmentation and rigidity of existing approaches reveal even greater challenges when applied to non-humanoid robots. On one hand, the state of the art is very dispersed; on the other hand, Industry 4.0 is moving towards a future where humans and industrial robots are going to coexist. In this context, the proper design of a robotic personality can lead to more successful interactions. This research takes a first step in that direction by integrating a comprehensive cognitive architecture built upon the definition of robotic personality - validated on humanoid robots - into a robotic Kinova Jaco2 arm. The robot personality is defined through the cognitive architecture as a vector in the three-dimensional space encompassing Conscientiousness, Extroversion, and Agreeableness, affecting how actions are executed, the action selection process, and the internal reaction to environmental stimuli. Our main objective is to determine whether users perceive distinct personalities in the robot, regardless of its shape, and to understand the role language plays in shaping these perceptions. To achieve this, we conducted a user study comprising 144 sessions of a collaborative game between a Kinova Jaco2 arm and participants, where the robot's behavior was influenced by its assigned personality. Furthermore, we compared two conditions: in the first, the robot communicated solely through gestures and action choices, while in the second, it also utilized verbal interaction.