The concept of “Industry 4.0” relies heavily on the utilization of collaborative robotic applications. As a result, the need for an effective, natural, and ergonomic interface arises, as more workers will be required to work with robots. Designing and implementing natural forms of human–robot interaction (HRI) is key to ensuring efficient and productive collaboration between humans and robots. This paper presents a gestural framework for controlling a collaborative robotic manipulator using pointing gestures. The core principle lies in the ability of the user to send the robot’s end effector to the location towards, which he points to by his hand. The main idea is derived from the concept of so-called “linear HRI”. The framework utilizes a collaborative robotic arm UR5e and the state-of-the-art human body tracking sensor Leap Motion. The user is not required to wear any equipment. The paper describes the overview of the framework’s core method and provides the necessary mathematical background. An experimental evaluation of the method is provided, and the main influencing factors are identified. A unique robotic collaborative workspace called Complex Collaborative HRI Workplace (COCOHRIP) was designed around the gestural framework to evaluate the method and provide the basis for the future development of HRI applications.