## 1 Introduction  
Manipulators replacing direct human activity are increasingly used in the world. They have been used both in medicine as surgical manipulators [1; 2; 3], and in military applications, rescue services, or the construction industry in the form of specialist manipulators or equipment [1, 4, 5]. In dangerous scenarios such as chemical plants [6], disaster sites [7], explosives demolition [8; 9], and teleoperated manipulators are needed. Robotic teleoperation satisfies the demands of scenarios in which human access is dangerous but human intelligence is required [10, 11]. For this work, the operator is required to constantly control the position of the effector using the system HMI (Human-machine Interface) consisting of visualization system (cameras and displays or goggles) and control devices. The efficiency of teleportation dramatically depends on the quality of the control system and operation space visualization. All manipulator movements are executed on the effector placement observation, but very often the quality of the control system limits the operation speed and productivity. As the most common human-machine interface controllers, which are easy to use to provide simple commands in teleoperation tasks, keyboards, joysticks, gamepads, mouses, or 3D mouses are used [12; 13; 14]. These devices force human operators to learn how to use them because their usage is unnatural. It is problematic for the operation of the manipulator with higher DOF (Degrees of Freedom) because the operators have to generate the command for every joint motion of the manipulator. It demands long operator training and limits the productivity and efficiency of operation [15]. For those reasons, more complex taskmaster-slave devices are used like master exoskeleton, optical motion capture technology, data gloves or gloves with markers, and haptic devices [13; 16; 17; 18]. New solutions improve the control efficiency and enable higher speed of effector motions [19; 20; 21]. The use of this type of control is particularly desirable and important if an inexperienced operator controls the manipulator. Thanks to this, operators are able to achieve high control efficiency comparable to experienced operators in a relatively short time [22; 23; 24]. It is very important for operations with heavy, high lifting capacity, and long reach manipulators equipped with hydraulic drive systems. The modern control system can increase their movement velocity and overall productivity. In such construction, the speed limit should be adapted to human perception and the possibility of system control. An additional problem is the size ratio. Due to the large working area, there is a large-scale ratio between the HMI size and the effector workspace of these manipulators [25]. Knowledge of the influence of size ratio on the permissible effector velocities of these manipulators is essential for the effective design of their drive systems and power demand. This will allow to increase the velocity of movements, overall efficiency, and effector movement accuracy [26]. The main element of the intuitive control system is a suitably shaped track device with various types of construction solutions [26; 27; 28; 29; 30]. Starting from specially shaped structures with the same kinematic structure as the controlled manipulator [26], through parallel structures used in medical applications [29; 30] up to those adapted to the operator's upper limb [27; 28]. The effectiveness of using this type of control systems depends on the operator's perception and scale ratio and the velocity and acceleration of the operator's hand [31]. According to [32] presented research involving moving the cursor on the monitor screen between points spaced every few centimeters, using a tracking device with haptic feedback for scale ratios 1:1, 1:2, and 2:1, for the 1:2 size ratio, the time increased by 30% compared to the 1:1 size ratio, while in the case of the 2:1 size ratio, there was no significant difference in this aspect.