## 2 Methodology  
### Experimental Setting and User Task  
The primary purpose of the research was to learn about the mean maximum velocity and mean maximum acceleration of human hand movement during the implementation of manipulation tasks and the influence of the direction of movement on the achieved speeds and accelerations.  
The study was divided into two stages. The first stage concerned the analysis of the reaching movements, which did not require high precision of the final position. They were made in three directions--longitudinal, lateral, and vertical--and were rectilinear movements. In the second stage, the hand movement during a task requiring precision and obtaining the required accuracy when moving the object between designated areas was examined.  
All subjects performed reaching and precise movements with their dominant hand. Each subject performed trials with four reaching movements for each. Therefore, the number of recorded, reaching movements was 360 (30 subjects \(\times\) 4 movements \(\times\) 3 directions), and for precise movements, it was 150 (30 subjects \(\times\) 5 movements \(\times\) 1 direction). This test was measured after two practice trials.  
The operator's task during the study of reaching movements was to move the handle ((2) in Figure 2) from the adopted initial position to the fixed end position, defined by flexible bumpers mounted on the guides. The operator's task was to make a one-way movement and return to the position close to the initial position, with a normal hand movement speed. For each type of movement, the position of the guides (3) and bumpers (5) (Figure 2) was changed. Due to the ergonomics of hand movements [92; 93], it was assumed that the distance between the bumpers for longitudinal movement (x\({}_{i}\)) is 430 mm, for transverse (y\({}_{i}\)) it is 730 mm, and for vertical (z\({}_{i}\)) it is 930 mm (Figure 2). The basic measuring element of the test stand was a linear encoder with a measuring range of 0-1.25 m and an accuracy of 0.625 mm [94].  
Figure 2: Cont.  
During the study of precise movements, the operator's task was to transfer the cylinder from circle A to circle B (Figure 3). The distance between the centers of the circles was 500 mm. The circle in which the object should be placed was equal to its diameter. For displacement measurement, the position of optical markers (3) was recorded by stereovision cameras ((4) in Figure 4). The displacement in the two axes was recorded so that it was possible to assess the correctness and accuracy of putting down the object.  
Figure 3: Scheme of precise hand movement tests. (A) Initial position of the carried object; (B) final position of the carried object; (a) actual distance of reference markers in relation to the \(x\) axis; (b) actual distance of reference markers in relation to the \(y\) axis.  
Figure 2: Studies of reaching hand movements: (**a**) longitudinal movement tests; (**b**) lateral movement tests; (**c**) vertical movement tests; (**d**) test stand: 1—linear encoder, 2—moved element (handle grabbed by the operator’s hand), 3—guides, 4—data acquisition device, 5—spring stop, 6—power supply, 7—measurement card, A—starting point, B—point determining the goal of the movement.  
The basic measuring elements of the test stand based on the MyoVideo (Noraxon U.S.A. Inc., Scottsdale, AZ, USA) system were two stereovision cameras with a horizontal field of view of 57.5\({}^{\circ}\), a vertical field of view of 43.1\({}^{\circ}\), and an accuracy of less than 0.1 mm [95]. To assess the accuracy of the task, it was assumed that the error of putting the object down should not exceed 2 mm on both the \(x\) and \(y\) axes. The value of the setdown error corresponded to 5% of the diameter of the transferred object.