## 4 The Layout Designing of the Collaborative Workplace Supported by a Modeling Paradigm
### Modeling Paradigm
#### 4.1.1 Elements of Modeling Paradigm
Finally, the collaborative workplace is seen as the combination of several main workspaces: (i) the _elementary workspaces_ dedicated to human operators and cobot, (ii) the _composed workspaces_ identified through the combination of the elementary workspaces [5], and (iii) the logistic spaces. _Elementary workspaces._ The collaborative workplace includes two elementary workspaces dedicated, respectively, to humans and cobots. _Human Space_ (HS) is the space where the operator can perform their tasks; it is the result of the envelope of N Unitary Human Spaces (UHSs), each dedicated to a specific task. The UHS is a circular area around the operator with a diameter equal to the arm span (AS). The AS is defined as the measurement of the length from one end of a person's arms to the other, when raised parallel to the ground at shoulder height and at a 90 deg angle. The space occupied by the operator is described by means of the body ellipse whose minor and major axes, respectively, represent depth and width of the human body. To be thorough, it is necessary to consider the increase in space due to the operator's clothing [55]. Zones of convenient reach are the areas that can be reached comfortably through movements that do not involve effort. These areas are included inside the UHSs and contain the Human Task Area (HTA). The HTA is a circular area dedicated to carry out the tasks that compose the whole operation. The center of this circular area is called Human Task Center (HTC). Figure 4 depicts the above-defined areas. _Robot Space_ (RS) is the space needed by the robot system (including attached tool and workpiece) to perform all its tasks. This space does not necessarily correspond to the maximum space that the robot can reach. It is usually defined through a safety-rated soft axis and space limiting, as described in ISO 2018-1:2011. Practically, the robot system motion is software-defined and the space limiting is used to identify a space of any geometric shape where robot motion is limited [23]. However, robot space may be seen as the composition of N elementary robot spaces one for each task. The center of each intended space is named a Robot Task Center (RTC). _Composed workspaces._ Composed workspaces are obtained from the combination of the elementary workspaces: _Collaborative Space_ (CS) is the intersection of the human and robot space. It is present only if one of the established tasks is carried out in collaborative modes. In this case, it is possible to define a Collaborative Task Center (CTC) as the center of the CS. Figure 3: Most common applications for cobots installed by the key vendors. _Operational space_ (OS) is the sum of the elementary spaces and represents the space needed to perform all the intended tasks. It includes the Collaborative Space. Logistic spaces. The spaces through which the workplace interfaces with the parts coming from the outside and the materials directed toward the outside are defined as logistic spaces. The logistic spaces are classified as follows:  
1. The infeed spaces receive from the outside the workpiece, supply materials as screws, nuts, bolts, single parts to be assembled, sub-assemblies to be completed, and groups to be processed. 2. The outfeed spaces receive the processed parts directed outwards. The outfeed spaces dedicated to correctly processed parts should be different from the outfeed spaces dedicated to parts which do not satisfy quality standards and must be reworked or discarded. Shape and size of the logistic spaces are dependent on the geometric features of the logistic resources used to load/unload, for storage, and to handle the workpieces. The position of the logistic spaces depends on the specific case. A valid solution could be to place the logistic spaces on the workplace sides. The possible scenarios are the following (Figure 5):  
1. Infeed and outfeed spaces are placed near consecutive sides;
2. Infeed and outfeed spaces are placed near opposite sides;
3. Infeed and outfeed spaces are placed near the same side.