# A Conceptual Model for Joint Graphic Representation of
## 5 MMCS Design Examples
### Coordinated Axes Motion Applied to Cartesian Configuration  
Coordinated movements involve two or more servo axes in order to position a specific point of a tool along a path that is defined with respect to a coordinate system [40]. For this case study, rectilinear trajectories with absolute coordinates were chosen, together with a mechanical system of three Cartesian servo axes. First, the simplified drawing of the mechanics was obtained. Figure 10 shows the Cartesian system used in this example. It shows the names assigned to the servo axes, according to the axes naming conventions of the CNC standard, ISO841 [12]. Some pieces are also highlighted, such as the one joining the mobile carriage of the X servo axis with the servo axis Y, or the one that joins the mobile carriage of the servo axis Y with the servo axis Z, the one that joins the mobile carriage of the servo axis Z with the tool, and even the tool itself (a basic but adequate tool for this example). Those parts are also relevant for the motion control point of view, since they define the positional relation of the tool with the moving elements of the servo axes and their respective coordinate systems. Due to the complexity of this machine, the use of views seems convenient. Figures 11a and 12a show the top and side views of the 3D model of Figure 10. In Figures 11b and 12b, the result of the simplification process applied to each view can be seen, as previously explained in Section 4. The X and Y servo axes take advantage of the simplified versions shown in Figure 6.  
Figure 11: Top view. (**a**) 3D Version. (**b**) MMCS version. Figure 10: 3D representation of the Cartesian system of the example. The assembly parts between the servo axes can be depicted with a more symbolic shape and filled with a specific pattern to better identify them, for instance, a striped one. The same pattern may be used within the tool and its supporting structure (Figures 11b and 12b). One of the main characteristics of the MMCS proposal is that it explicitly identifies moving parts (in white), and it distinguishes them from those mechanical structures used to guide them (represented in black), as Figure 13 illustrates. In Figure 11, servo axes X and Y have the same structure of the linear actuator in Section 4.3, but servo axis Z has a mechanically different structure because the guide is shorter than the moving part (Figure 12b). Figure 13 is an example of two possible positions of the Z axis. Now, movement specifications may be incorporated. The trajectory of the TCP with respect to the coordinate system and the individual movement of each servo axis can be seen in the joint representation. The \"position\" parameter of the motion commands specifies the destination coordinates of the specific point of the tool with respect to which the position is measured. That point is usually known as \"tool center point\", or TCP, and it is indicated graphically with the center of a cross inscribed in a circle. The coordinates of the TCP, in turn, are specified with respect to a coordinate system, which could be, for example, the \"machine coordinate system\" or the \"product coordinate system\" (MCS and PCS, respectively, using PLCopen terminology). Two concentric circumferences with a cross are proposed to represent the origin of the coordinate system, with arrows indicating the positive direction of the measurement axes. The motion controller will calculate the linear path of the TCP to the destination position, with respect to the coordinate system, starting from the final position of the previous movement. Its graphic representation can be seen in Figure 14, where Figure 14a is the top view, and Figure 14b the side view. In this case, the arrows represent the path followed by the TCP, accompanied by the coordinates of the end point and an identifier to associate it with the corresponding motion command of the source code. Figure 12: Side view. (**a**) 3D Version. (**b**) MMCS equivalent version. Figure 13: Cartesian system movement.