# A Framework for 3D Plant Simulation of Meal-Kit-Packaging Robot Automation System
## 2 Materials and Methods
### Development of Robot-Automated 3D Simulation of Meal Kit Packaging Process
To generate a hybrid, meal kit, 3D simulation model, a kinematic of the delta robot, to generate a trajectory for the pick-and-place movement, should be implemented in the 3D simulation software. After configuration of the production machinery, the kinetic mechanisms of the implemented-robot and individual meal kit pick-and-place gripper joint are defined. To define the robot kinematic, we set the initial physical characteristics of the delta robot such as the length of the arm, location of the rotation joint, the distance from the end of the moving platform of the delta robot to the end of gripper, etc. To create a robot trajectory, we applied the inverse-position kinematic of the delta robot [22]. There are two major revolute-input delta robot kinematics: inverse-position kinematic and forward-position kinematic. The inverse-position kinematic uses \(x\), \(y\), and \(z\) coordinates as inputs to get 3 rotation angles,whereas the forward-position kinematic uses three rotation angles as inputs to get the position value [23]. \[\text{the origin of }\{\text{P}\}\textit{ where }P=\textit{base frame}\]  
\[P_{p}=\{x\,y\,z\}^{T}\]  
\[\boldsymbol{\Theta}=\{\theta_{1}\,\theta_{2}\,\theta_{3}\}^{T}\]  
The delta robot's inverse position kinematics (IPK) is accomplished by using the three constraint equations applied to a vector loop-closure equation. The three independent, scalar IPK equations are of the form which can solved using the Tangent Half-Angle Substitution:  
\[E_{i}cos\theta_{i}+F_{i}sin\theta_{i}+G_{i}=0\;i=1,\;2,\;3\]  
\[\theta_{i}=2 tan^{-1}(t_{i})\]  
After importing the 3D model of the delta robot to the Siemens software, the defined, delta-robot kinematic is shown in Figure 6. We created a robot simulation using the kinematic model to pick individual meal kit items and place them on the tray--as shown in figure below--and repeat for each item. Figure 6: Representative generated trajectory of single delta robot for pick-and-place process in 3D simulation. In addition, after defining the robot kinematic, a rotational gripper mounted on the end effector of the delta robot, translation direction of the end effector as well as the motion speed and motion type of point to point are applied, and the trajectory is also defined. Figure 7 represents the single delta robot and mounted gripper motion generated for the simulation. The process of the individual meal kit product for pick-and-place motion starts with picking the transferring noodle on the conveyor, the gripper rotating 90 degrees, picking the transferring powder on the conveyor, picking the soup transferring on the conveyor, moving to the next conveyor belt and each transfer tray, placing the powder and soup in the tray, the gripper rotating 90 degrees, and placing the noodle in tray, simultaneously. The developed 3D simulation of the single-delta-robot-implemented meal kit packaging process is constructed with 5 major, automatic, individual meal kit product feeders, which is performed by works in the manual packaging process. The machineries, such as the automatic feeder (Figure 8A), tray loader (Figure 8B), and pillow packaging machine's characteristic and parameters (Figure 8C), are defined. For example, the size, moving path direction, and speed of the pillow packaging machine are defined as shown in Figure 8.  
Next, 3D simulation, which applied two delta robots for the individual meal kit's pick-and-place process, is shown in Figure 9 to determine the optimal assembly line for meal kit packaging to achieve the best KPIs. The robot and gripper kinematic and motion  
Figure 5:0 Configuration and parameters for automatic feeder or loader. (**A**) Tray loading to conveyor; (**B**) pneumatic, soup-feeder rotation and drop point to conveyor setting; (**C**) transfer time for elevated conveyor. Figure 5:1 Representative 3D simulation of single delta robot and peripheral machinery for meal kit packaging process. are defined in the same manner as the single-delta-robot-implemented 3D simulation.