# Design and Testing of Torveastro: An Outer Space Service Robot
## 5 A Kinematic Simulation  
The approximation of the design values generated from the previous calculations from Equations (1)-(3) yields a body diameter of 370 mm and a link length of 195 mm, resulting in an arm length of 390 mm. As illustrated in Figure 4, all indicated factors were used to construct a 2D CAD model for kinematic simulation.  
The simulation illustrates only one limb during a 10-s closure phase that restores the arms to a launch configuration where they are entirely wrapped around the central body. In Figure 4a, the motion begins with fully extended limbs. In the second phase of the movements, the limbs are moved at the same pace, with the limb reaching the middle position in Figure 4b 70 degrees after moving. In the posture depicted in Figure 4c, the limb remains motionless while the forearms continue to ascend 14 degrees until they make contact with the robot body. In Figure 4d's final closing position, only the end-effector rotates 88 degrees to achieve the fully closed launch configuration.  
Figure 5 illustrates the computed angular velocities of the arm's three segments: the arm, the forearm, and the end-effector. During the closing procedure, it is worth observing that the arm travels from second 0.00 to second 3.00 with a maximum velocity of \(-35.00\) deg/s. Continuously spinning from second zero to second ten, the forearm reaches a top speed of \(-2.10\) deg/s. During the last phase of the closing procedure, the end-effector (EE) is triggered between 8.0 and 10.0 s with a maximum velocity of \(-43.93\) degrees per second.  
Figure 4: Kinematic simulation phases: (**a**) starting position, (**b**) middle position, (**c**) approaching position, (**d**) closed position.  
Figure 5: Computed results for the kinematic simulation in Figure 4 in terms of angular velocities.  
Figure 6 illustrates the computed angular accelerations of the three arm segments. The arm movement presents one step of angular acceleration from second 0.00 to second 1.50 with a maximum value of \(-\)45.75 deg/s\({}^{2}\); the second step from second 1.50 to second 3.00 represents deceleration with a maximum value of 46.36 deg/s\({}^{2}\) until stopping, allowing the forearm to continue for a more smooth closure while avoiding body impacts. The linear angular acceleration relates to the constant and uniform behavior displayed by the angular velocities.  
As illustrated by the velocity trend, the forearm is in constant motion from second 0.00 to second 10.00. From second 0.00 to second 5.00, the linear angular acceleration is \(-\)0.83 deg/s\({}^{2}\) to 0.83 deg/s\({}^{2}\), and from second 5.00 to second 10.00, the linear deceleration is \(-\)0.83 deg/s\({}^{2}\) to 0.83 deg/s\({}^{2}\). Lastly, between seconds 8.00 and 10.00, when the EE is triggered, its angular acceleration reaches a maximum of 57.00 deg/s\({}^{2}\).  
The computed kinematic simulation proved that the operation's intended angular velocities and angular accelerations are realizable with components that are commercially available.  
The size and positioning of the three motor units controlling the three degrees of freedom (DoFs) per limb, the control unit, the vision system, and the battery are represented in Figure 7. The central body protects and houses all electronics, actuators, and controls. When designing the layout, the size of the three commercial Dynamixel MX-64T actuators that will be contained within the motor unit is taken into account. In addition, the size and location of a maximum of three LiPo 14.8 V 6200 mAh batteries utilized for proper operational autonomy have been included. As a microcontroller, a Raspberry Pi 4 will be positioned in the center of the body and connected to three Raspberry cameras. The approximate weight of the designed prototype is 50 N. In conclusion, commercial components have been chosen based on the calculated results to construct a laboratory prototype for testing in a terrestrial gravity field.  
Figure 6: Computed results for the kinematic simulation in Figure 4 in terms of angular accelerations.