# Electromagnetically Driven Robot for Multipurpose Applications
## 4 Movement Analysis  
This section presents a proof of concept for the bending mechanism of a single robot segment. At the system level, the segment has a single input--the desired bending angle--and an output, which is the current needed to achieve that angle. This current driven through the coil is designed to generate either a repulsive or attractive electromagnetic force relative to the permanent magnet. This magnetic interaction disrupts the segment's initial force equilibrium, governed by Equation (3), where the forces of the spring and permanent magnet are balanced in a neutral state. And their behavior can be represented by Equations (11) and (19) for a single segment for proof of concept.  
When one of the coils shown in Figure 3 is active, the segment's equilibrium forces shown in Equation (1) will be disrupted or imbalanced to create more force at a specific angle of interest. This imbalance creates an angle of interest that causes the segment to bend in a particular direction based on the position of the active coil and polarity. When the bending angle increases, the current increases in the active coil and vice versa. This relationship ensures that the bending mechanism is responsive and precise, with fine adjustments to the current enabling accurate control over the angle.  
As the segment bends, its radial position changes due to the angle adjustment. As shown in Figure 8, the radial distance component also rises based on the change in the angle of motion. Moreover, Figure 8 shows the variations in the angle by around 60 degrees, which can cause a radial shift of the segment by around 0.8 cm.  
The current and electrical flux density required to opt for this bending in this segment are depicted in Figure 9. Both of them rise if the angle increases. For the system to achieve this 60-degree bend, a current of approximately \(4A\) is needed in the active coil, as illustrated in Figure 9. Additionally, this amount of current passing through the coil will generate around \(0.2T\). This increase in current and flux disrupts the balance between the electromagnetic force, the permanent magnet, and the spring, creating the extra force needed for bending.  
Figure 10 shows the magnetic force between the electromagnet and the permanent magnet, which acts opposite to the spring force with a margin of \(1N\). It also shows the difference between them, creating the desired angle in the segment. It can be seen that as the angle increases, the required magnetic force increases. In Figure 11, we can observe the direction and amount of movement in both the radial (\(x\)) and vertical (\(y\)) directions. Here,  
Figure 8: Variation in angle during robot movement.  
In summary, this analysis demonstrates how the bending mechanism in a robot segment relies on precise interactions between magnetic and spring forces to achieve controlled movement. By adjusting the current in the coil, the system generates the magnetic force needed to reach a specific angle, with each increase in angle requiring proportionately more force and current. The combined effects of magnetic force, spring tension, and radial displacement provide the control and stability essential for accurate bending. This proof of concept offers a strong foundation for understanding how to achieve precise angular adjustments in robotic applications.