# Analysis and Comparison of Electromagnetic Microrobotic Platforms for Biomedical Applications
## 3 The Electromagnetic Microrobotic Systems
[88] investigate a robot-assisted magnetic manipulation system with several mobile electromagnetic coils as represented in Figure 5b, where a robotic system keeps full dexterity for the use of electromagnetic coils while reducing energy consumption by a nearer manipulation. Furthermore, [PERSON] et al. [89] demonstrate an electromagnetic manipulation system with three parallel mobile coils named DeltaMag and represented in Figure 5b. The proposed EMA system can remotely control the magnetic untethered devices in an enlarged workspace, moreover, the electromagnetic coils are actuated through the parallel mechanism to achieve the flexibility of their placement. Thus, the DeltaMag system proves that the mobile sources generated by moving electromagnets can improve the manipulability of localization to close the vicinity of the desired area and bring the good space utilization. Here, we present a brief overview of different EMA setups in the following paragraphs. These electromagnetic microrobotic platforms can be divided into two-dimensional and three-dimensional manipulations. The status of electromagnetic coils could be stationary or mobile. The functions of designed electromagnetic platform vary according to the configuration of electromagnets. The Helmholtz coils pair, Maxwell coils pair, uniform saddle coils pair and gradient saddle coils pair are basic electromagnets configurations as shown in Figure 6 and are commonly used to generate a uniform magnetic field or gradient in a given workspace. The magnetic field intensity \(H_{h}\), \(H_{m}\), \(H_{u}\) and \(H_{g}\) of them can be computed as follows, respectively:  
\[H_{h} =\left(d_{h}x\quad 0\quad 0\right)^{\intercal} \tag{6}\] \[d_{h} =\left(\frac{4}{5}\right)^{\frac{3}{2}}\frac{i_{h}}{r_{h}}\] (7) \[H_{m} =\left(g_{m}x\quad-0.5g_{m}y\quad-0.5g_{m}z\right)^{\intercal}\] (8) \[g_{m} =\frac{16}{3}\left(\frac{3}{7}\right)^{\frac{5}{2}}\frac{i_{m}}{r _{m}^{2}}\] (9) \[H_{u} =\left(0,d_{u},0\right)^{\intercal}\] (10) \[d_{u} =0.6004\frac{i_{u}}{r_{u}}\] (11) \[H_{g} =\left(g_{g}x\quad-2.4398g_{g}y\quad 1.4398g_{g}z\right)^{\intercal}\] (12) \[g_{g} =\cos^{-1}\left(1-\frac{3}{2a^{2}}\frac{16}{3\pi}\left(\frac{3}{ 7}\right)^{\frac{5}{2}}\frac{i_{g}}{r_{g}^{2}}\right) \tag{13}\]  
where \(i_{h}\) and \(r_{h}=r\) are the current and the radius of the Helmholtz coils; \(i_{m}\) and \(r_{m}=r\) are the current and the radius of the Maxwell coils; \(i_{u}\) and \(r_{u}=r\) are the current and the radius of the uniform saddle coils; and \(i_{g}\) and \(r_{u}=g\) are the current and the radius of the gradient saddle coils. Figure 4: Examples of EMA systems with moving permanent magnets: (**a**) conceptual image of a rotating-permanent-magnet manipulator proposed by [PERSON] et al. [51], and (**b**) the Stereotaxis Niobe\({}^{\text{\textregistered}}\) consisting of two robotically-controlled magnets next to the table. \[H_{h} =\left(d_{h}x\quad 0\quad 0\right)^{\intercal} \tag{6}\]0 Examples of EMA systems with moving electromagnets: (**a**) the robot-assisted magnetic manipulation proposed by [PERSON] et al. [88], and (**b**) the DeltaMag system consisting of three parallel mobile coils [89]. As shown in Figure 6a, the Helmholtz set includes two solenoids with same radius \(r_{h}\) separated by the distance: \(l=r_{h}\), and the Maxwell coil consists of a pair of same coils of radius \(r_{m}\) separated with a distance \(l=\sqrt{3}r_{m}\). The currents flowing in an Helmholtz coil pair have same intensity and phase, that is: \(i_{h}=i_{h\mathrm{left}}=i_{h\mathrm{right}}\), while the currents of Maxwell coils are flowing in opposite phases, that is: \(i_{m\mathrm{left}}=-i_{m\mathrm{right}}\) and \(i_{m}=|i_{m\mathrm{left}}|=|i_{m\mathrm{right}}|\). It is clear that the magnetic fields generated by the combination of a Helmholtz coils pair and a Maxwell coils pair are different from that produced by two Helmholtz coils pairs. Hence, the different configurations of platforms composed of different coils pairs will be investigated.