Design and optimization of a novel magnetically-actuated micromanipulator

Abstract

The ability of external magnetic fields to precisely control micromanipulators has received a great deal of attention from researchers in recent years due to its off-board power source. Researchers have proposed a number of designs for magnetically-actuated micromanipulators for various applications. However, in most of the proposed magnetically-actuated micromanipulators, the manipulator workspace area is small relative to the manipulator volume, and the ratio of the generated magnetic force to manipulator weight is low. In this paper, we introduce design and optimization procedures for a portable magnetically-actuated micromanipulator. The proposed micromanipulator has many potential applications, such as medical applications, pick and place operations, micro-assembly, and micro-machining processes. The proposed micromanipulator has two main subsystems: a magnetic actuator and an electromagnetic end-effector that is connected to the magnetic actuator by a needle. In this paper, we focus on the magnetic actuation concept of the proposed micromanipulator system. We present the optimal configuration that will maximize the micromanipulator actuation force, and a closed form solution for micromanipulator actuation force. We also present the force measurement experimental setup and results of finite element methods (FEM) analysis to validate the developed model. The results show an agreement between the model, the experiment, and the FEM results. The error difference between the FEM, experimental, and model data is approximately 0.05 N.

Appendix

1.1 The shell method in (Robertson et al. 2012)

The axial magnetic force F_m between a cylindrical magnet and electromagnetic coil in Fig. 6 can be found using the shell method as following:

$$F_{m} = \frac{1}{{N_{r} }}\,\sum\limits_{{n_{r} = 1}}^{{N_{r} }} {F_{s} \left( {R_{m} ,r(n_{r} ),l_{m} ,l_{c} ,z + \frac{{l_{m} + l_{c} }}{2}} \right),}$$

(21)

where:

$$r(n_{r} ) = R_{ci} + \frac{{n_{r} + 1}}{{N_{r} + 1}}(R_{co} - R_{ci} ),$$

(21.a)

$$F_{s} \left( {R_{m} ,r,l_{m} ,l_{c} ,z + \frac{{l_{m} + l_{c} }}{2}} \right) = \frac{{J_{1} J_{2} }}{{2M_{0} }}\sum\limits_{{e_{1} = 1}}^{{e_{1} = 2}} {\sum\limits_{{e_{2} = 3}}^{{e_{2} = 4}} {e_{1} e_{2} m_{1} m_{2} m_{3} F_{x} } } ,$$

(21.b)

$$J_{2} = \frac{{\mu_{0} N_{z} I}}{{l_{c} }},$$

(21.c)

$${\text{J}}_{ 1} = {\text{B}}_{\text{r}} ,$$

(21.d)

$$F_{x} = K(m_{4} ) - \frac{1}{{m_{2} }}E(m_{4} ) + \left[ {\frac{{m_{1}^{2} }}{{m_{3}^{2} }} - 1} \right]\prod {\left( {\frac{{m_{4} }}{{1 - m_{2} }}\left| {m_{4} } \right.} \right)} ,$$

(21.e)

$$m_{1} = z + \frac{{l_{m} + l_{c} }}{2} - \frac{1}{2}e_{1} l_{m} + \frac{1}{2}e_{1} l_{c} ,$$

(21.f)

$$m_{2} = \frac{{(R_{m} - r)^{2} }}{{m_{1} }} + 1,$$

(21.g)

$$m_{3} = \sqrt {(R_{m} + r)^{2} + m_{1}^{2} } ,$$

(21.h)

$$m_{4} = \frac{{4R_{m} r}}{{m_{3} }}.$$

(21.i)

The function Π(n|m) is the complete elliptic integral of the third kind with parameter m.