  Planar electromagnetic actuators based on the principle of linear motors are
widely employed for micro and nano positioning applications. These actuators
usually employ a planar magnetic platform driven by a co-planar electromagnetic
coil. While these actuators offer a large motion range and high positioning
resolution, their actuation bandwidth is limited due to relatively small
electromagnetic stiffness. We report optimization of the design parameters of
the electromagnetic coil and the magnetic assembly to maximize the
electromagnetic force and stiffness. Firstly, we derive closed-form expressions
for the electromagnetic forces and stiffness, which enable us to express these
quantities in terms of the design parameters of the actuator. Secondly, based
on these derived expressions, we estimate the optimum values of the design
parameters to maximize force and stiffness. Notably, for the optimum design
parameters, the force and stiffness per unit volume can be increased by two and
three orders of magnitude, respectively by reducing the pitch of the
electromagnetic coil by a factor of 10. Lastly, we develop an electromagnetic
actuator and evaluate its performance using a Microelectromechanical system
(MEMS) based force sensor. By operating the force sensor in a feedback loop, we
precisely measure the generated electromagnetic forces for different design
parameters of the actuator. The experimental results obtained align closely
with the analytical values, with an error of less than 15%.
