Possible Directions I looked at:
If a microgripper such as this MEMS microgripper for gripping 100 micron objects were to be made of Mechanical and Electronic digital bricks (Will's digital material), what are the overhead in terms of real estate, material and fabrication cost and power requirements ?
How to create a Switchable mechanical connection with tunable attraction force for modular robots such as Ara's Robot Pebbles ?
Other things related to robotic pebbels: How to increase the force of attraction between two robotic blocks to be able to resist shearing and rotation. This would be required when robotic pebbles are scaled to assemble into 3d shapes. Can we use Van der Wall's adhesion or some sort of mechanical interlock or electrostatic force ?
As robotic pebbles are scaled down, how far does the electropermanent magnets scale ? Electrostatic field and forces are limited by deielctric breakdown and magnetic field is limited by scaling of coils and magnetization. In what regime does electrostatic connection take over electropermanent magnet ?
SRI made these really cute tiny robots that collectively assemble materials to build electrical and mechanical structures. If these were to be scaled down, how do we do that ? What physical forces can be used to control the maneuver of the robots?
Given an array of addressable coplanar electrodes can we use elctric field to maneuver these robots? How can we use them to manipulate a block of neutral untethered material ?Manipulating objects at micrometer scale has interesting applications such as assembling electrical and mechanical systems at small-scale. Manipulation in this context would mean gripping and transporting. One way to move micrometer scale objects between known positions is to use untethered microrobots controlled through an external electrostatic field. The microrobot in this case is a block of isotropic dielectric. In the scope of this project I will be looking at the transportation of materials in 1μm to 100μm scale.
A dielectric when suspended in an electric field undergoes polarization. The dipoles induced in the block experience forces due to the field. If the field was to be uniform (∇E = 0), with uniform polarization, the force experienced by the dielectric averages to zero. In a non-uniform electric field (∇E > 0), a block of dielectric expereinces a net force due to finite charge density. The net force expereinced by the block depends on:
For a dielectric particle, net force is given by
$$ F = P\cdot \nabla E$$
For a spherical particle of radius r,
$$ P = 4 * Pi * r^3*k*E$$
where k is a complex quantity that depends on the permittivity of the dielectric and the surrounding medium and E is the electric field. Combining these we get,
$$ F= 2 * Pi * r^3*k*\nabla |E^2|$$
The 2*Pi*r3 can be seen as shape factor, and hence more generically the force is prpotional to volume of the particle and gradient of the suqare of the field norm
$$ F \alpha Volume* Dielectric Constant* \nabla |E^2|$$
With Silicon dioxide as the dielectric material and static field, the dielectric of the target block remains constant. For this project I will be looking at the effect of scaling of object volume and field gradient. The next question would be to find out the field gradients that can be achieved at micron sepration between electrodes. For a 5-10 um separation between electrodes the maximum voltage before air breaksdown is 300V. See this reference more details.
For a 10um separation between the electrodes and 1V between the electrodes, from COMSOL simulation, the order of magnitude of the gradient is $$ V=1 V, \nabla |E^2| = 10\exp15 V^2/m^3 $$ $$ V=100 V, \nabla |E^2| = 10\exp19 V^2/m^3 $$
Weight of 10um SiO2 particle | Static Friction Foec | Dielectric Force (Voltage between two electrodes = 1V ) | Dielectric Force (Voltage between two electrodes = 100V ) |
---|---|---|---|
100pN | 75pN | 216pN | 216 X 10e4 pN |
The scaling of the dielectric object that is being manipulated and the Polarization force generated is dependent on several factors:
Manipulating the object would involve positioning on a horizontal XY plane and even levitation in Z direction. These manipulations depend on the design of the next 3 paramaters -- geometry of electrodes, dielectric constant of material and field gradient. Within the scope of this project I would be focussing on moving the object from Point A to Point B on an horizontal plane in the X-direction and possibly then extend this to XY-plane.
Electrodes for manipulating the object can have various geometry. Some of the common ones found in the literature are parallel finger, comb-like interdigitated, semi-infinite arrays and so on. I started out by looking at coplanar rectangular electrodes placed next to each other. In the simplest case of motion along the X-axis, my analysis starts with just two electrodes. In the later part of the project I will be exploring various geomteries and their effect on the scaling.
The force experienced by a dielectric is proportional to its polarizability. The dependance of polarizability on dielectric constant comes from the fact that the effective dielectric contant is a complex quantity that depends on the permittivity of the dielectric particle, surrounding medium and the frequency. This is given given by Clausius–Mossotti relationship: $$\alpha = \frac{\epsilon_p - \epsilon}{\epsilon_p + 2\epsilon}$$ However, for our calcultations, we keep the electric field constant and medium to be air. This gives the order of magnitude of the dielectric constant to be $$10e12 F/m^2$$
The dependence on E2 indicates that the force direction is independent of the polarity of the applied field E and thus both DC and AC fields can be used. If the particle is surrounded by or immersed in a medium whose complex conductivity (or permittivity) is less than that of the particle, then the factor the resulting DEP force will be directed towards thehigh-field region. This is known as positive dielectrophoresis. See this paper[11] for details.
The magnitude and direction of the electric field gradient is heavily governed by the geometry of the electrodes and the voltage between the electrodes. For the simple case of two coplanar rectangular electrodes, for us to be able to move an object along X-axis the field gradient must be along the X-direction. Directionality of the field gradient is strongly coupled with the geometry of the electrodes. However, the key take away is that the dielectric moves up the gradient.
I looked at scaling of size of the objects at 3 sizes of electrodes, 1um, 10um and 100um. Following conditions hold good for all 3 cases:
Clearly, as the size of the electrode and the object is scaled up, the potential has to be scaled up as well. The dielectric force scales more strongly with L, as F ∼ V^{2}/L^{3}. This means that in scaling from a system with L = 100 μm to one where L = 10 μm, one can reduce the voltage by ∼100× and get the same force. As further scale up to macroscale the voltage required grows to 1000V. One would need to apply 1000 V in the macroscale system to get the same force achievable with 1V in a microscale system.
As for scaling up the voltage, dielectric breakdown sets an upper bound on maximumn size of object that can be manipulated. Putting it differently, as the density (mass per unit volume) of the material increases, the size of the object that can be manipulated goes down.
A simple geometry consisiting of two electrodes of equal length gives no gradient in field ∇|E^{2}| = 0.
This paper talks about manipulation of particles suspended in an aqueous medium through dielectrophoretic force. Given below is a snippet of a plot of dielectrophoretic forces experienced by a particle of radius 5μm for an electrode of width and gap 20μm. At 1V between two electrodes of same size and particle size of simialr order, the results and analysis in this page are comparable with those in this plot.
One possible way to design the electrode design procedure is based on the assumption that the electrical potential at any point (x,y,z) created by an electrode system of interest is defined by a polynomial that obeys Laplace’s equation. By substituting this polynomial into Laplace’s equation the corresponding equipotentials can be determined, and these in turn can be used to define the required electrode boundaries. Although the method can readily applied to three-dimensional systems, for the sake of planar manipulation we can restrict it to two dimensions.
References: