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Schematic of the glass actuator design. The design combines two elements. A comb-array that consists of a series of beams, parallel one to another and a flexure made of four leaf springs. The working principle of the variable capacitive actuator is illustrated on the right (for clarity, only forces viewed from the mobile element are shown). When a voltage is applied, the electrostatic force pulls the two parallel plates together. As one side of the mechanism is fixed, this electrostatic force results in a net force applied on the mobile element only. As such, comb-array actuators are mechanically unstable (i.e., a slight off-axis disturbance would collapse it). A mechanical guiding element that here consists of four leaf springs forming a double-compound linear guidance is used to keep the comb-array beams parallel to one another during actuation, preventing it from collapsing. A transparent conductive layer (indium-tin-oxide) is deposited everywhere on the material except for a small portion which remains uncovered and isolates electrically the two sides of the actuator.
Graphical representations of the actuators force/gap relation for various voltages (plain colored lines) and flexure mechanical characteristic (dashed line). The intersection points of the dashed line and plain curves are the positive solutions of Eq. (3). Among these positive solutions, only one set forms mechanically stable equilibrium points (shown here with a black dot).
Measured profile and schematic of a trench cross section after exposure of a single line pattern across the substrate thickness. The measurement is performed using a digital holographic microscope (Lyncée Tec, DHM 10020).
Scanning electron microscope image (left) of the micro actuator. The comb-array electrode and part of the leads springs are shown. The surface of the substrate has a 100 nm-conductive ITO layer. Video capture (right) of the micro actuator at approximately 1 Hz and an applied voltage of 35 V. A 1-cent Euro-coin is visible in the background. The leaf springs are 3 mm long, 20 μm in height, and 0.5 mm thick (enhanced online). [URL: http://dx.doi.org/10.1063/1.4750236.1]10.1063/1.4750236.1
Positive solutions (see Eq. (6)) of Eq. (5) as a function of the applied voltage and actual measurement points (circles). The black curve is the mathematical solution corresponding to a stable equilibrium while the red one forms unstable points. Above a given voltage—the so-called “pull-in” voltage (here around 35 V), the actuators enters an unstable regime. Errors bars for the measurements are estimated to be ± 0.2 V and ± 0.1 μm.
Dynamic response of the transparent capacitive actuator. The red and blue curves correspond, respectively, to a simulation and the actual measurement. The two first vibrations modes are highlighted with two finite-element modeling shown above.
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