A 5 mg micro-bristle-bot fabricated by two-photon lithography

The micro-bristle-bots excited by external piezoelectric shaker is described by the free body diagram in figure 2, and the corresponding equations describing the locomotion principle are shown in equations (1)–(3), based on equations of motion presented in [20, 21]. The 2D model consists of a passive robot on a vertically oscillating shaker, and is considered as a rigid body with essentially mass-less legs. The force that is applied to the tip of the legs from the shaker will be translated to the body of the bristle-bot. Thus, the effect of the oscillatory force from the shaker is similar to the force applied from the on-board PZT actuator [19]. The micro-bristle-bot is modeled as a main body with mass, m, and six legs with weightless support elements of length l and connected by rotational springs, c, and dampers, k. $\varphi$ is the inclination of the legs. η is the sinusoidal function of vertical displacement delivered by the pizeo shaker. $\mu$ is the friction coefficient between tips of legs and the ground (0.20 for static and 0.15 for kinetic coefficient between acrylic and glass [22]), and $\omega ~$ is the input angular frequency of actuation of the piezoelectric shaker.

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \ddot{x}=~-\mu \left[ g+\ddot{\eta }-l\ddot{\varphi }\sin \varphi -l{{{\dot{\varphi }}}^{2}}\cos \varphi \right]sign\left( \dot{x}-l\dot{\varphi }\cos \varphi \right),~\nonumber \end{align} \tag{ 1 }$$

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle &\left[ \ddot{\varphi }\sin \varphi +{{{\dot{\varphi }}}^{2}}\cos \varphi -\frac{g}{l}-\frac{{\ddot{\eta }}}{l} \right]\left[ \sin \varphi +\mu \cos \varphi sign\right. \nonumber \\&\quad \left.\left( \dot{x}-l\dot{\varphi }\cos \varphi \right) \right]+\frac{6k}{m{{l}^{2}}}\dot{\varphi }+\frac{6c}{m{{l}^{2}}}\left( \varphi -{{\varphi }_{0}} \right)=0,\nonumber \end{align} \tag{ 2 }$$

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \ddot{\eta }=~-A{{\omega }^{2}}\sin (\omega t).\nonumber \end{align} \tag{ 3 }$$

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Equation (1) describes the relationship between position of leg tips, x, with the displacement of piezoelectric shaker, η, and angle of legs, φ. Equation (2) describes the relationship between the angle of legs, φ, roatational spring constant, c, rotational damping constant, k, and equilibrium angle of legs, ${{\varphi }_{0}}$. Equation (3) represents the acceleration applied by the piezoelectric shaker as function of amplitude, A, and input frequency, ω.

The net horizontal movement of a bristle-bot is achieved by the modulation of frictional force due to oscillations of the normal force from vertical displacement of piezoelectric shaker, leading to a stick-slip motion of their legs [12, 20, 21, 23]. Figure 3 demonstrates the two phases of stick-slip cycle of micro-bristle-bot, operating based on buckling of the legs. In order to study the directionality of the bristle-bots, two leg designs are investigated in this work: (1) straight legs (0${}^\circ$ angle from the normal line to ground), and (2) tilted legs (30${}^\circ$ angle from the normal line to ground). When the legs of the bristle-bots are straight, all the energy from the vertical oscillation will be stored in the legs as they buckle. However, the directions of the buckling will vary, and thus, the displacement of leg tips generated from the oscillations would likely work against each other, resulting in a zero or close-to-zero net movment of the bristle-bot. When the legs are all tilted or offset in a single direction, the buckling direction of the legs will be more uniform and thus lead to a directional movement. The difference in directionalities of the micro-bristle-bots is observed and discussed in the following experimental result sections.

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In this paper, we investigated two different leg geometries: (1) straight legs and (2) legs tilted by 30°. The straight leg design serves as a control group to characterize the locomotion of micro-bristle-bot with no directionality of the legs. The 30° tilted leg design is a standard bristle-bot design [21].

The presented micro-bristle-bots can be actuated at a larger range of frequencies at high levels of input voltage amplitudes. However, the voltage is maintained below 25 V to ensure that the movement is caused from stick-and-slip motion described previously instead of jumping motions, where the bristle-bots release stored energy in the legs for the vertical motion [16, 21]. This also minimizes the required power for the locomotion. However, low actuation voltages would translate into small displacements generated per cycle. Thus, to boost the speed of the micro-bristle-bot at low input voltage amplitudes, the micro-bristle-bots are excited at resonant frequency corresponding to the leg bending mode shape to increase the displacement of legs per cycle. The desired resonant mode shape of the straight leg design is shown in figure 4(a) and that of 30° tilted leg design is shown in figure 4(b). The material properties used in COMSOL finite element analysis (FEA) simulations shown in figure 4, are taken from Nanoscribe for Ip-S [24], as well as standard acrylic material properties, shown in table 1. The tips of the legs that touch the xy-plane are fixed in the simulation and eigen frequency study is used to find the displacement resonant mode shapes of the micro-bristle-bot.

Table 1. Material properties of Ip-S polymer from nanoscribe [24].

Young's modulus	4.6 GPa
Hardness	160 MPa
Storage modulus	5 GPa
Loss modulus	150–350 MPa
Shrinkage after polymerization	2%–12%
Density (liquid)	1.111 ${\rm g}\,{\rm c}{{{\rm m}}^{-3}}$

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The small discrepancy between the simulated resonant frequencies of the mode-shapes in figure 4 and the measured frequency of 6.3 kHz (shown in section 3.2) can be explained by non-ideal fabrication and material properties. Furthermore, the leg tips are fixed to the ground in the simulation, whereas in practice, the friction forces applied to the leg tips shift the resonant frequencies of the two designs.

The 5 mg micro-bristle-bot is composed of two parts: a polymer base and a small diced PZT plate placed between a top and a bottom metal electrode. It must be noted that the PZT actuator in this work serves as a passive mass and is not used for actuation. A 300 µm thick PZT plate from APC International, Ltd [25] is diced into 2 mm  ×  1.5 mm rectangles. The polymer base includes the housing for the PZT mass and legs of the micro-bristle-bot. The diameter of the legs is 100 µm, and the overall height of the legs is 500 µm for all designs. Autodesk Inventor was used for creating 3D models of the polymer base.

As shown in figure 5(a), the designed polymer base was fabricated with Ip-S photoresist droplet on indium tin oxide (ITO) coated glass slide using two-photon lithography with Nanoscribe Photonic Professional. The monomer polymerizes around the focal point of the laser where the two-photons meet [26]. Once the Ip-S polymer base has been written, it is developed in a SU-8 developer. Once the polymer base been washed and dried with isopropyl alcohol, it is removed from the ITO glass slide, with gentle nudge from a tweezer placed on the legs. Adhesive is applied onto the diced PZT by using a needle as shown in figure 5(b). Then the polymer base and the diced PZT mass are manually assembled using a plier as shown in figure 5(c). Next the assembly is flipped onto the PZT side and middle section of polymer base is gently pressured with a tweezer to ensure even spread of the adhesive. Finally, the 5 mg micro-bristle-bot is placed on its leg as shown in figure 5(d). A completed micro-bristle-bot is shown in figure 6.

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A concern with polymer based flexural elements is the performance degradation due to self-heating from high frequency operations as described in [27]. However, polymerized Ip-S resin used in this work for fabrication of bristle-bots does not show degradation below T  =  300 °C as it is a thermoset polymer [24].

A lead zirconate titanate or PZT-4 crystal disc supplied by Stem, Inc [28] is utilized as a piezoelectric shaker. PZT disc is connected to a Krohn-Hite 7602M amplifier which in turn is connected to an Agilent 33220A Function Generator. The disc vibrates in the out-of-plane mode with a ${{d}_{33}}$ piezoelectric coefficient of 320  ×  10⁻¹² m V⁻¹ underneath a glass substrate with marked distances. A dot was painted on top of the micro-bristle-bots as a marker, and a Olympus SZ-12 14MP digital camera is used to capture the motion of the bristle-bot at 30 fps with a 1280  ×  720 resolution. DLTdv digitizing tool from [29] is used for analyzing the motion by tracking the painted marker on the micro-bristle-bot.

Two different variations of the micro-bristle-bots with different leg angles were placed on the piezoelectric shaker with distance markers. A sinusoidal wave was applied to the piezoelectric shaker with varying frequencies and voltage amplitudes, ranging from 4 kHz to 8 kHz and 5 V to 25 V corresponding to 1.6 nm to 8 nm of vertical displacement. Figure 7 shows four time frames of the locomotion of the two micro-bristle-bots. More trajectories of straight leg and tilted leg designs are shown in figure 8. The trajectories of straight leg design is erratic and random as the robot tends to turn and spin, whereas the trajectories of the bristle-bot with tilted legs are smooth and directional. The resulting variance of distances between each end coordinate of the trajectories shown in figure 8 is 28.58 ${\rm m}{{{\rm m}}^{2}}$ for straight leg design and 5.21 ${\rm m}{{{\rm m}}^{2}}$ for the tilted leg design.

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3D plots of the micro-bristle-bot speed versus input frequency and displacement of the PZT shaker are shown in figures 9(a) and (b) for the straight leg design and 30° tilted leg design, respectively. The speed of micro-bristle-bots depend on the periodic displacement of leg tips, d, as shown in figure 3, which in turn depends on the input voltage, and the input frequency of the oscillations according to equations (1)–(3). As demonstrated in the figure 9, a resonant behaviour is observed around 6.3 kHz corresponding to the bending of the legs, matching the FEA results shown in figure 4. As vertical displacement of piezoelectric shaker increases, the speed shows an increasing trend. Larger displacement amplitudes can result in jumping and flipping of the micro-bristle-bots which is not desired. Therefore, the actuation voltage was kept below 25 V. Although the resulting speed of straight leg design is only slightly lower than that of the tilted leg design, the straight leg design's trajectory is less directional, as each of the six legs can buckle in any arbitrary direction, and thus suffers from erratic movement.

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