Justin Beroz

Extensible-Link Kinematic Model for Characterizing and Optimizing Compliant Mechanism Motion

We present an analytical model for characterizing the motion trajectory of an arbitrary planar compliant mechanism. Model development consists of identifying particular material points and their connecting vectorial lengths in a manner that represents the mechanism topology; whereby these lengths may extend over the course of actuation to account for the elastic deformation of the compliant mechanism. The motion trajectory is represented within the model as an analytical function in terms of these vectorial lengths, whereby its Taylor series expansion constitutes a parametric formulation composed of load-independent and load-dependent terms. This adds insight to the process for designing compliant mechanisms for high-accuracy motion applications because: (1) inspection of the load-independent terms enables determination of specific topology modifications that reduce or eliminate certain error components of the motion trajectory; and (2) the load-dependent terms reveal the polynomial orders of principally uncorrectable error components in the trajectory. The error components in the trajectory simply represent the deviation of the actual motion trajectory provided by the compliant mechanism compared to the ideally desired one. A generalized model framework is developed, and its utility demonstrated via the design of a compliant microgripper with straight-line parallel jaw motion. The model enables analytical determination of all geometric modifications for minimizing the error trajectory of the jaw, and prediction of the polynomial order of the uncorrectable trajectory components. The jaw trajectory is then optimized using iterative finite elements simulations until the polynomial order of the uncorrectable trajectory component becomes apparent; this reduces the error in the jaw trajectory by 2 orders of magnitude over the prescribed jaw stroke. This model serves to streamline the design process by identifying the load-dependent sources of trajectory error in a compliant mechanism, and thereby the limits with which this error may be redressed by topology modification.

Universal handheld micropipette

The handheld micropipette is the most ubiquitous instrument for precision handling of microliter-milliliter liquid volumes, which is an essential capability in biology and chemistry laboratories. The range of one pipette is typically adjustable up to 10-fold its minimum volume, requiring the use and maintenance of multiple pipettes for liquid handling across larger ranges. Here we propose a design for a single handheld pipette adjustable from 0.1 μl to 1000 μl (i.e., 104-fold) which spans the range of an entire suite of current commercial pipettes. This is accomplished by placing an elastic diaphragm between the existing pipette body and tip, thereby de-amplifying its native volume range while maintaining its simple manual operating procedure. For proof-of-concept, we adapted a commercial pipette (100-1000 μl nominal range) with a selection of rubber sheets to function as the diaphragms and confirmed the accuracy and precision of drawn volumes are within international ISO-8655 standards across the entire 104-fold volume range. The presence of the diaphragms introduces a nonlinear mechanical behavior and a time-dependency due to heat transfer, however, by model and experiment, these are redressed so as to maintain the pipettes accuracy and precision.

EXTENSIBLE-LINK KINEMATIC MODEL FOR DETERMINING MOTION CHARACTERISTICS OF COMPLIANT MECHANISMS

We present an extensible-link kinematic model for characterizing the motion trajectory of an arbitrary planar compliant mechanism. This is accomplished by creating an analogous kinematic model consisting of links that change length over the course of actuation to represent elastic deformation of the compliant mechanism. Within the model, the motion trajectory is represented as an analytical function. By Taylor series expansion, the trajectory is expressed in a parametric formulation composed of load-independent and load-dependent terms. Here, the load-independent terms are entirely defined by the shape of the undeformed compliant mechanism topology, and all load-geometry interdependencies are captured by the load-dependent terms. This formulation adds insight to the process for designing compliant mechanisms for high accuracy motion applications because: (1) inspection of the load-independent terms enables determination of specific topology modifications for improving the accuracy of the motion trajectory; and (2) the load-dependent terms reveal the polynomial orders of principally uncorrectable error components of the motion trajectory. The error components in the trajectory simply represent the deviation of the actual motion trajectory provided by the compliant mechanism compared to the ideally desired one. We develop the generalized model framework, and then demonstrate its utility by designing a compliant micro-gripper with straight-line parallel jaw motion. We use the model to analytically determine all topology modifications for optimizing the jaw trajectory, and to predict the polynomial order of the uncorrectable trajectory components. The jaw trajectory is then optimized by iterative finite elements (FE) simulation until the polynomial order of the uncorrectable trajectory component becomes apparent.

Four degree of freedom liquid dispenser for direct write capillary self-assembly with sub-nanoliter precision.

Capillary forces provide a ubiquitous means of organizing micro- and nanoscale structures on substrates. In order to investigate the mechanism of capillary self-assembly and to fabricate complex ordered structures, precise control of the meniscus shape is needed. We present a precision instrument that enables deposition of liquid droplets spanning from 2 nl to 300 μl, in concert with mechanical manipulation of the liquid-substrate interface with four degrees of freedom. The substrate has sub-100 nm positioning resolution in three axes of translation, and its temperature is controlled using thermoelectric modules. The capillary tip can rotate about the vertical axis while simultaneously dispensing liquid onto the substrate. Liquid is displaced using a custom bidirectional diaphragm pump, in which an elastic membrane is hydraulically actuated by a stainless steel syringe. The syringe is driven by a piezoelectric actuator, enabling nanoliter volume and rate control. A quantitative model of the liquid dispenser is verified experimentally, and suggests that compressibility in the hydraulic line deamplifies the syringe stroke, enabling sub-nanoliter resolution control of liquid displacement at the capillary tip. We use this system to contact-print water and oil droplets by mechanical manipulation of a liquid bridge between the capillary and the substrate. Finally, we study the effect of droplet volume and substrate temperature on the evaporative self-assembly of monodisperse polymer microspheres from sessile droplets, and demonstrate the formation of 3D chiral assemblies of micro-rods by rotation of the capillary tip during evaporative assembly.

Direct‐Write Freeform Colloidal Assembly

Colloidal assembly is an attractive means to control material properties via hierarchy of particle composition, size, ordering, and macroscopic form. However, despite well-established methods for assembling colloidal crystals as films and patterns on substrates, and within microscale confinements such as droplets or microwells, it has not been possible to build freeform colloidal crystal structures. Direct-write colloidal assembly, a process combining the bottom-up principle of colloidal self-assembly with the versatility of direct-write 3D printing, is introduced in the present study. By this method, centimeter-scale, free-standing colloidal structures are built from a variety of materials. A scaling law that governs the rate of assembly is derived; macroscale structural color is tailored via the size and crystalline ordering of polystyrene particles, and several freestanding structures are built from silica and gold particles. Owing to the diversity of colloidal building blocks and the means to control their interactions, direct-write colloidal assembly could therefore enable novel composites, photonics, electronics, and other materials and devices.

Tunable-Volume Handheld Pipette Utilizing a Pneumatic De-Amplification Mechanism

We present the design, analysis, and validation of a tunable-volume handheld pipette that enables precise drawing and dispensing of ml and μl liquid volumes. The design builds upon the standard mechanism of a handheld micropipette by incorporating an elastic diaphragm that de-amplifies the volume displacement of the internal piston via compression of an entrapped air volume. The degree of de-amplification is determined by the stiffness of the elastic diaphragm and the amount of entrapped air. An analytical model of the diaphragm mechanism is derived, which guides how to achieve linear de-amplification over an extended range where leading-order nonlinear contributions are significant. In particular, nonlinearities inherent in the mechanical behavior of the diaphragm and entrapped air volume may exactly cancel one another by careful design of the pipette’s parameter constants. This linearity is a key attribute for enabling the pipette’s tunable volumetric range, as this allows diaphragms with different stiffnesses to be selectively used with a conventional linear-stepping piston mechanism. Design considerations regarding the range, accuracy, and precision of the proposed pipette are detailed based on the model. Additionally, we have constructed a handheld prototype that uses a planar latex sheet as the diaphragm. Our pipetting experiments validate the derived model and exhibit linearity between the piston stroke and drawn liquid volume. We propose that this design enables a single handheld mechanical pipette to achieve drawing and dispensing of liquids over a 1μl-10ml range (i.e., the range of the entire micropipette suite), with volumetric resolution and precision comparable to commercially available counterparts.Copyright