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Biomechanical assays offer a good alternative to biochemical assays in diagnosing disease states and assessing the efficacy of drugs. In view of this, we have designed, fabricated and tested a miniature compliant tool to estimate the bulk stiffness of cells, particularly MCF-7 (Michigan Cancer Foundation) cells. The compliant tool comprises a gripper and a Displacement-amplifying Compliant Mechanism (DaCM), where the former helps in grasping the cell and the latter enables vision-based sensing of force. A DaCM is necessary because the field of view of a microscope at the required magnification is not large enough to simultaneously observe the cell and a point on the gripper that move sufficiently to estimate the force. Therefore, a DaCM is strategically embedded within an existing gripper design leading to a composite compliant mechanism. The DaCM is designed using the inetoelastostatic map technique to achieve a resolution 42 nN. The gripper, microfabricated with SU-8 polymer using photolithography, is within the footprint of about 10 mm by 10 mm with the smallest feature size of about 5 microns. The gripper was tested in air and was found to be satisfactory in grasping and squeezing objects as small as 15 microns in size. However, testing in aqueous medium encountered an unanticipated problem due to buoyancy, which curled the jaws of the gripper up by as much as 40 microns and thus losing contact with the cell that is to be grasped. A design modification is suggested to fix this problem.

Understanding mechanical advantage of a compliant mechanism is not straightforward for two reasons: (i) it uses a part of the input energy in elastic deformation and (ii) its kinetoelastic behavior depends on the stiffness of the workpiece. In this paper, we study mechanical advantage using non-dimensional analysis of compliant mechanisms. We use parameterized kinetoelastostatic maps that show mechanical advantage against a non-dimensional number that captures geometric and material properties as well as forces. The maps help compare different topologies of compliant mechanisms based on mechanical advantage. The maps also help delineate kinematic and elastic contributions to mechanical advantage. Case studies reveal that while mechanical advantage usually increases with increasing external stiffness and slenderness ratio, but it decreases with increasing gap between the output port and an elastic workpiece. A noteworthy observation in this work is that there can be exceptions to this general trend and that kinematic and elastic contributions can both be positive so that the mechanical advantage of a compliant mechanism can exceed that of a rigid-body counterpart. This work also revisits the fact that it is possible to design a compliant mechanism such that its mechanical advantage is not affected by the stiffness of the workpiece

Presented in this paper is an improvement over a spring-steel dual-axis accelerometer that we had reported earlier.The fabrication process (which entails wire-cut electro discharge machining of easily accessible and inexpensive spring-steelfoil) and the sensing of the displacement (which is done using off-the-shelf Hall-effect sensors) remain the same. Theimprovements reported here are twofold: (i) the footprint of the packaged accelerometer is reduced from 80 mm square to 40mm square, and (ii) almost perfect de-coupling and symmetry are achieved between the two in-plane axes of the packageddevice as opposed to the previous embodiment where this was not the case. Good linearity with about 40 mV/g was measuredalong both the in-plane axes over a range of 0.1 to 1 g. The first two natural frequencies of the devices are at 30 Hz and 100Hz, respectively, as per the experiment. The highlights of this work are cost-effective processing, easy integration of the Hall-effect sensing capability on a customised printed circuit board, and inexpensive packaging without overly compromising eitherthe overall size or the sensitivity of the accelerometer. Through this work, we have reaffirmed the practicability of spring-steelaccelerometers towards the eventual goal of making it compete with micro machined silicon accelerometers in terms of sizeand performance. The cost is likely to be much lower for the spring-steel accelerometers than that of silicon accelerometers, especially when the volume of production is low and the sensor is to be used as a single packaged unit.

In this paper, we present a methodology for designing a compliant aircraft wing, which can morph from a given airfoil shape to another given shape under the actuation of internal forces and can offer sufficient stiffness in both configurations under the respective aerodynamic loads. The least square error in displacements, Fourier descriptors, geometric moments, and moment invariants are studied to compare candidate shapes and to pose the optimization problem. Their relative merits and demerits are discussed in this paper. The `frame finite element ground structure' approach is used for topology optimization and the resulting solutions are converted to continuum solutions. The introduction of a notch-like feature is the key to the success of the design. It not only gives a good match for the target morphed shape for the leading and trailing edges but also minimizes the extension of the flexible skin that is to be put on the airfoil frame. Even though linear small-displacement elastic analysis is used in optimization, the obtained designs are analysed for large displacement behavior. The methodology developed here is not restricted to aircraft wings; it can be used to solve any shape-morphing requirement in flexible structures and compliant mechanisms.

When computing the change in electrical resistivity of a piezoresistive cubic material embedded in a deforming structure, the piezoresistive and the stress tensors should be in the same coordinate system. While the stress tensor is usually calculated in a coordinate system aligned with the principal axes of a regular structure, the specified piezoresistive coefficients may not be in that coordinate system. For instance, piezoresistive coefficients are usually given in an orthogonal cartesian coordinate system aligned with the crystallographic directions and designers sometimes deliberately orient a crystallographic direction other than along the principal directions of the structure to increase the gauge factor. In such structures, it is advantageous to calculate the piezoresistivity tensor in the coordinate system along which the stress tensors are known rather than the other way around. This is because the transformation of stress will have to be done at every point in the structure but piezoresistivity tensor needs to be transformed only once. Here, using tensor transformation relations, we show how to calculate the piezoresistive tensor along any arbitrary Cartesian coordinate system from the piezoresistive coefficients for the coordinate system. Some of the software packages that simulate the piezoresistive effect do not have interfaces for calculation of the entire piezoresistive tensor for arbitrary directions. This warrants additional work for the user because not considering the complete piezoresisitive tensor can lead to large errors. This is illustrated with an example where the error is as high as 33%. Additionally, for elastic analysis, we used hybrid finite element formulation that estimates stresses more accurately than displacement-based formulation. Therefore, as shown in an example where the change in resistance can be calculated analytically, the percentage error of our piezoresistive program is an order of magnitude lower relative to displacement-based finite element method.

During the motion of one dimensional flexible objects such as ropes, chains, etc., the assumption of constant length is realistic. Moreover,their motion appears to be naturally minimizing some abstract distance measure, wherein the disturbance at one end gradually dies down along the curve defining the object. This paper presents purely kinematic strategies for deriving length-preserving transformations of flexible objects that minimize appropriate ‘motion’. The strategies involve sequential and overall optimization of the motion derived using variational calculus. Numerical simulations are performed for the motion of a planar curve and results show stable converging behavior for single-step infinitesimal and finite perturbations 1 as well as multi-step perturbations. Additionally, our generalized approach provides different intuitive motions for various problem-specific measures of motion, one of which is shown to converge to the conventional tractrix-based solution. Simulation results for arbitrary shapes and excitations are also included.

We present concepts and an optimization-based methodology for the design of micro-mechanical stages that have not only high precision but also an enhanced range. Joint-free distributed compliant designs provide high precision and easy manufacturability at macro and micro scales. The range of motion is enhanced by using displacement-amplifying compliant mechanisms (DaCMs). The main issue addressed in this paper is how to retain the decoupling between the X and Y motions in the stage when it is equipped with DaCMs. The natural frequency of the stage is also not compromised in enhancing the range. The optimized design has 2.5 times more range than the designs reported in the literature. Furthermore, the sensitivity improved by a factor of two when the stage is optimized for an accelerometer.

We present the concept, prototypes, and an optimal design method for a compliant mechanism kit as a parallel to the kits available for rigid-body mechanisms. The kit consists of flexible beams and connectors that can be easily hand-assembled using snap fits. It enables users, using their creativity and mechanics intuition, to quickly realize a compliant mechanism. The mechanisms assembled in this manner accurately capture the essential behavior of the topology, shape, size and material aspects and thereby can lead the way for a real compliant mechanism for practical use. Also described in this paper are the design of the connector to which flexible beams can be added in eight different directions; and prototyping of the spring steel connectors as well as beams using wire-cut electro discharge machining. It is noted in this paper that the concept of the kit also resolves a discrepancy in the finite element (FE) modeling of beam-based compliant mechanisms. The discrepancy arises when two or more beams are joining at one point and thus leading to increased stiffness. After resolving this discrepancy, this work extends the topology optimization to automatically generate designs that can be assembled with the kit. Thus, the kit and the accompanying analysis and optimal synthesis procedures comprise a self-contained educational as well as a research and pragmatic toolset for compliant mechanisms. The paper also illustrates how human creativity finds new ways of using the kit beyond the original intended use and how it is useful even for a novice to design compliant mechanisms.

This paper presents concepts, designs, and working prototypes of enhanced laparoscopic surgical tools. The enhancements are in equipping the tool with force and temperature sensing as well as image acquisition for stereo vision. Just as the pupils of our eyes are adequately spaced out and the distance between them is adjustable, two minute cameras mounted on a mechanism in our design can be moved closer or farther apart inside the inflated abdomen during the surgery. The cameras are fitted to a deployable mechanism consisting of flexural joints so that they can be inserted through a small incision and then deployed and moved as needed.A temperature sensor and a force sensor are mounted on either of the gripping faces of the surgical grasping tool to measure the temperature and gripping force, which need to be controlled for safe laparoscopic surgery. The sensors are small enough and hence they do not cause interference during surgery and insertion.Prototyping and working of the enhanced laparoscopic tool are presented with details

We present a real-time haptics-aided injection technique for biological cells using miniature compliant mechanisms. Our system consists of a haptic robot operated by a human hand, an XYZ stage for micro-positioning, a camera for image capture, and a polydimethylsiloxane (PDMS) miniature compliant device that serves the dual purpose of an injecting tool and a force-sensor. In contrast to existing haptics-based micromanipulation techniques where an external force sensor is used, we use visually captured displacements of the compliant mechanism to compute the applied and reaction forces. The human hand can feel the magnified manipulation force through the haptic device in real-time while the motion of the human hand is replicated on the mechanism side. The images are captured using a camera at the rate of 30 frames per second for extracting the displacement data. This is used to compute the forces at the rate of 30 Hz. The force computed in this manner is sent at the rate of 1000 Hz to ensure stable haptic interaction. The haptic cell-manipulation system was tested by injecting into a zebrafish egg cell after validating the technique at a size larger than that of the cell.

An external pipe-crawling device presented in this paper aids the inspection of pipes in hazardous environments and areas inaccessible to humans. The principal component of our design, which uses inchworm type motion, is a compliant ring mechanism actuated using shape memory alloy (SMA) wire. It was fabricated and tested and was reported in our earlier work. But this device had a drawback of low crawling speed (about 1 mm/min) owing to the delay in heating and cooling of the SMA strips in the linear actuation. Additionally, that design also had the difficulties of mounting on pipes with closed ends, large radial span, and the need for housing for electrical insulation and guiding of the SMA wire. In this paper we present a compact design that overcomes the difficulties of the earlier design. In particular, we present a compact compliant mechanism with two halves so as to enable mounting and un-mounting on any closed or open pipe. Another feature is the presence of insulation and guiding of the SMA wire without housing. This design results in a reduction of the radial span of the ring from 22 mm to 12 mm, and the stiffness of the mechanism and the SMA wire are matched. An SMA helical spring is to used in the place of an SMA strip to increase the crawling speed of the device. A microcontroller-based circuitry is also fitted to cyclically.activate the SMA wires and springs.

This Study is concerned with the accurate computation of the unknown forces applied on the boundary of an elastic body using its measured displacement data with noise. Vision-based minimally intrusive force-sensing using elastically deformable grasping tools is the motivation for undertaking this problem. Since this problem involves incomplete and inconsistent displacement/force of ail elastic body, it leads to an ill-posed problem known as Cauchy's problem in elasticity. Vision-based displacement measurement necessitates large displacements of the elastic body for reasonable accuracy. Therefore, We use geometrically non-linear modelling of the elastic body, which was not considered by others who attempted to solve Cauchy's elasticity problem before. We present two methods to solve the problem. The first method uses the pseudo-inverse of an over-constrained system of equations. This method is shown to be not effective when the noise in the measured displacement data is high. We attribute this to the appearance of spurious forces at regions where there should not be any forces. The second method focuses on minimizing the spurious forces by varying the measured displacements within the known accuracy of the measurement technique. Both continuum and frame elements are used in the finite element modelling of the elastic bodies considered in the numerical examples. The performance of the two methods is compared using seven numerical examples, all of which show that the second method estimates the forces with an error that is not more than the noise in the measured displacements. An experiment was also conducted to demonstrate the effectiveness of the second method in accurately estimating the applied forces.

The topology optimization problem for the synthesis of compliant mechanisms has been formulated in many different ways in the last 15 years, but there is not yet a definitive formulation that is universally accepted. Furthermore, there are two unresolved issues in this problem. In this paper, we present a comparative study of five distinctly different formulations that are reported in the literature. Three benchmark examples are solved with these formulations using the same input and output specifications and the same numerical optimization algorithm. A total of 35 different synthesis examples are implemented. The examples are limited to desired instantaneous output direction for prescribed input force direction. Hence, this study is limited to linear elastic modeling with small deformations. Two design parameterizations, namely, the frame element based ground structure and the density approach using continuum elements, are used. The obtained designs are evaluated with all other objective functions and are compared with each other. The checkerboard patterns, point flexures, the ability to converge from an unbiased uniform initial guess, and the computation time are analyzed. Some observations are noted based on the extensive implementation done in this study. Complete details of the benchmark problems and the results are included. The computer codes related to this study are made available on the internet for ready access.

The notion of optimization is inherent in protein design. A long linear chain of twenty types of amino acid residues are known to fold to a 3-D conformation that minimizes the combined inter-residue energy interactions. There are two distinct protein design problems, viz. predicting the folded structure from a given sequence of amino acid monomers (folding problem) and determining a sequence for a given folded structure (inverse folding problem). These two problems have much similarity to engineering structural analysis and structural optimization problems respectively. In the folding problem, a protein chain with a given sequence folds to a conformation, called a native state, which has a unique global minimum energy value when compared to all other unfolded conformations. This involves a search in the conformation space. This is somewhat akin to the principle of minimum potential energy that determines the deformed static equilibrium configuration of an elastic structure of given topology, shape, and size that is subjected to certain boundary conditions. In the inverse-folding problem, one has to design a sequence with some objectives (having a specific feature of the folded structure, docking with another protein, etc.) and constraints (sequence being fixed in some portion, a particular composition of amino acid types, etc.) while obtaining a sequence that would fold to the desired conformation satisfying the criteria of folding. This requires a search in the sequence space. This is similar to structural optimization in the design-variable space wherein a certain feature of structural response is optimized subject to some constraints while satisfying the governing static or dynamic equilibrium equations. Based on this similarity, in this work we apply the topology optimization methods to protein design, discuss modeling issues and present some initial results.

The field of microsystems, or microelectromechanical systems (MEMS) as it is popularly known, is a truly multidisciplinary area of research. It combines a wide variety of physical, chemical, and biological phenomena into an integrated system on a chip. This unprecedented integration naturally calls for new systems design approaches as well as efficient ways to analyze a single system or a component that is governed by many types of partial and ordinary differential equations from different physical and chemical domains. The key component of almost all MEMS devices, with the exception of microfluidic systems, is a movable mechanical structure of micron dimensions. Since the early works in this area dating back to the late sixties of the 20th Century, simple mechanical structures such as beams and diaphragms have dominated MEMS. Thus, the mechanical design in MEMS is mainly concerned with the design of such elastically deforming structures subjected to a variety of forces ranging from electrostatic, thermal, magnetic, piezoelectric, radiation pressure, etc. In addition to these unconventional forces and the accompanying complex equations that govern them, micromachining brings additional difficulties in microsystem design.