G. K. Ananthasuresh

Topological Synthesis of Compliant Mechanisms Using Multi-Criteria Optimization

Compliant mechanisms are mechanical devices that achieve motion via elastic deformation. A new method for topological synthesis of single-piece compliant mechanisms is presented, using a “design for required deflection” approach. A simple beam example is used to illustrate this concept and to provide the motivation for a new multi-criteria approach for compliant mechanism design. This new approach handles motion and loading requirements simultaneously for a given set of input force and output deflection specifications. Both a truss ground structure and a two-dimensional continuum are used in the implementation which is illustrated with design examples.

Comprehensive thermal modelling and characterization of an electro-thermal-compliant microactuator

A comprehensive thermal model for an electro-thermal-compliant (ETC) microactuator is presented in this paper. The model accounts for all modes of heat dissipation and the temperature dependence of thermophysical and heat transfer properties. The thermal modelling technique underlying the microactuator model is general and can be used for the virtual testing of any ETC device over a wide range of temperatures (300-1500 K). The influence of physical size and thermal boundary conditions at the anchors, where the device is connected to the substrate, on the behaviour of an ETC microactuator is studied by finite element simulations based on the comprehensive thermal model. Simulations show that the performance ratio of the microactuator increased by two orders of magnitude when the characteristic length of the device was increased by one order of magnitude from 0.22 to 2.2 mm. Restricting heat loss to the substrate via the device anchors increased the actuator stroke by 66% and its energy efficiency by 400%, on average, over the temperature range of 300-1500 K. An important observation made is that the size of the device and thermal boundary conditions at the device anchor primarily control the stroke, operating temperature and performance ratio of the microactuator for a given electrical conductivity.

Micromechanical devices with embedded electro-thermal-compliant actuation

Abstract At the micro-scale, thermal actuation provides larger forces compared to the widely-used electrostatic actuation. In this paper, we highlight another advantage of thermal actuation, viz. the ease with which it can be utilized to achieve a novel embedded electro-thermal-compliant (ETC) actuation for MEMS. The principle of ETC actuation is based on the selective non-uniform Joule heating and the accompanying constrained thermal expansion. It is shown here that appropriate topology and shape of the structures give rise to many types of actuators and devices. Additionally, selective doping of silicon ETC devices is used to enhance the non-uniform heating and thus the deformation. A number of novel ETC building blocks and devices are described, and their analysis and design issues are discussed. The devices were microfabricated using MCNC’s MUMPs foundry process as well as a bulk-micromachining process called PennSOIL (Penn silicon-on-insulator layer). The designs are validated with the simulations and the experimental observations. The experimental measurements are quantitatively compared with the theoretical predictions for a novel ETC microactuator with selective doping.

Design of Distributed Compliant Mechanisms

Abstract The optimization problem formulations currently used to synthesize compliant mechanism topologies aim to maximize the flexibility for obtaining the desired output motion while maximizing the overall stiffness for satisfactorily bearing the applied loads. The best solution to this problem, as posed, is a linkage consisting of rigid members connected together with revolute joints. The current elastic mechanics-based formulations do generate compliant topologies that closely imitate a rigid-body linkage by means of lumped compliance as in flexural pivots. Systematically generating such topology solutions could serve as a creative aid in the conceptual design of mechanisms, especially when the force-deflection specifications are nonintuitive to human designers. However, flexural pivot-based compliant designs are not useful in most applications when large displacements and/or high strength are desired. Ideally, compliant designs should distribute flexibility uniformly throughout the structure rather than limiting it to a few pivots. In this article, we discuss why current formulations often lead to lumped compliant designs, put forth a proper quantitative measure for distributed compliance, and present a novel formulation that guarantees distributed compliant topologies. The method is explained in detail and is illustrated with examples.

Freeform Skeletal Shape Optimization of Compliant Mechanisms

Compliant mechanisms are elastic continua used to transmit or transform force and motion mechanically. The topology optimization methods developed for compliant mechanisms also give the shape for a chosen parameterization of the design domain with a fixed mesh. However, in these methods, the shapes of the flexible segments in the resulting optimal solutions are restricted either by the type or the resolution of the design parameterization. This limitation is overcome in this paper by focusing on optimizing the skeletal shape of the compliant segments in a given topology. It is accomplished by identifying such segments in the topology and representing them using Bezier curves. The vertices of the Bezier control polygon are used to parameterize the shape-design space. Uniform parameter steps of the Bezier curves naturally enable adaptive finite element discretization of the segments as their shapes change. Practical constraints such as avoiding intersections with other segments, self-intersections, and restrictions on the available space and material, are incorporated into the formulation. A multi-criteria function from our prior work is used as the objective. Analytical sensitivity analysis for the objective and constraints is presented and is used in the numerical optimization. Examples are included to illustrate the shape optimization method.

A Comparative Study of the Formulations and Benchmark Problems for the Topology Optimization of Compliant Mechanisms

The topology optimization problem for the synthesis of compliant mechanisms has been formulated in many different ways in the past 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 parametrizations, 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, and the ability to converge from an unbiased uniform initial guess are analyzed. Some observations and recommendations 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.

Vision-based sensing of forces in elastic objects

Abstract A minimally intrusive, vision-based, computational force sensor for elastically deformable objects is proposed in this paper. Estimating forces from the visually measured displacements is straightforward in the case of the linear problem of small displacements, but not in the case of the large displacements where geometric non-linearities must be taken into account. From the images of the object taken before and after the deformation, we compute the deformation gradients and logarithmic strains. Using the stress–strain relationships for the material, we compute the Cauchy’s stresses and from this we estimate the locations and magnitudes of the external forces that caused the deformation. A sensitivity analysis is performed to examine the effect of small deviations in the experimentally captured displacements on the estimated external forces. This analysis showed that the small-strain case is more sensitive and prone to numerical errors than the large-strain case. Additionally, a related method that is indirect and iterative is also presented in which we assume that we know the locations of the external forces. Numerical and experimental studies are presented for both micro- and macro-scale objects. The main conclusion of this work is that the vision-based force estimation is viable if the displacements of the deforming object can be captured accurately.

Design and Fabrication of Microelectromechanical Systems

An attempt has been made to summarize some of the important developments in the emerging technology of microelectromechanical systems (MEMS) from the mechanical engineering perspective. In the micro domain, design and fabrication issues are very much different from those of the macro world. The reason for this is twofold. First, the limitations of the micromachining techniques give way to new exigencies that are nonexistent in the macromachinery. One such difficulty is the virtual loss of the third dimension, since most of the microstructures are fabricated by integrated circuit based micromachining techniques that are predominantly planar. Second, the batch-produced micro structures that require no further assembly, offer significant economical advantage over their macro counterparts. Furthermore, electronic circuits and sensors can be integrated with micromechanical structures. In order to best utilize these features, it becomes necessary to establish new concepts for the design of MEMS. Alternate physical forms of the conventional joints are considered to improve the manufacturability of micromechanisms and the idea of using compliant mechanisms for micromechanical applications is put forth. The paper also reviews some of the fabrication techniques and the micromechanical devices that have already been made. In particular, it discusses the fabrication of a motor-driven four-bar linkage using the “boron-doped bulk-silicon dissolved-wafer process” developed at The University of Michigan’s Center for Integrated Sensors and Circuits.

Mechanical Design of Compliant Microsystems-A Perspective and Prospects

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.

Optimal Embedding of Rigid Objects in the Topology Design of Structures

Abstract Extensive published research results exist on the topology design of single-component structures, while multicomponent structural systems have received much less attention. In this article, we present a technique for optimizing the topology of a structure that should be connected to one or more predesigned polygon-shaped components to maximize the stiffness of the overall ensemble. We call it an embedding problem in topology design because predesigned components are to be optimally positioned and oriented within a design region while the connecting structures topology is optimized simultaneously. Continuous design variables are used to vary the locations of the embedded objects smoothly along with the topology of the connecting structure to apply gradient-based continuous optimization algorithms. A new material interpolation function on the basis of normal distribution function was used for this purpose. An optimality criteria method combined with the steepest descent method was used to minimize the mean compliance to obtain the stiffest structure for a given volume of material for the connecting structure. As a special case of this method, topology optimization of multicomponent structural systems connected with fasteners was also considered. Illustrative examples are presented.