Nadim Diab

Optimum Synthesis of Mechanisms Using Tabu-Gradient Search Algorithm

A tabu-gradient search is herein presented for optimum synthesis of planar mechanisms. The solution generated by a recency-based, short term memory tabu search is used to start a gradient search to drive the solution ever closer to the global minimum. A brief overview of the tabu-search method is first presented. A tabu-gradient algorithm is then used to synthesize four-bar mechanisms for path generation tasks by way of three examples, including two benchmark examples used before to test other deterministic and intelligent optimization schemes. Compared with the corresponding results generated by other schemes, the tabu-gradient search rendered the most optimal solutions of all.

A NEW APPROACH TO SHAPE OPTIMIZATION FOR CLOSED PATH SYNTHESIS OF PLANAR MECHANISMS

ABSTRACT A method for the synthesis of four-bar mechanisms to generate closed paths through shape optimization is herein introduced. The objective function is not based on Fourier descriptors, rather on the cyclic angular deviation (CAD) vector associated with a set of desired points on the curve. A simple method is introduced to account for the starting point shift between the desired CAD and the generated one. Following shape optimization, a simple mathematical approach is devised to properly scale, rotate, and translate the mechanism to the desired configuration. A case study is presented to demonstrate the effectiveness and robustness of the proposed method. KEYWORDS Synthesis; Shape Optimization, CAD vector; Optimization; Ant Colony; 1. INTRODUCTION Methods of dimensional synthesis of planar mechanisms have evolved with time to encompass a wide range of possibilities. Precision point synthesis methods are adequate for a limited number of points [1]. If the number of desired points exceeds a few (5 pos for four-bar motion generator), optimum synthesis becomes necessary [2-23]. A hybrid of exact/approximate point synthesis schemes have also been suggested [24-28]. Exact/approximate synthesis results in a mechanism that satisfies the desired trajectory at two or three points precisely, while generating many other points approximately. The main focus of previous synthesis efforts have been on single-task applications - motion, function, or path, synthesis. A method for a hybrid task synthesis was recently introduced [29]. Mechanism synthesis involves a large number of design parameters and searching the entire design space (DS) would be expensive. One method that has been suggested to reduce the size of the DS is to optimally find a solution that satisfies the shape of the desired trajectory. Then, the final solution is obtained by scaling, rotating, and translating the solution for the final mechanism. This paper follows this approach, but in a new way. The design objective is usually to determine the optimal link lengths (and angles between them) such that the motion generated by the mechanism is as close as possible to the desired trajectory. For the discussion to follow, the parameters of the four-bar mechanism are first introduced (see Fig. 1). The following notations are adopted hereafter. An uppercase boldface letter indicates a vector representing a link; the lowercase counterpart denotes the corresponding length; and the Greek letter counterpart denotes its angle. Thus,

DSMC Simulations of Squeeze Film Between a Micro Beam Undergoing Large Amplitude Oscillations and a Substrate

This paper investigates the behavior of a gas film in a micro RF switch. A Two-dimensional numerical study of the flow field is performed as the micro-beam oscillates harmonically between its equilibrium position and the fixed substrate underneath. Unlike previous work in literature, the beam undergoes large displacements throughout the film gap thickness and the behavior of the gas film along with its impact on the moving RF switch (force exerted by gas on the beam’s front and back faces) are discussed. Since the gas film thickness is of the order of few microns (i.e. 0.01<Kn<1), the rarefied gas exists in the non-continuum regime and, as such, the Direct Simulation Monte Carlo (DSMC) method is used to simulate the fluid behavior. The impact of the squeeze film on the beam is investigated over a range of frequencies, velocity amplitudes, and for different film gases, corresponding to ranges of dimensionless flow parameters such as the Reynolds (Re), Strouhal (St) and Mach (Ma) numbers on the gas film behavior.© 2012 ASME

A New Approach for Exact/Approximate Point Synthesis of Planar Mechanisms

The aim of this article is to provide a simple method to solve the mixed exact-approximate dimensional synthesis problem of planar mechanism. The method results in a mechanism that can traverse a closed path with the choice of any number of exact points while the rest are approximate points. The algorithm is based on optimum synthesis rather than on precision position methods. Ant-gradient search is applied on an objective function based on log10 of the error between the desired positions and those generated by the optimum solution. The log10 function discriminates on the side of generating miniscule errors (on the order of 10−14 ) at the exact points while allowing for higher errors at the approximate positions. The algorithm is tested by way of five examples. One of these examples was used to test exact/approximate synthesis method based on precision point synthesis approach.Copyright

An Elitist Ants-Search Based Method for Optimum Synthesis of Rigid-Linkage Mechanisms

Mechanical linkages are widely used in the industry and the synthesis of such mechanisms may require optimization depending on the number of precision positions required. Many intelligent optimization techniques (Genetic, Tabu, Simulated Annealing, etc) have been proposed in the literature, one of them being the Ant-Search which was first proposed by the authors in 2007. In this paper, a Modified Ant-Search (MAS) technique is proposed to optimize the synthesis of a four-bar mechanism with a path generation task. Two major improvements are applied over the previous algorithm: ants pheromone update and exploration/exploitation techniques are both modified. Unlike the previous work where a constant quantity of pheromones was added during each iteration, in this paper, the pheromone deposit rate is proportional to the error of the objective function. Such a modification in the pheromone update rule is expected to differentiate between the behaviors of different ants and better govern their motion in the subsequent iterations. Moreover, the second major improvement targets the exploration/exploitation techniques followed by the ants. Unlike the previous work where exploration dominates during the early iteration stages and exploitation during the late ones, this work implements a more dynamic strategy where ants enter and leave the exploration/exploitation processes as governed by parameters related to the objective function error and pheromone deposit levels. Such modifications applied to the Ant-Search (AS) technique are expected to ensure a better chance of converging to a global minimum. The MAS technique is applied for a few path generation tasks with prescribed timing along with a set of linear constraints. Results are compared with previous work in the literature where the newly proposed technique showed appreciable improvement as evaluated by the structural error objective function. Future work possibilities are also introduced.Copyright

Modeling Squeeze Films in the Vicinity of High Inertia Oscillating Microstructures

This work investigates the effect of various assumptions proposed by the classical Reynolds lubrication equation. In particular, a microplate oscillating at high frequencies (beyond cutoff) and high velocities leading to appreciable displacement within the film gap is studied. An analytical model is derived with special emphasis on the fluid’s inertia effect on the fluid/solid interface. By implementing the direct simulation Monte Carlo (DSMC) method, a numerical method for modeling rarefied gas flow, the analytically based model is adjusted for the force exerted by the gas on the oscillating microstructure to capture various significant effects related to the fluid’s inertia, compressibility, stiffness, and damping. [DOI: 10.1115/1.4026588]

Analysis and Optimum Synthesis of Planar Mechanisms With Clearances and Tolerances Using Interval Analysis

This paper presents an interval analysis based approach for analysis and optimization of planar mechanisms including the effect of link lengths tolerances and joint clearances. Mathematical models describing the effect of the mechanical errors on the desired output parameters of the mechanism are derived, followed by the commissioning of an ant-gradient based optimization scheme to find the maximum possible deviations in them. A new optimization approach is also devised to design a four bar mechanism with “minimal” sensitivity to clearances and tolerances. An analysis case study is presented and the results are displayed in the form of fuzzy membership functions and compared with results obtained using a similar approach. An example on optimum synthesis of a four-bar mechanism with joint clearances and link tolerances for hybrid exact/approximate points trajectory is also presented. Insights based on the assessment of the results are introduced.Copyright

Investigation of the Squeeze Film Dynamics Underneath a Microstructure With Large Oscillation Amplitudes and Inertia Effects

This paper presents Direct Simulation Monte Carlo numerical investigation of the dynamic behavior of a gas film in a microbeam. The microbeam undergoes large amplitude harmonic motion between its equilibrium position and the fixed substrate underneath. Unlike previous work in literature, the beam undergoes large displacements throughout the film gap thickness and the behavior of the gas film along with its impact on the moving micro structure (force exerted by gas on the beams front and back faces) are discussed. Since the gas film thickness is of the order of few microns (i.e. 0.01<Kn<1), the rarefied gas exists in the non-continuum regime and, as such, the DSMC method is used to simulate the fluid behavior. The impact of the squeeze film on the beam is investigated over a range of frequencies and velocity amplitudes, corresponding to ranges of dimensionless flow parameters such as the Reynolds, Strouhal and Mach numbers on the gas film behavior. Moreover, the behavior of compressibility pressure waves as a function of these dimensionless groups is discussed for different simulation case studies.

An Ants-Search Based Method for Optimum Synthesis of Compliant Mechanisms

Compliant mechanisms are widely used in the industry and have gained more popularity in the past few decades with the advancements in smart materials and micro-electro mechanical systems (MEMS). Compliant mechanisms offer huge advantages over the classical rigid linkages due to their flexible behavior. Such flexible mechanisms reduce production time and cost especially that they eliminate the need of joints that can get pretty hectic especially at micro level manufacturing and assembly. By avoiding multi-joints in the design and their consequent clearances, a compliant mechanism can offer higher precision over its rigid counterpart. However, these advantages come with a price; compliant mechanisms are more challenging in terms of design and analysis. Many compliant mechanisms are designed to undergo relatively large deflections which in turn impose geometric nonlinearities. In the past, many compliant designs were based on intuition, experience, and trial and error. Later on, many theories developed to assist in designing and analyzing compliant mechanisms before proceeding with the manufacturing phase. This paper covers topology optimization of compliant structures using beam elements. The swarm intelligence technique known as Ant Search (AS) is used to find the optimum design that satisfies the required mechanism performance. A case study that involves the topology design of a miniature compliant displacement amplifier is presented and results are compared with the finite element solver ANSYS. The optimized topology mechanism produced a much larger amplification ratio as compared to that presented in literature. Results produced show the high potential of swarm intelligence and AS in particular at solving multi-disciplinary optimization problems that should not be limited to designs that involve physical paths.Copyright

DSMC Simulations of Squeeze Film Under a Harmonically Oscillating Micro RF Switch With Large Tip Displacements

The two-dimensional unsteady behavior of a rarefied gas film under an oscillating micro-cantilever RF switch is presented. The microbeam, undergoing a parabolic deflection profile, is allowed to oscillate harmonically between its equilibrium position and the fixed substrate underneath for large beam-tip displacements. The gas film dynamics in terms of the flow field velocity and fluid forces exerted on the oscillating microbeam are discussed. The numerical technique used to model the rarefied gas flow is the Direct Simulation Monte Carlo (DSMC) method where the Knudsen (Kn) number is greater than 0.01 (ie. non-continuum regime). Unlike previous work in literature, the beam undergoes large deflections, which requires implementation, in DSMC, of a more realistic molecule-beam reflection behavior based on the instantaneous beam’s position and velocity. The effects of inertia, both local acceleration (St) and convection term (Re), and compressibility (Ma) on the gas film dynamics are examined over ranges of oscillating frequencies, velocity amplitudes, and microbeam’s lengths.Copyright