Showing papers in "Journal of Mechanical Design in 1994"

Genetic Algorithms as an Approach to Configuration and Topology Design

Abstract: The genetic algorithm, a search and optimization technique based on the theory of natural selection, is applied to problems of structural topology design. An overview of the genetic algorithm will first describe the genetics-based representations and operators used in a typical genetic algorithm search. Then, a review of previous research in structural optimization is provided. A discretized design representation, and methods for mapping genetic algorithm “chromosomes” into this representation, is then detailed. Several examples of genetic algorithm-based structural topology optimization are provided: we address the optimization of cantilevered plate topologies, and we investigate methods for optimizing finely-discretized design domains. The genetic algorithm’s ability to find families of highly-fit designs is also examined. Finally, a description of potential future work in genetic algorithm-based structural topology optimization is offered.

The Linear Approximated Equation of Vibration of a Pair of Spur Gears (Theory and Experiment)

Abstract: The nonlinear equation for the rotational vibration of a pair of spur gears has a restriction that the analytical solution of the equation cannot be obtained. In this paper, the linear equation of vibration is derived theoretically and its physical model, i.e., the linear model of vibration is presented. The analytical solution of the linear equation, which is derived by analytical method, agrees well with the numerically calculated result by the nonlinear equation. By analyzing the analytical solution of the linear equation in detail, we clarified the relation between the waveforms of the vibration and the profile error of gear pairs, and also found that the effect of the contact ratio to the vibration is large and complex. The equivalent error, accounting for effects of the static load, the time-varying stiffness, and the profile error of gear pairs, is proposed in this paper. It can be considered as promising for evaluating the profile error, because the vibration of gear pairs is excited mainly by the equivalent error. Finally, for confirming the above results, the vibration of two tested gear pairs has been measured by an experimental set-up for this purpose.

Forward Position Analysis of Nearly General Stewart Platforms

Abstract: This paper presents the closed-form solution of the forward position analysis of the nearly general Stewart platform, which consists of a base and a moving planar platform connected by six extensible limbs through spherical joints in the two planar platforms. It becomes a general Stewart platform if the centers are not constrained to those two planes. In this study, the coordinate transformation matrix is used to represent the position of the moving platform. Based on the six dependency equations of the rotation matrix and the six constraint equations related to the six link lengths, a set of six 4th degree equations in three unknowns are derived. Further derivations produce 21 dependent constraint equations. By simultaneous elimination of two unknowns a 20th order polynomial equation in one unknown is obtained. Due to dual solutions of other unknowns, this indicates a maximum of 40 possible solutions. The roots of this polynomial are then solved numerically and the realistic solutions are constructed using computer graphics.

Spherical Maps: Their Construction, Properties, and Approximation

Abstract: The Gaussian map and its allied visibility map on a unit sphere find wide applications for orientating the workpiece for machining by numerical control machines and for probing by coordinate measurement machines. They also provide useful aids in computerized scene analysis, computation of surface-surface intersection, component design for manufacturing and fabrication procedures. Spherical convex hulls and spherical circles are two geometric constructs used to approximate the Gaussian maps and the visibility maps. The duality and the complementarity of these spherical maps are examined so as to derive efficient algorithms.

Computer-Aided Sketching of Epicyclic-Type Automatic Transmission Gear Trains

Abstract: The enumeration of epicyclic gear mechanisms in the form of graphs gives rise to the need of a methodology for reverse transformation, that is, for constructing the mechanisms from graphs. This paper addresses the issue by discretizing an epicyclic gear mechanism into Fundamental Geared Entities. Further, these geared entities are shown to be a conglomeration of four primitives; namely, the carrier, sun, ring, and the planet gear. An algorithm is formulated to create the entities from a graph by using these primitives. The entities are then connected together to form a mechanism.

Design and Fabrication of Microelectromechanical Systems

Abstract: 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.

Geometric Elimination of Constraint Violations in Numerical Simulation of Lagrangian Equations

Abstract: Conventional holonomic or nonholonomic constraints are defined as geometric constraints The total enregy of a dynamic system can be treated as a constrained quantity for the purpose of accurate numerical simulation In the simulation of Lagrangian equations of motion with constraint equations, the Geometric Elimination Method turns out to be more effective in controlling constraint violations than any conventional methods, including Baumgarte’s Constraint Violation Stabilization Method (CVSM) At each step, this method first goes through the numerical integration process without correction to obtain updated values of the state variables These values are then used in a gradient-based procedure to eliminate the geometric and energy errors simultaneously before processing to the next step For small step size, this procedure is stable and very accurate

Reliability-Based Optimal Design of a Bistable Compliant Mechanism

Abstract: Compliant mechanisms obtain at least some of their motion from the deflection of their flexible members. Advantages of such mechanisms include the reduction of manufacturing and assembly cost and time. Bistable mechanisms are particularly useful in applications where two stable equilibrium positions are required, such as switches, gates, and closures. Fatigue is a major concern in many compliant mechanisms due to the cyclic stresses induced on the flexible members. In this paper, a method for the probabilistic design of a bistable compliant slider-crank mechanism is proposed. Link lengths, material properties, and cross-section dimensions are taken as random variables. Probabilistic constraints on the maximum and minimum required input torque, location of stable equilibrium position, and overall size are included. The objective function is the maximization of the mechanism reliability in fatigue. Several design studies are performed to gain further insight into the nature of the problem.

Structural Parameters Which Reduce the Number of Manipulator Configurations

Abstract: The inverse kinematics of series-chain, six-degree-of-freedom manipulators has been developed to the point where it yields all possible configurations for a given end-effector position and orientation. In this paper we use the methods of inverse kinematics to uncover the conditions on the structural parameters which cause a manipulator to yield a lower maximum number of configurations than its general class. It is shown that the following conditions can cause a diminution in the maximum number of possible configurations: parallel joint axes, perpendicular joint axes, intersecting joint axes, and Bennett geometries. Using these geometries in 6R, 5R1P, 4R2P, and 3R3P chains, this paper determines the reduction in degree of their characteristic polynomials.

On the Limitations of Predictions of the Dynamic Response of Machines with Clearance Connections

Abstract: The results of experimental and analytical studies of the dynamic response of machines with flexible links and connection clearances are presented. These results suggest that both a large amount of variability and high sensitivity to small parameter changes and operating conditions are inherent properties of the dynamic response of such systems. This work indicates that the accuracy of dynamic force predictions given by computer simulations for such systems may be fundamentally limited, and therefore such simulations should be used with care in system design.

Computerized design and generation of low-noise helical gears with modified surface topology

Abstract: An approach for design and generation of low-noise helical gears with localized bearing contact is proposed. The approach is applied to double circular arc helical gears and modified involute helical gears. The reduction of noise and vibration is achieved by application of a predesigned parabolic function of transmission errors that is able to absorb a discontinuous linear function of transmission errors caused by misalignment. The localization of the bearing contact is achieved by the mismatch of pinion-gear tooth surfaces. Computerized simulation of meshing and contact of the designed gears demonstrated that the proposed approach will produce a pair of gears that has a parabolic transmission error function even when misalignment is present. Numerical examples for illustration of the developed approach are given.

Structural Configuration Examples of an Integrated Optimal Design Process

Abstract: Structural optimization procedures usually start from a given design topology and vary proportions or boundary shapes of the design to achieve optimality of an objective under various constraints. This article presents examples of the application of a novel approach for initiating formal structural optimization at an earlier stage, where the design topology is rigorously generated. A three-phase design process is used. In Phase I, an optimal initial topology is created by a homogenization method as a gray-scale image. In Phase II, the image is transformed to a realizable design using computer vision techniques. In Phase III, the design is parameterized and treated in detail by conventional size and shape optimization techniques. Fully-automated procedures for optimization of two-dimensional solid structures are outlined, and several practical design problems for this type of structures are solved using the proposed procedure, including a crane hook and a bicycle frame.