Topology Synthesis Research Articles

Design of Nonlinear Springs for Prescribed Load-Displacement Functions

A nonlinear spring has a defined nonlinear load-displacement function, which is also equivalent to its strain energy absorption rate. Various applications benefit from nonlinear springs, including prosthetics and microelectromechanical system devices. Since each nonlinear spring application requires a unique load-displacement function, spring configurations must be custom designed, and no generalized design methodology exists. In this paper, we present a generalized nonlinear spring synthesis methodology that (i) synthesizes a spring for any prescribed nonlinear load-displacement function and (ii) generates designs having distributed compliance. We introduce a design parametrization that is conducive to geometric nonlinearities, enabling individual beam segments to vary their effective stiffness as the spring deforms. Key features of our method include (i) a branching network of compliant beams used for topology synthesis rather than a ground structure or a continuum model based design parametrization, (ii) curved beams without sudden changes in cross section, offering a more even stress distribution, and (iii) boundary conditions that impose both axial and bending loads on the compliant members and enable large rotations while minimizing bending stresses. To generate nonlinear spring designs, the design parametrization is implemented into a genetic algorithm, and the objective function evaluates spring designs based on the prescribed load-displacement function. The designs are analyzed using nonlinear finite element analysis. Three nonlinear spring examples are presented. Each has a unique prescribed load-displacement function, including a (i) “J-shaped,” (ii) “S-shaped,” and (iii) constant-force function. A fourth example reveals the methodology’s versatility by generating a large displacement linear spring. The results demonstrate the effectiveness of this generalized synthesis methodology for designing nonlinear springs for any given load-displacement function.

Designing globally optimal delta–sigma modulator topologies via signomial programming

AbstractWe present a design methodology for globally optimizing the topologies of delta–sigma modulators (DSMs). Previous work cast the design task into a general non‐convex, nonlinear programming problem, whereas we propose to recast it as a signomial programming problem. Convexification strategies are presented for transforming the signomial programming problem into its equivalent convex counterpart, thereby enabling the solution of globally optimal design parameters. It is also possible to include circuit non‐ideal effects that affect the transfer function of the modulator into the formulation without affecting the computational efficiency. The proposed framework has been applied to topology synthesis problems of single‐loop and multi‐loop low‐pass DSMs based on discrete‐time circuitry. Numerical results confirm the effectiveness of the proposed approach over conventional nonlinear programming techniques. Copyright © 2008 John Wiley & Sons, Ltd.

Synthesis and Design of a Novel 3T1R Fully-Parallel Manipulator

In this paper a new topology of four degrees-of-freedom 3T1R fully-parallel manipulator is presented, which is defined only using lower kinematic pairs. The paper starts with a complete type synthesis of different topologies of fully-parallel manipulators that can perform the so-called Schönflies motion, based on the Theory of Groups of Displacements. After imposing some practical requirements, the different possibilities of manipulators are reduced to only one topology of fully-parallel and fully-symmetrical parallel manipulator. Then, the kinematic analysis of the manipulator is shown, including the closed-form resolution of both forward and inverse position problems, the velocity and the singularity analysis. Finally, a prototype of the manipulator is presented, which is intended to be used in pick and place applications.

Topological and Geometrical Synthesis of Three-Degree-of-Freedom Fully Parallel Manipulators by Instantaneous Kinematics

This paper presents a new synthesis procedure of fully parallel manipulators (PMs) of three degrees of freedom (DOFs) that could be implemented in a computer-aided synthesis process. Possible designs of PMs are represented by a set of unit joint twists at an initial configuration, called here topological and geometric parameters (TGPs). This makes it possible to represent PMs of all topologies and geometries in an easy and consistent way. The kinematic bond between the end effector (EE) and the base is then formulated as a set of equations involving TGPs, actuated-joint variables, and non-actuated-joint variables (passive joints). To achieve the required type of EE motion, possible topologies are first derived from tangent space analysis, and then the feasible topologies are retained by further displacement analysis. The geometries are determined such that the set of equations should be isoconstrained when passive-joint variables are taken as unknowns. The synthesis procedure of 3DOF PMs is illustrated with three numerical examples: one producing a new architecture of one translation and two rotations, while the other two producing existing architectures of translational PMs.

Topology synthesis of geometrically nonlinear compliant mechanisms using meshless methods

This paper presents a new method for topology optimization of geometrical nonlinear compliant mechanisms using the element-free Galerkin method (EFGM). The EFGM is employed as an alternative scheme to numerically solve the state equations by fully taking advantage of its capability in dealing with large displacement problems. In the meshless method, the imposition of essential boundary conditions is also addressed. The popularly studied solid isotropic material with the penalization (SIMP) scheme is used to represent the nonlinear dependence between material properties and regularized discrete densities. The output displacement is regarded as the objective function and the adjoint method is applied to finding the sensitivity of the design functions. As a result, the optimization of compliant mechanisms is mathematically established as a nonlinear programming problem, to which the method of moving asymptotes (MMA) belonging to the sequential convex programming can be applied. The availability of the present method is finally demonstrated with several widely investigated numerical examples.

Mobile backbone synthesis for ad hoc wireless networks

In this paper, we present an extended mobile backbone network topology synthesis algorithm (ETSA) for constructing and maintaining a dynamic backbone structure for mobile ad hoc wireless networks. We present and analyze the mathematical features of the proposed scheme. Using these results, we prove that: (1) The ETSA scheme converges in constant time; (2) The length of each control packet is bounded by a constant value that is independent of the number of network nodes; (3) The size of the backbone network depends only on the size of the operational area and is independent of nodal density. We compare the performance features of this scheme with those characterizing other protocols that employ clustering operations and/or use selective forwarding on demand routing methods. In addition, we present an on-demand routing protocol (MBNR) that makes use of the underlying dynamically self-configuring backbone network infrastructure and demonstrate its performance advantages when compared with an on-demand routing protocol that is based on a flat architecture, as well as with other backbone-based routing protocols.

On honeycomb representation and SIGMOID material assignment in optimal topology synthesis of compliant mechanisms

This paper introduces a new honeycomb based domain representation and SIGMOID material function to model continuum topology optimization domains with fixed grids. The two-point connectivity ensured with hexagonal cells is shown to circumvent singularities related to checkerboard patterns and point flexures that are typically observed with one-point connected rectangular cells. The novel SIGMOID function is developed to assign the ‘solid’ material for very low values of design variables (probabilities) and ‘void’ material for those further lower than the threshold, thus encouraging the binary material assignment. The performance of the SIGMOID function is compared with the previously proposed SIMP and PEAK material assignment functions. It is shown that both SIMP and PEAK functions can be over-restrictive in that the material is assigned only for probabilities close to one. The proposed modeling is suitable for topology optimization objectives wherein the number of constraints is large and gradient-based algorithms are chosen. Numerous examples on material layout determination for compliant mechanisms are solved with flexibility-stiffness and flexibility-strength multi-criteria formulations to illustrate the essence of this paper.

Topology of serial and parallel manipulators and topological diagrams

This paper deals with manipulator topology. The term topology was first introduced into robotics to characterize the kinematic structure of a manipulator without reference to its dimensions. Its dimension-independent aspect does not pose a considerable problem to planar manipulators, but makes it no longer appropriate to describe spatial manipulators especially spatial parallel manipulators, because such important properties as the degree of freedom of a manipulator and the degree of mobility of its end-effector as well as the nature of the mobility are highly dependent on some dimensional elements. In order to address this fundamental issue in kinematic synthesis, we introduced essential constraints into the concept of topology through the analysis of representative architectures, proposed a topological representation which provides a better correspondence between the representation and the intended manipulators, a necessity for topological synthesis and documentation. Introducing the essential constraints can also improve the efficiency of some synthesis methods.

Topology Synthesis of Distributed Actuation Systems for Morphing Wing Structures

This paper presents a novel topology optimization methodology for a synthesis of distributed actuation systems with specific applications to morphing air vehicle structures. The main emphasis is placed on the topology optimization problem formulation and the development of computational modeling concepts. The analysis model is developed to meet several important criteria: It must allow a large rigid-body displacement, as well as a variation in planform area, with minimum strain on structural members while retaining acceptable numerical stability for finite element analysis. For demonstration purposes, the in-plane morphing wing model is presented. Topology optimization is performed on a semiground structure with design variables that control the system configuration. In other words, the state of each element in the model is controlled by a corresponding design variable that, in turn, is determined through the optimization process. In effect, the optimization process assigns morphing members as soft elements, nonmorphing load-bearing members as stiff elements, and nonexistent members as voids. The optimization process also determines the optimum actuator placement, where each actuator is represented computationally by equal and opposite nodal forces with soft axial stiffness. In addition, the configuration of attachments that connect the morphing structure (i.e., morphing wing) to a nonmorphing structure (i.e., fuselage) is determined simultaneously in the same process. Several different optimization problem formulations are investigated to understand their potential benefits in solution quality, as well as meaningfulness of the formulations. Sample in-plane morphing problems are solved to demonstrate the potential capability of the methodology introduced in this paper.

Classical carbonyl reactivity enables a short synthesis of the core structure of acutumine

The development of a direct synthesis of the complex core topology of the alkaloid acutumine from a simple keto proline derivative is described. An efficient sequence of three carbonyl-dependent reactions is at the heart of this design for synthesis.

Relaxing Toward Rotaxanes

Traditional approaches to the chemical synthesis of complex molecular topologies, such as knots and interlocked rings, have focused on reducing kinetic barriers. More recently, an alternative approach has relied on the reversible assembly of comparatively simple building blocks that relax eventually into the desired topological conformation because it is the most favorable thermodynamic arrangement. Northrop et al. apply this second strategy to the preparation of [4]pseudorotaxanes, in which a Y-shaped core bears a ring on each of its three axes, and the rings in turn are linked to one another through either one or two central capping groups parallel to the planar core.

A two-stage topological optimum design for monolithic compliant microgripper integrated with flexure hinges

The formation of hinge-like portions typically is encountered in the structural topological synthesis. This paper proposes an optimum synthesis integrated with the analytic single-axis flexure hinge as a second-stage design process to obtain optimum flexure configuration and location for promoting the overall performance of a compliant microgripper after the topology optimization. The locations of hinge-like in topology synthesis are verified to be the exact locations of flexures. A simplifying optimization applying ANSYS is consequently done in the second-stage optimum design. The proposed process can be extended to other types of compliant structural design.

STUDY ON TOPOLOGICAL SYNTHESIS OF EPICYCLIC GEAR TRAINS BASED ON FUNCTIONAL FRACTIONATION

Topological graph using functional fractionation methods is presented to describe epicyclic gear trains (EGTs). Three levels of topological units are established. It is summarized that three basic units compose complex EGTs. Based on the combinational characteristics of basic units, four combination modes are put forward. Micro-transformation is performed on topological graph and stratified adjacency matrix is established, approaches of isomorphism criterion are given that provide theoretical basis for topological synthesis of EGTs. According to the characteristics of loops in topological graphs, common EGTs are divided into four kinds of gear trains. By taking EGTs containing six gears for instance, statistical methods for four sorts of EGTs are derived. For each combination of basic units, topological atlases are synthesized by evolution rules and various possible EGTs are deduced by inversion rules. The results show that topological synthesis method is a convenient and effective method for constructing innovative planetary mechanisms. The method may be universally applied to the topological synthesis of multimember EGTs.

Topology and Dimensional Synthesis of Compliant Mechanisms Using Discrete Optimization

A unified approach to topology and dimensional synthesis of compliant mechanisms is presented in this paper as a discrete optimization problem employing both discrete (topology) and continuous (size) variables. The synthesis scheme features a design parameterization method that treats load paths as discrete design variables to represent various topologies, thereby ensuring structural connectivity among the input, output, and ground supports. The load path synthesis approach overcomes certain design issues, such as “gray areas” and disconnected structures, inherent in previous design schemes. Additionally, multiple gradations of structural resolution and a variety of configurations can be generated without increasing the number of design variables. By treating topology synthesis as a discrete optimization problem, the synthesis approach is incorporated in a genetic algorithm to search for feasible topologies for single-input single-output compliant mechanisms. Two design examples, commonly seen in the compliant mechanisms literature, are included to illustrate the synthesis procedure and to benchmark the performance. The results show that the load path synthesis approach can effectively generate well-connected compliant mechanism designs that are free of gray areas.

Topological Synthesis of a Parallel Wrist Mechanism

To determine a suitable kinematic structure for a specific application is a complex task. Some available methods may provide a list of possible architectures for a robot wrist. However, a systematic method for selecting one among others is still an open problem. The paper presents a qualitative procedure for topological synthesis based on criteria that consider wrist design requirements and parallel mechanism peculiarities. The performance of chosen topology is evaluated according to desired requirements.

FOTG: fault-oriented stress testing of IP multicast

Network simulators provide a useful tool, for protocol evaluation. However, the results depend heavily on the simulated scenarios, especially for complex protocols such as multicast. There has been little work on scenario generation. In this work we present a fault-oriented test generation (FOTG) algorithm for automated stress testing of multicast protocols. FOTG processes an extended FSM model and uses a mix of forward and backward search techniques. Unlike traditional verification approaches, instead of starting from initial states, FOTG starts from a fault and uses cause-effect relations for automatic topology synthesis then uses backward implication to generate tests. Using FOTG we test various mechanisms commonly employed by multicast routing and validate our results through simulation.

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.

Modular Petri Net based modeling, analysis, synthesis and performance evaluation of random topology dedicated production systems

Ordinary t-timed modular Petri Nets are used for modeling, analysis, synthesis and performance evaluation of random topology dedicated production systems. Each system is first decomposed into production line, assembly, disassembly and parallel machine modules followed by derivation of their modular Petri Net models. Two sets of modules, generic and generalized respectively, are derived corresponding to the simplest and most general cases. Overall system Petri Net model is obtained via synthesis of the individual modules satisfying system features (production rates, buffer capacities, machine expected up, down or idle times). Detailed mathematical expressions are derived for modules P-invariants (and T-invariants when exist); they are further generalized for a random topology and complexity dedicated production system. Total number of the individual Petri Net module nodes as well as of the combined system Petri Net model is also calculated. Results show the applicability of the proposed methodology and justify its modeling power and generality.

Joint application mapping/interconnect synthesis techniques for embedded chip-scale multiprocessors

As transistor sizes shrink, interconnects represent an increasing bottleneck for chip designers. Several groups are developing new interconnection methods and system architectures to cope with this trend. New architectures require new methods for high-level application mapping and hardware/software codesign. We present high-level scheduling and interconnect topology synthesis techniques for embedded multiprocessor systems-on-chip that are streamlined for one or more digital signal processing applications. That is, we seek to synthesize an application-specific interconnect topology. We show that flexible interconnect topologies utilizing low-hop communication between processors offer advantages for reduced power and latency. We show that existing multiprocessor scheduling algorithms can deadlock if the topology graph is not strongly connected, or if a constraint is imposed on the maximum number of hops allowed for communication. We detail an efficient algorithm that can be used in conjunction with existing scheduling algorithms for avoiding this deadlock. We show that it is advantageous to perform application scheduling and interconnect synthesis jointly, and present a probabilistic scheduling/interconnect algorithm that utilizes graph isomorphism to pare the design space.

Topological Synthesis of Compliant Mechanisms Using Nonlinear Beam Elements

The article presents a methodology for generating topology of complaint mechanisms using nonlinear deformation theory. In an earlier work, (Joo, J., Kota, S., Kikuchi, N., (2000) Topological synthesis of compliant mechanisms using linear beam elements. Mechanics of Structures and Machines 28(4):245–280), we presented a topology synthesis methodology using linear beam elements. Using large deformation analysis, the article presents a methodology for topology synthesis based on a multicriteria objective function as a ratio of geometrical advantage to strain energy is employed to capture the conflicting functional requirements that are inherent in compliant mechanisms design. The benefits of using nonlinear methods for large deformation problems are illustrated by using three design examples and comparing results from a nonlinear implementation of the optimization procedure with a linear scheme.