Structural optimization using graphic statics

This paper presents a method for structural optimization of discrete trusses using Graphic Statics. As opposed to traditional structural optimization techniques, which are typically conducted by manipulating the geometry of the structure (the form diagram), the approach presented in this paper establishes a Graphic Statics solution to the problem, where structural optimization is conducted using design variables in the force domain (force diagram). The proposed approach presents several attractive features compared to traditional approaches. Since it is based on reciprocal graphical relationships between form geometry and forces, member stiffnesses need not be calculated. Additionally, by working on the force diagram, equilibrium of the solution is guaranteed, and no additional methods are required to enforce this condition; for example, there is no need to triangulate the structure or to add small area members. Furthermore, because only solutions that are in equilibrium are permitted, the number of design variables can be reduced. Also, subject to certain relationships, the location of the loads (or reactions) do not need to be set a priori. Through examples, it is shown that the proposed methodology can readily accommodate different tensile and compressive stresses for volume optimization problems and that, through the use of Graphic Statics, other restrictions or constraints on the member forces can easily be incorporated.     

基于功能特征的间隔线路图形设计技术的研究

本文介绍基于功能特征技术,设计变电系统倒闸操作主接线间隔线路图形的方法。通过图元功能特征(几何特征点、属性特征等)定义建立间隔线路动态父子关系链,以间隔线路组成一个系统的结构群体,采用人工智能的方法自动生成间隔线路图形,同时,基于特征点的约束机制,动态编辑线路模板中的子图元,以使主接线图形满足设计要求。     

Global stability predictions for flexible workpiece milling using time domain simulation

This paper describes the use of peak-to-peak (PTP) force diagrams for machining stability prediction and validates its suitability for milling processes where the workpiece is considerably more flexible than the machine-tool system. These diagrams result from numerous executions of a time domain simulation which includes both the tool and workpiece dynamics and a mechanistic force model. The applicability of the PTP force diagram is validated experimentally through peripheral milling tests of thin-walled structures. Measured and simulated cutting forces are compared. It is shown that the PTP diagrams offer the global stability information which is provided by the traditional lobe diagram, while preserving the detailed, local information provided by time domain simulation.     

基于衍型的模式标注方法

设计模式在面向对象软件设计、开发和维护中发挥着非常重要的作用。为了克服现有设计模式标注方法的缺陷与不足,提出一种基于衍型的模式标注方法SBPN。基于UML衍型机制,SBPN不仅提供了一套规则用于精确标注结构图中类、方法或属性等模型元素的模式角色相关信息,还可以标注交互图中的模式信息。此外,SBPN为源代码中模式信息的标注也提供了相应的解决方案。给出了使用SBPN方法标注类图、交互图和源代码中的模式信息的实例,最后还将SBPN应用于一个较为复杂的排序系统。     

Application of principles of event related open systems to business process reengineering

This paper is focused on analysing the complete business environment with the help of information technology. It takes into account various interactions between different business processes while conducting BPR exercise. It also provides a framework based on event diagrams to record logical flow and other relevant details, which can be used for design of an information system. The event diagrams are useful for intelligent information system design. This methodology can also be used to develop a system for system design. Each event can be analysed for requirement of data, operations and resources. Interactions between various forces, events, modules, applications can be shown through interaction diagrams. The paper also lists out the driving forces for BPR and their contents.     

Maxwell’s reciprocal diagrams and discrete Michell frames

This paper unites two major legacies of James Clerk Maxwell’s ground-breaking paper, “On Reciprocal Figures, Frames, and Diagrams of Forces” (Maxwell, Philos Mag 26:250-261, 1864; Edinb Roy Soc Proc 7:160–208, 1870): (i) the fundamental theorem used by Michell (Philos Mag 8(47):589–597, 1904) to derive trusses of least weight and (ii) reciprocal frames. This paper presents some remarkable relationships between discrete Michell frames and their corresponding reciprocal force polygons using Graphic Statics. Several examples are given to illustrate the notions of duality and self-reciprocity in these diagrams, with particular emphasis placed on discrete optimal benchmark structures. For a given connectivity of nodes, Graphic Statics provides all of the information needed to determine the total load path of the structure in the form and force diagrams. Because the form and force diagrams are reciprocal, in the course of finding one minimum load path structure, a second minimum load path structure is also found. These observations between the corresponding form and force diagrams are generalized for discrete cantilever Michell frames, and several comments on the extensions of this work are included.     

Automated fixture configuration for rapid manufacturing planning

The wide adoption of agile manufacturing systems has necessitated the design and use of fixtures or work holding devices that have in-built flexibility to rapidly respond to part design changes. Despite the availability of reconfigurable fixtures, practical fixture configuration largely remains an experience driven manual activity to enable customization for varying workpiece geometry, and most automated solutions do not scale well to accommodate such variation. In this paper, we address the problem of rapidly synthesizing a realistic fixture that will guarantee stability and immobility of a specified polyhedral work-part. We propose that the problem of automated fixture layout may be approached in two distinct stages. First, we determine the spatial locations of clamping points on the work piece boundary using the principles of force and form closure, to ensure immobility of the fixtured part under external perturbation. In particular, we show that the candidate restraints mapped to the six dimensional vector space of wrenches (force–moment pairs) may be hashed in a straightforward manner to efficiently generate force closure configurations that restrain part movement against large external wrenches. When clamps are allowed to exert arbitrarily high reaction forces on the part, the spatial arrangement of the clamping locations ensures the part is in form closure. On generating force/form closure configurations, the chosen locations are matched against a user-specified library of reconfigurable clamps to synthesize a valid fixture layout comprising clamps that are accessible and collision free with each other and the part. Additionally, in the case of determining machining setups the clamps are chosen to avoid collisions with the moving cutting tool. We demonstrate fast algorithms to perform both location selection and fixture matching, and show several results that underscore the practical application of our solution in automated manufacturing process planning.     

Grasp evaluation and contact points planning for polyhedral objects using a ray-shooting algorithm

Grasp evaluation and planning are two fundamental issues in robotic grasping and dexterous manipulation. Most traditional methods for grasp quality evaluation suffer from non-uniformity of the wrench space and a dependence on the scale and choice of the reference frame. To overcome these weaknesses, we present a grasp evaluation method based on disturbance force rejection under the assumption that the normal component of each individual contact force is less than one. The evaluation criterion is solved using an enhanced ray-shooting algorithm in which the geometry of the grasp wrench space is read by the support mapping. This evaluation procedure is very fast due to the efficiency of the ray-shooting algorithm without linearization of the friction cones. Based on a necessary condition for grasp quality improvement, a heuristic searching algorithm for polyhedral object regrasp is also proposed. It starts from an initial force-closure unit grasp configuration and iteratively improves the grasp quality to find the locally optimum contact points. The efficiency and effectiveness of the proposed algorithms are illustrated by a number of numerical examples.     

Perception of Order and Ambiguity in Leonardo’s Design Concepts

Leonardo da Vinci used geometry to give his design concepts both structural and visual balance. The paper examines aesthetic order in Leonardo’s structural design, and reflects on his belief in analogy between structure and anatomy. Leonardo’s drawings of grids and roof systems are generated from processes best known from ornamentation and can be developed into spatial structures assembled from loose elements with no need for binding elements. His architectural plans are patterns based on principles of tessellation, tiling and recursion, also characteristic of the reversible, ambiguous structures which led to Leonardo’s further inventions in structural and mechanical design as well as dynamic representations of space in his painting. In recent times, the ambiguous structures in the art of Joseph Albers, the reversible and impossible structures of M. C. Escher, the recurring patterns and spherical geometry of Buckminster Fuller and the reciprocal grids in structural design of Cecil Balmond display a similar interest. Computer models and animations have been used to simulate processes of perceiving and creating ambiguity in structures.     

Extensions to the design structure matrix for the description of multidisciplinary design, analysis, and optimization processes

While numerous architectures exist for solving multidisciplinary design optimization (MDO) problems, there is currently no standard way of describing these architectures. In particular, a standard visual representation of the solution process would be particularly useful as a communication medium among practitioners and those new to the field. This paper presents the extended design structure matrix (XDSM), a new diagram for visualizing MDO processes. The diagram is based on extending the standard design structure matrix (DSM) to simultaneously show data dependency and process flow on a single diagram. Modifications include adding special components to define iterative processes, defining different line styles to show data and process connections independently, and adding a numbering scheme to define the order in which the components are executed. This paper describes the rules for constructing XDSMs along with many examples, including diagrams of several MDO architectures. Finally, this paper discusses potential applications of the XDSM in other areas of MDO and the future development of the diagrams.     

Modelling polyhedral solids bounded by multi-curved parametric surfaces

Since the beginning of geometric modelling as a field of CAD a decade ago, the methods for interactive design of solid objects and interactive design of free-formed surfaces (of degree three and higher) were developed along parallel yet disjoint lines. One led to the development of techniques for representing and manipulating the shape of polyhedral solids bounded mostly by planes, while the other led to the development of techniques for the mathematical representation of curved surfaces, without paying attention to their combination into volumetric solids. Though the need for integrating solid object modelling with surface modelling for the design of such artefacts as machine parts, aircraft, cars and ships has been widely recognized, there is so far no single modelling system which provides such capabilities in a general way.An integrated solids modelling system for representing and manipulating polyhedral objects bounded by bicubic parametric surfaces is presented. Its basic capabilities include the representation of solids through a surface-based model, such that the surface underlying any face can be replaced by another surface that has been modelled independently. Other functionalities include scaling, rotation and translation of shapes and their pairwise combination into more complex shapes by means of spatial set operators.     

The Reciprocalizer: an Agile Design Tool for Reciprocal Structures

This paper presents the reciprocalizer, a grasshopper plugin developed to design reciprocal structures. The plugin can handle the full set of geometric parameters necessary to describe the geometry of reciprocally connected elements in real-time. This makes it an agile design tool for the exploration of the geometrical richness of reciprocal structures.     

Computing minimal distances on polyhedral surfaces

The authors implement an algorithm that finds minimal (geodesic) distances on a three-dimensional polyhedral surface. The algorithm is intrinsically parallel, in as much as it deals with all nodes simultaneously, and is simple to implement. Although exponential in complexity, it can be used with a companion gradient-descent surface-flattening algorithm that produces an optimal flattening of a polyhedral surface. Together, these two algorithms have made it possible to obtain accurate flattening of biological surfaces consisting of several thousand triangular faces (monkey visual cortex) by providing a characterization of the distance geometry of these surfaces. The authors propose this approach as a pragmatic solution to characterizing the surface geometry of the complex polyhedral surfaces which are encountered in the cortex of vertebrates     

Flow-induced forces on two circular cylinders in proximity

Flow-induced forces on two nearby circular cylinders of equal diameter immersed in the cross flow at Re = 100 were numerically studied. We consider all possible arrangements of the two circular cylinders in terms of the distance between the two cylinders and the inclination angle of the line connecting the cylinder centers with respect to the direction of the main flow. It turns out that significant changes in the characteristics of flow-induced forces are noticed depending on how the two circular cylinders are positioned, resulting in quantitative changes of force coefficients on both cylinders. Collecting all the numerical results obtained, we propose contour diagrams for mean force coefficients and rms values of force coefficient fluctuations for each of the two cylinders. The perfect geometrical symmetry implied in the flow configuration allows one to use those diagrams to estimate flow-induced forces on two circular cylinders of equal diameter arbitrarily positioned in physical space with respect to the main flow direction.     

Adaptive Shape Diagrams for Multiscale Morphometrical Image Analysis

Shape diagrams are integral geometric representations in the Euclidean plane introduced to study 2D connected compact sets. Such a set is represented by a point within a shape diagram whose coordinates are morphometrical functionals defined as normalized ratios of geometrical functionals. In addition, the General Adaptive Neighborhoods (GANs) are spatial neighborhoods defined around each point of the spatial support of a gray-tone image, that fit with the image local structures. The aim of this paper is to introduce and study the GAN-based shape diagrams, which allow a gray-tone image morphometrical analysis to be realized in a local, adaptive and multiscale way. The GAN-based shape diagrams will be illustrated on standard images and also applied in the biomedical and materials areas.     

A Polyhedral Bound on the Indeterminate Contact Forces in Planar Quasi-Rigid Fixturing and Grasping Arrangements

This paper considers multiple-contact arrangements where several bodies grasp, fixture, or support an object via frictional point contacts. Within a strictly rigid-body modeling paradigm, when an external wrench (i.e., force and torque) acts on the object, the reaction forces at the contacts are typically indeterminate and span an unbounded linear space. This paper analyzes the contact reaction forces within a generalized quasi-rigid-body framework that keeps the desirable geometric properties of rigid-body modeling, while also including more realistic physical effects. We describe two basic principles that govern the contact mechanics of quasi-rigid bodies. The main result is that for any given external wrench acting on a quasi-rigid object, the statically feasible contact reaction forces lie in a bounded polyhedral set that depends on the external wrench, the grasp's geometry, and the preload forces. Moreover, the bound does not depend upon any detailed knowledge of the contact mechanics parameters. When some knowledge of the parameters is available, the bound can be sharpened. The polyhedral bound is useful for “robust” grasp and fixture synthesis. Given a set of external wrenches that may act upon an object, the grasp's geometry and preload forces can be chosen such that all of these external wrenches would be automatically supported by the contacts.     

Type synthesis of a class of spatial lower-mobility parallel mechanisms with orthogonal arrangement based on Lie group enumeration

Type synthesis of lower-mobility parallel mechanisms (PMs) has drawn extensive interests, particularly two main approaches were established by using the reciprocal screw system theory and Lie group theory, respectively. Although every above approach provides a universal framework for structural design of general lower-mobility PMs, type synthesis is still a comparably difficult task for the PMs with particular geometry or required to fulfill some specified tasks. This paper aims at exploring a simple and ef...     

Reciprocal Systems Based on Planar Elements: Morphology and Design Explorations

The concept of transferring forces in a reciprocal way has always been related to the use of timber beams, that is, elongated elements. However, planar components can also be considered; circular tiles, squares, triangles and more articulated or irregular geometrical shapes are all valid alternatives. This report proposes an initial exploration of reciprocal systems based on planar elements in order to guide further morphological studies. It also presents some prototypes, which were developed by the students of the École des Ponts in Paris during two design workshops run in 2012 and 2013.