Stability Concept for Surfaces

In CAD/CAM technology, the design of free form surfaces is the beginning of a chain of operations, which ends with the numerically controlled (NC) production of the designed object. An important part of this chain is shape analysis. We present a stability concept for surfaces based on infinitesimal bendings. The infinitesimal rigidity is enforced by certain boundary conditions.

This paper focuses on the design, fabrication, and metrology technologies of the ultra-precision optical freeform surface for progressive addition lens (PAL). The PAL, which has a front surface with far-view zone, near-view zone, and intermediate zone, was used to remedy presbyopia by distributing optical powers of the three zones. The PAL surface is a freeform surface because of its non-symmetrical power distribution. We introduce the PAL freeform surface design methodologies, including B-spline description and its optimization. After optimization of B-spline parameters of the PAL surface, we demonstrate the fabrication and measurement technologies of the mold for PAL surface by using ultra-precision freeform machining machine with slow tool servo function and ultra-precision 3D metrology system with user-defined function.

More and more lighting applications require the design of dedicated optics to achieve a given radiant intensity or irradiance distribution. Freeform optics has the advantage of providing such a functionality with a compact design. It was previously demonstrated in [Bäuerle et al., Opt. Exp. 20, 14477-14485 (2012)] that the up-front computation of the light path through the optical system (ray mapping) provides a satisfactory approximation to the problem, and allows the design of multiple freeform surfaces in transmission or in reflection. This article presents one natural extension of this work by introducing an efficient optimization procedure based on the physics of the system. The procedure allows the design of multiple freeform surfaces and can render high resolution irradiance patterns, as demonstrated by several examples, in particular by a lens made of two freeform surfaces projecting a high resolution logo (530 × 160 pixels).

Computation of double freeform optical surfaces using a Monge–Ampère solver: Application to beam shaping

Efficient optimal design of smooth optical freeform surfaces using ray targeting

A novel approach is introduced for the design of freeform axisymmetric optical surfaces using an optimization technique based on quadratic Bézier curves. Notably, the continuity (or lack thereof) of the freeform surface produced using the proposed technique is largely unaffected by the source-target mapping function. The validity of the proposed methodology is demonstrated through its application to the design of several laser beam shapers. The results show that the proposed technique requires only a small number of structural points to converge to the optimum design solution. The freeform design method presented herein is mathematically straightforward and can be easily implemented in code. Thus, it offers significant advantages for the design and analysis of a diverse range of optical systems.

ABSTRACTHigh-performance machining of free-form surfaces is highly critical in automotive, aerospace, and die–mold manufacturing industries. Therefore, electrochemical machining (ECM) process has been used in such cases in that sense. The most important challenges of using ECM process are the lack of accuracy and difficulty in designing proper machining tool (cathode) surfaces. In this article, a simplified mathematical model is presented to obtain a cathode surface for ECM of free-form surfaces which have high curvatures. In this theoretical approach, the finite-element method (FEM) is used to solve the 3-D Laplace equation and to determine the potential distribution between the anode (workpiece) and cathode (tool) surfaces. A compact and simple program was developed to obtain a proper cathode surface that only requires some nodal coordinates on the anode surface and boundary conditions. In this work, a trial cathode surface is constructed for a given gap distance. For the determined ECM parameters, cathode shape that satisfies the boundary conditions is obtained for the 45th layer. The results are compared with the literature and ANSYS Workbench for verification. The developed theoretical approach benefits simpler and faster FEM solutions, accurate cathode surface, and consequently correct form of machined surface.

We investigate use of the anisotropic radial basis functions expansion as a means to represent surface errors on aspheric and freeform surfaces. We show how the optimal choice of the shape parameter and the placement of radial basis function (RBF) nodes can increase accuracy of the surface approximation. We show an example of the adaptive grid refinement. In our approach, complex surfaces are modeled with general arbitrary representation while the anisotropic RBFs expansion models perturbation of the base surface. We show how both the global and the localized surface errors can be modeled across a wide spatial frequency range. With our method, the impact of the structured surface errors on the arbitrary surfaces when applied on the standardized image quality metrics can be assessed for the purpose of optical tolerancing.

Twisting motion plays an important role in kinematics of soft robots. However, current twisting actuators usually suffer from complex mechanical design with multiple materials and undesired coupling with bending and stretching motions. In this letter, we propose a new class of soft twisting pneumatic actuators that purely rely on the freeform chamber geometry to achieve large bi-directional twisting rotations. The freeform chamber surface integrates geometric flexibility in the cross section, lateral profile, and axial chirality, which are parameterized as design variables. We develop a finite element analysis model and investigate the effect of the geometry parameters on the actuators' mechanical behavior. The actuator naturally undergoes combined twisting and axial motions, and achieves a bi-directional twisting rotation of 116.7 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> , blocking torque of 0.81 N · m, and energy density of 1907 J/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> , well in line with the theoretical prediction. When it is constrained from axial motions, the actuator delivers pure twisting motion, achieving a bi-directional twisting rotation of 72.5 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> , blocking torque of 0.56 N· m, and energy density of 925 J/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> . This letter represents an important step toward leveraging the full potential of the freeform geometry design to create novel compact soft-bodied actuators and robots.

This Special Issue of JCISE is drawn from outstanding papers presented at the 2002 ACM Solid Modeling symposium. This is the second year that JCISE and ACM have collaborated to produce such a Special Issue, in what promises to become an annual tradition. Previously, JCISE V1, N4 (December 2001) contained selected papers from the 2001 symposium. The ACM/SIGGRAPH Symposia on Solid Modeling and Applications provide a premier international forum for the exchange of original research results and important practical applications in all areas of solid modeling and its applications. The symposia series brings together leading researchers, practitioners and graduate students working in this field. The seventh ACM Symposium on Solid Modeling and Applications was held at the Max Planck Institute for Informatics in Saarbruecken, Germany on June 17–21, 2002, the first to be held outside North America. The symposium was co-chaired by Hans-Peter Seidel of the Max Planck Institute and Vadim Shapiro of the University of Wisconsin, Madison, USA. The international program committee was co-chaired by Kunwoo Lee of Seoul National University, Seoul, Korea and Nicholas M. Patrikalakis of the Massachusetts Institute of Technology, Cambridge, Mass., USA. The program committee comprised of 25 leading experts on solid modeling theory and its applications from academia and industry working in 10 different countries from around the world. Previous symposia in this series were held in Austin, Texas, 1991; Montreal, Canada, 1993; Salt Lake City, Utah, 1995; Atlanta, Georgia, 1997; Ann Arbor, Michigan, 1999 and 2001. Starting with 2002, the Symposium is expected to be held annually, alternating in location between the USA and other countries within a two year period. Ninety-three papers were submitted to the 2002 symposium and reviewed by one member of the program committee and at least three additional referees. Based on these review results, the program co-chairs selected 26 papers for plenary presentation and 17 papers for poster presentation at the symposium. From the 26 plenary papers, the program co-chairs selected 9 papers for this special issue of JCISE. The selection was based on quality and engineering relevance. All selected papers were updated and extended since the version published in the conference proceedings, and were reviewed again by at least two additional referees and revised accordingly. The topics of the papers selected cover the following solid modeling areas: editing of free-form surfaces with haptic methods; reverse engineering of surface models; meshing of implicit surfaces; topological frameworks for part families; free-form surface design; design of transport elements in complex aircraft structures; collaborative framework for part and assembly modeling; modeling of heterogeneous solids; and iso-surface extraction methods. We wish to thank the authors for revising and extending their papers for this special issue of JCISE and the referees for their valuable comments, which improved the quality of the papers included. We hope that you the readers of JCISE will find these papers stimulating and interesting and that this will encourage you to participate in future solid modeling conferences and submit papers on this important area to these conferences and to regular issues of this ASME Transactions, JCISE, which also officially co-sponsored by ACM.

Just recently Flank Milling has opened up new possibilities in detailing large-scale architectural building envelopes. Whereas examples such as the Hungerburgbahn by Zaha Hadid show the application of Flank Milling at the end of the architectural manufacturing process, our research, in contrast, focuses on the implementation of constraints immanent to manufacturing techniques as early architectural design parameters. This process is explored by the help of generative modeling tools, to allow an intuitive design of freeform parametric curves and surfaces while at the same time obeying crucial geometric conditions.In this paper, we will focus on the "digital design to digital production" process on a 7-axis industrial CNC -robot.

Computer-aided geometric design is a subject which involves the representation, specification, design, manipulation, display, and analysis of free-form curves and surfaces. This eclectic field draws on techniques and principles from numerical analysis, approximation theory, computer graphics, interactive computer systems, mechanical and geometric design, and many other areas. Nevertheless, computer-aided geometric design is an endeavor with a character, emphasis, and purpose of its own, combining techniques and principles from other fields with unique approaches that are often somewhat enigmatic and confusing to the novice. Many things sound and seem familiar, yet the directions and motivations are distinct to this discipline. This decade is proving to be an era of intense interest in computer-aided geometric design, an activity attracting people from many sectors including computing and manufacturing. As the discipline more firmly establishes valid principles and standard techniques, it will undoubtedly be of increasing importance in computer-aided manufacturing and a wide range of other applications.

In this paper, we present exact analysis and representation of the swept surfaces of a cylindrical object undergoing two-parameter rational Bézier motions. Instead of using the well-known approach for analysing the point trajectory of an object motion for swept volume analysis, this paper seeks to develop a new method for swept volume analysis by studying the plane trajectory of a two-parameter rational motion. It brings together recent work in swept volume analysis, plane representation of developable surfaces, and computer aided synthesis of two-parameter freeform rational motions. The results have applications in design and approximation of freeform surfaces as well as in tool path planning for five-axis machining of freeform surfaces.

In a manufacturing area, design changes for an original surface model are frequently required: for example, when the physical parts are modified or when the parts are partially manufactured from analogous shapes. In this case, an efficient surface updating method by locally adding scan data for the modified area is highly desirable. For this purpose, this paper presents a new procedure to update an initial model that is composed of combinatorial triangular facets based on a set of locally added point data. Nowadays, many people are using surface models that are represented by triangular facets in reverse engineering, since it is fast and easy to create the triangular meshes directly from large amounts of point data. The initial surface model is first created from the initial point set by tight cocone, which is a water-tight surface reconstructor; and then the point cloud data for the updates is locally added onto the initial model maintaining the same coordinate system. In order to update the initial model, the special region on the initial surface that needs to be updated is recognized through the detection of the overlapping area between the initial model and the boundary of the newly added point cloud. After that, the initial surface model is eventually updated to the final output by replacing the recognized region with the newly added point cloud. The proposed method has been implemented and tested with several examples. This algorithm will be practically useful to modify the surface model with physical part changes and free-form surface design.

Manufacturing technologies as injection molding or embossing specify their production limits for minimum radii of the vertices or draft angle for demolding, for instance. These restrictions may limit the system optical efficiency or affect the generation of undesired artifacts on the illumination pattern when dealing with optical design. A novel manufacturing concept is presented here, in which the optical surfaces are not obtained from the usual revolution symmetry with respect to a central axis (z axis), but they are calculated as free-form surfaces describing a spiral trajectory around z axis. The main advantage of this new concept lies in the manufacturing process: a molded piece can be easily separated from its mold just by applying a combination of rotational movement around axis z and linear movement along axis z, even for negative draft angles. The general designing procedure will be described in detail.