scholarly journals Developable mechanisms on developable surfaces

2019 ◽  
Vol 4 (27) ◽  
pp. eaau5171 ◽  
Author(s):  
Todd G. Nelson ◽  
Trent K. Zimmerman ◽  
Spencer P. Magleby ◽  
Robert J. Lang ◽  
Larry L. Howell
Keyword(s):  
Mechanical Systems ◽  
Relative Orientation ◽  
Developable Surface ◽  
Curved Surfaces ◽  
Surface Type ◽  
Complex Tasks ◽  
Rigid Link ◽  
Developable Surfaces ◽  
Flat Sheet ◽  
Wide Range

The trend toward smaller mechanism footprints and volumes, while maintaining the ability to perform complex tasks, presents the opportunity for exploration of hypercompact mechanical systems integrated with curved surfaces. Developable surfaces are shapes that a flat sheet can take without tearing or stretching, and they represent a wide range of manufactured surfaces. This work introduces “developable mechanisms” as devices that emerge from or conform to developable surfaces. They are made possible by aligning hinge axes with developable surface ruling lines to enable mobility. Because rigid-link motion depends on the relative orientation of hinge axes and not link geometry, links can take the shape of the corresponding developable surface. Mechanisms are classified by their associated surface type, and these relationships are defined and demonstrated by example. Developable mechanisms show promise for meeting unfilled needs using systems not previously envisioned.

Geometric Design and Fabrication of Developable Bezier Surfaces

1992 ◽  
Author(s):  
R. M. C. Bodduluri ◽  
B. Ravani
Keyword(s):  
Geometric Design ◽  
Developable Surface ◽  
Developable Surfaces ◽  
Surface Patches ◽  
Bézier Surfaces ◽  
Point Representation ◽  
Cad Cam ◽  
C2 Continuity ◽  
Type Construction ◽  
Bezier Surfaces

Abstract In this paper we study Computer Aided Geometric Design (CAGD) and Manufacturing (CAM) of developable surfaces. We develop direct representations of developable surfaces in terms of point as well as plane geometries. The point representation uses a Bezier curve, the tangents of which span the surface. The plane representation uses control planes instead of control points and determines a surface which is a Bezier interpolation of the control planes. In this case, a de Casteljau type construction method is presented for geometric design of developable Bezier surfaces. In design of piecewise surface patches, a computational geometric algorithm similar to Farin-Boehm construction used in design of piecewise parametric curves is developed for designing developable surfaces with C2 continuity. In the area of manufacturing or fabrication of developable surfaces, we present simple methods for both development of a surface into a plane and bending of a flat plane into a desired developable surface. The approach presented uses plane and line geometries and eliminates the need for solving differential equations of Riccatti type used in previous methods. The results are illustrated using an example generated by a CAD/CAM system implemented based on the theory presented.

scholarly journals Optomechanical state reconstruction and nonclassicality verification beyond the resolved-sideband regime

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 125 ◽  
Author(s):  
Farid Shahandeh ◽  
Martin Ringbauer
Keyword(s):  
Quantum State ◽  
Tomographic Reconstruction ◽  
Mechanical Systems ◽  
Mechanical Resonators ◽  
Optical Cavities ◽  
Novel Approach ◽  
State Transfer ◽  
Wide Range ◽  
Coherent Pulse ◽  
Quantum Optomechanics

Quantum optomechanics uses optical means to generate and manipulate quantum states of motion of mechanical resonators. This provides an intriguing platform for the study of fundamental physics and the development of novel quantum devices. Yet, the challenge of reconstructing and verifying the quantum state of mechanical systems has remained a major roadblock in the field. Here, we present a novel approach that allows for tomographic reconstruction of the quantum state of a mechanical system without the need for extremely high quality optical cavities. We show that, without relying on the usual state transfer presumption between light an mechanics, the full optomechanical Hamiltonian can be exploited to imprint mechanical tomograms on a strong optical coherent pulse, which can then be read out using well-established techniques. Furthermore, with only a small number of measurements, our method can be used to witness nonclassical features of mechanical systems without requiring full tomography. By relaxing the experimental requirements, our technique thus opens a feasible route towards verifying the quantum state of mechanical resonators and their nonclassical behaviour in a wide range of optomechanical systems.

scholarly journals Robot Modeling for Physical Rehabilitation

Robotics ◽  
2013 ◽  
pp. 1212-1232 ◽  
Author(s):  
Rogério Sales Gonçalves ◽  
João Carlos Mendes Carvalho
Keyword(s):  
Mathematical Models ◽  
Three Dimensional ◽  
Mechanical Systems ◽  
Industrial Robots ◽  
Limb Movements ◽  
Rehabilitation Robots ◽  
Wide Range ◽  
Movable Platform ◽  
Human Limb ◽  
Robot Modeling

The science of rehabilitation shows that repeated movements of human limbs can help the patient regain function in the injured limb. There are three types of mechanical systems used for movement rehabilitation: robots, cable-based manipulators, and exoskeletons. Industrial robots can be used because they provide a three-dimensional workspace with a wide range of flexibility to execute different trajectories, which are useful for motion rehabilitation. The cable-based manipulators consist of a movable platform and a base, which are connected by multiple cables that can extend or retract. The exoskeleton is fixed around the patient's limb to provide the physiotherapy movements. This chapter presents a summary of the principal human limb movements, a review of several mechanical systems used for rehabilitation, as well as common mathematical models of such systems.

Design of a Two-Piece Brassiere Cup From its Data Points Toward its Automation

2020 ◽  
Author(s):  
Kotaro Yoshida ◽  
Hidefumi Wakamatsu ◽  
Eiji Morinaga ◽  
Takahiro Kubo
Keyword(s):  
Three Dimensional ◽  
Developable Surface ◽  
Two Dimensional ◽  
Trial And Error ◽  
Design Efficiency ◽  
Developable Surfaces ◽  
Data Points ◽  
Dimensional Shape ◽  
The Given ◽  
Three Dimensional Shape

Abstract A method to design the two-dimensional shapes of patterns of two piece brassiere cup is proposed when its target three-dimensional shape is given as a cloud of its data points. A brassiere cup consists of several patterns and their shapes are designed by repeatedly making a paper cup model and checking its three-dimensional shape. For improvement of design efficiency of brassieres, such trial and error must be reduced. As a cup model for check is made of paper not cloth, it is assumed that the surface of the model is composed of several developable surfaces. When two lines that consist in the developable surface are given, the surface can be determined. Then, the two-piece brassiere cup can be designed by minimizing the error between the surface and given data points. It was mathematically verified that the developable surface calculated by our propose method can reproduce the given data points which is developable surface.

scholarly journals Parameterisation of developable surfaces by asymptotic lines

1996 ◽  
Vol 54 (3) ◽  
pp. 411-421 ◽  
Author(s):  
Vitaly Ushakov
Keyword(s):  
Explicit Form ◽  
Gaussian Curvature ◽  
Developable Surface ◽  
Developable Surfaces ◽  
Asymptotic Lines

An example of a “non-developable” surface of vanishing Gaussian curvature from W. Klingenberg's textbook is considered and its place in the theory of 2-dimensional developable surfaces is pointed out. The surface is found in explicit form. Other examples of smooth developable surfaces not allowing smooth asymptotic parametrisation are analysed. In particular, Hartman and Nirenberg's example (1959) is incorrect.

V. On certain developable surfaces

1863 ◽  
Vol 12 ◽  
pp. 279-280 ◽  
Keyword(s):  
Developable Surface ◽  
Developable Surfaces

If U = 0 be the equation of a developable surface, or say a developable, then the hessian HU vanishes, not identically, but only by virtue of the equation U = 0 of the surface; that is, HU contains U as a factor, or we may write HU = U. PU. The function PU, which for the developable replaces, as it were, the hessian HU, is termed the prohessian; and since, if r be the order of U, the order of HU is 4 r —8, we have 3 r —8 for the order of the prohessian. If r =4, the order of the prohessian is also 4; and in fact, as is known, the prohessian is in this case = U.

scholarly journals Polar and Equatorial Aspects of Map Projections?

2019 ◽  
Vol 2 ◽  
pp. 1-6
Author(s):  
Miljenko Lapaine ◽  
Nedjeljko Frančula
Keyword(s):  
Perspective Projection ◽  
Developable Surface ◽  
Map Projection ◽  
Map Projections ◽  
Developable Surfaces

<p><strong>Abstract.</strong> There is no standard or generally accepted terminology of aspect in the theory of map projections. The term is probably derived from the concept that a graticule is produced by perspective projection of the meridians and parallels on a sphere onto a developable surface. Developable surfaces are widely accepted, and it is almost impossible to find a publication that deals with map projections in general and without developable surfaces story. If found, it usually classifies projections as cylindrical, conical and azimuthal, and applies developable surfaces to define the projection aspect. This paper explains why applying developable surfaces in the interpretation of map projections is not recommended, nor defining the aspect of all projections by the position of a midpoint as polar, equatorial, or oblique. In fact, defining a projection aspect this way is invalid in general, and obscures the fact that the aspect depends on the class to which a particular map projection belongs.</p>

A Computer-Aided Environment for Analysis and Design of Mechanical Systems

1991 ◽  
Author(s):  
Hamid M. Lankarani ◽  
Behnam Bahr ◽  
Saeid Motavalli
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
General Purpose ◽  
Design System ◽  
Integrated Analysis ◽  
Algebraic Equations ◽  
Efficient Design ◽  
Analysis And Design ◽  
Wide Range

Abstract This paper presents the description of an ideal tool for analysis and design of complex multibody mechanical systems. It is in the form of a general-purpose computer program, which can be used for simulation of many different systems. The generality of this computer-integrated environment allows a wide range of applications with significant engineering importance. No matter how complicated the mechanical system under consideration is, a numerical multibody model of the system is constructed. The governing mixed differential/algebraic equations of motion are automatically formulated and numerically generated. State-of-the-art numerical techniques and computational methods are employed and developed which produce in the response of the system at discrete time junctures. Postprocessing of the results in the form of graphical images or real-time animations provides an enormous aid in visualizing motion of the system. The analysis package may be merged with an efficient design optimization algorithm. The developed integrated analysis/design system is a valuable tool for researchers, design engineers, and analysts of mechanical systems. This computer-integrated tool provides an important bridge between the classical decision making process by an engineer and the emerging technology of computers.

Newer Theory and More Robust Algorithms for Computer-Aided Design of Developable Surfaces

2005 ◽  
Vol 42 (03) ◽  
pp. 71-79
Author(s):  
B. Konesky
Keyword(s):  
Computer Aided Design ◽  
Developable Surface ◽  
Robust Algorithms ◽  
Developable Surfaces ◽  
Space Curves ◽  
Surface Areas ◽  
C Programming ◽  
Computer Aided ◽  
Reliable Solution ◽  
Aided Design

The use of developable surfaces in design is of engineering importance because of the relative ease with which they can be manufactured. The problem of how to make surfaces developable is not new. The usual technique is by using two space curves, defining the edges of the surface. These are first created, and then a set of rulings are constructed between the space curves under the constraint of being developable. A problem with existing algorithms for designing developable surfaces is the tendency to include nondevelopable portions of the surface: areas of regression. A more reliable solution to the problem of creating a developable surface is presented. The key to the method is to define the developable surface in terms of a normal directrix. The shape of the normal directrix defines the resulting developable surface. Algorithms are defined to compute the shape of a normal directrix from a pair of space curves. Intersecting adjacent developable surfaces and generating the flat plate layouts were also accomplished. This paper presents research and development that started around 1987. The algorithms were implemented using ANSI C++ programming language and commercial computer-aided design and manufacturing (CAD and CAM) software programs.

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