Analysis of Approximate Four-Bar Straight-Line Mechanisms

1965 ◽  
Vol 87 (3) ◽  
pp. 291-296 ◽  
Author(s):  
D. Tesar ◽  
J. P. Vidosic
Keyword(s):  
Detailed Data ◽  
Design Data ◽  
Straight Line ◽  
Curvature Theory

Four-bar linkages possess many unique advantages as straight-line mechanisms. Formulations involving linkage geometry and curvature theory are developed to yield the lengths of the approximate straight line for specified accuracies. Design data such as link dimensions, transmission angles, and crank rotation angles are also obtained. Classical mechanisms including the Watt, Evans, Chebychev, and Roberts types are analyzed and compared. More detailed data, including a design data chart, are presented for linkages based on a Ball-double Burmester point.

Extended Camus Theory and Higher Order Conjugated Curves

2019 ◽  
Author(s):  
Cody Leeheng Chan ◽  
Kwun-Lon Ting
Keyword(s):  
Stationary Point ◽  
Higher Order ◽  
The Body ◽  
The Other ◽  
Body System ◽  
Straight Line ◽  
Pair Generation ◽  
Curvature Theory ◽  
Three Body ◽  
Two Bodies

Abstract According to Camus’ theorem, for a single DOF 3-body system with the three instant centers staying coincident, a point embedded on a body traces a pair of conjugated curves on the other two bodies. This paper discusses a fundamental issue not addressed in Camus’ theorem in the context of higher order curvature theory. Following the Aronhold-Kennedy theorem, in a single degree-of-freedom three-body system, the three instant centers must lie on a straight line. This paper proposes that if the line of the three instant centers is stationary (i.e. slide along itself), on the line of the instant centers a point embedded on a body traces a pair of conjugated curves on the other two bodies. Another case is that if the line of the three instant centers rotate about a stationary point, the stationary point embedded on the body also traces a pair of conjugated curves on the other two bodies. The paper demonstrates the use of instantaneous invariants to synthesize such a three-body system leading to a conjugate curve-pair generation. It is a supplement or extension of the Camus’ theorem. The Camus’ theorem may be regarded as a special singular case, in which all three instant centers are coincident.

Curvature Theory of Envelope Curve in Two-Dimensional Motion and Envelope Surface in Three-Dimensional Motion

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Wei Wang ◽  
Delun Wang
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Spatial Motion ◽  
Envelope Curve ◽  
Contact Conditions ◽  
Numerical Examples ◽  
Envelope Surface ◽  
Straight Line ◽  
Curvature Theory ◽  
Fixed Line

The curvature theories for envelope curve of a straight line in planar motion and envelope ruled surface of a plane in spatial motion are systematically presented in differential geometry language. Based on adjoint curve and adjoint surface methods as well as quasi-fixed line and quasi-fixed plane conditions, the centrode and axode are taken as two logical starting-points to study kinematic and geometric properties of the envelope curve of a line in two-dimensional motion and the envelope surface of a plane in three-dimensional motion. The analogical Euler–Savary equation of the line and the analogous infinitesimal Burmester theories of the plane are thoroughly revealed. The contact conditions of the plane-envelope and some common surfaces, such as circular and noncircular cylindrical surface, circular conical surface, and involute helicoid are also examined, and then the positions and dimensions of different osculating ruled surfaces are given. Two numerical examples are presented to demonstrate the curvature theories.

Novel Methodology for Inflection Circle based synthesis of Straight Line Crank Rocker Mechanism

2021 ◽  
pp. 1-13
Author(s):  
Prashant Shiwalkar ◽  
S. D. Moghe ◽  
J. P. Modak
Keyword(s):  
Compliant Mechanisms ◽  
Relative Length ◽  
Dimensional Synthesis ◽  
Straight Line ◽  
Synthesis Of Mechanisms ◽  
Acceptable Deviation ◽  
Curvature Theory ◽  
Path Curvature ◽  
Artificial Neural Network Ann ◽  
Line Path

Abstract Emerging fields like Compact Compliant Mechanisms have created newer/novel situations for application of straight line mechanisms. Many of these situations in Automation and Robotics are multidisciplinary in nature. Application Engineers from these domains are many times uninitiated in involved procedures of synthesis of mechanisms and related concepts of Path Curvature Theory. This paper proposes a predominantly graphical approach using properties of Inflection Circle to synthesize a crank rocker mechanism for tracing a coupler curve which includes the targeted straight line path. The generated approximate straight line path has acceptable deviation in length, orientation and extent of approximate nature well within the permissible ranges. Generation of multiple choices for the link geometry is unique to this method. To ease the selection, a trained Artificial Neural Network (ANN) is developed to indicate relative length of various options generated. Using studied unique properties of Inflection Circles a methodology for anticipating the orientation of the straight path vis-à-vis the targeted path is also included. Two straight line paths are targeted for two different crank rockers. Compared to the existing practice of selecting the mechanism with some compromise due to inherent granularity of the data in Atlases, proposed methodology helps in indicating the possibility of completing the dimensional synthesis. The case in which the solution is possible, the developed solution is well within the design specifications and is without a compromise.

Computer-Aided Synthesis of Linkage-Type Straight-Line and Dwell Mechanisms

1996 ◽  
Author(s):  
Pei-Lum Tso ◽  
Shan-Shun Yan
Keyword(s):  
Optimal Solution ◽  
Primary Methods ◽  
Programming Technique ◽  
The Third ◽  
The Past ◽  
Design Charts ◽  
Straight Line ◽  
Curvature Theory ◽  
Set Up ◽  
Position Synthesis

Abstract The synthesis of the four-bar mechanism has received a substantial amount of attention in the area of straight-line mechanisms. Various geometrical and analytical methods have been developed with numerous papers published in this area over the past few decades. Three primary methods are generally available for synthesis of the linkages. The first approach is the classical Burmester finite separated position synthesis technique. The precision points are assigned for describing the desired straight-line motion (Mahyuddin etc. 1986;Shagan,Fallahi and Lai 1989). The second approach uses the mathematical programming technique for finding the optimal solution which mimimizes the error between the desired straight line and the real tracing points of a linkage (Hwang and Hsiao 1989;Hwang and Lee 1987). The third approach is based on the curvature theory. Any point on the inflection circle generates an approximate straight Tine motion. A series of design charts was set up by Vidosic and Tesar (Vidosic and Tesar 1967) as the basis of synthesizing the mechanisms. However, the direction of the coupler point has generally not been controlled. The constraint was taken into consideration by Hsu (Hsu and Lee 1990).

Development of Knowledge Base for Designing Linkage-Type Dwell Mechanisms: Part 1—Theory

1987 ◽  
Vol 109 (3) ◽  
pp. 308-315 ◽  
Author(s):  
Sridhar Kota ◽  
Arthur G. Erdman ◽  
Donald R. Riley
Keyword(s):  
Expert System ◽  
Circular Arc ◽  
Design Charts ◽  
Circular Arcs ◽  
Straight Line ◽  
Parallel Motion ◽  
Curvature Theory ◽  
Path Curvature ◽  
Motion Characteristics ◽  
Straight Lines

Linkage-type mechanisms have certain advantages over cams for dwell applications. The design of a typical six-link dwell mechanism involves adding an output dyad to the basic four-bar mechanism that generates either a circular arc or a straight line portion of the coupler curve. The entire motion characteristics of these four-bar mechanisms should be considered in order to design a suitable dwell linkage. Part 1 of this paper is devoted to the study of four-bar linkages which generate straight line, circular arc and symmetrical curves. Part 2 discusses how the design experience gained in this study can be applied to develop an expert system for designing linkage-type dwell mechanisms. Using path curvature theory and design charts developed by Tesar, et al., hundreds of four-bar straight-line mechanisms are systematically investigated. Based on the typical shapes of coupler curves these mechanisms are then classified. A synthesis technique has been developed to design four-bar mechanisms for circular arc generation. Symmetrical coupler curves with straight-line or circular-arc segments, which are required for designing double-dwell mechanisms, are studied. This paper is part of the research that is underway to develop an “expert system” for designing mechanisms to generate straight lines, circular arcs, symmetrical curves, parallel motion and dwell.

scholarly journals Change in Entropy of the Spinning Black Holes

2014 ◽  
Vol 32 ◽  
pp. 95-103
Author(s):  
Dipo Mahto ◽  
Amresh Kumar Singh ◽  
Kumari Vineeta ◽  
Ashok Kumar
Keyword(s):  
Applied Sciences ◽  
Black Holes ◽  
Galactic Nuclei ◽  
Entropy Change ◽  
Future Research ◽  
Design Data ◽  
Massive Black Holes ◽  
Straight Line ◽  
University Department ◽  
X Ray Binaries

Aims: To derive an expression for change in entropy of spinning black holes on the basis of the model for the energy of spinning black holes ( Mahto et al. 2011a) & the model for entropy change ( Mahto et al. 2011b) and then calculate their values for different test spinning black holes. Study Design: Data for the mass of black holes have collected from the research paper entitled :Super massive Black Holes in Galactic Nuclei: Past Present & Future Research(2005), Space Science Reviews by L. Ferrarese & H. Ford and Black holes in Astrophysics(2005), New Journal Physics by R. Narayan. The data for black hole constant for spinning black holes () is taken from the paper entitled: Study of Schwarzschild radius with reference to the spinning black holes. Bulletin of Pure and Applied Sciences (2011a). Place and Duration of Study: Department of Physics, Marwari College Bhagalpur and University Department of Physics, T.M.B.U. Bhagalpur, between December 2013 and March 2014. Methodology: A theoretical based work using Laptop to calculate the calculation for change in entropy of different test spinning black holes at Marwari College Bhagalpur and the residential research chamber of the first author. Results: The calculation shows that the change in entropy of spinning black holes of the rest masses for stellar – mass black holes (M ~ 5 ­ 20 Mʘ) in X-ray binaries is to J/K and for the super massive black holes (M ~ 106 – 109.5 Mʘ) in active galactic nuclei is to J/K. The nature of the graph for XRBs is the same to the Hawking entropy with the event horizon and straight line for AGN which confirms the validity of equations and . Conclusion: The change in energy and entropy of black holes are mainly dependent on the mass and independent of their event horizons.

Microdensitometer—computer correlation analysis of ultrastructural periodicity

1978 ◽  
Vol 36 (2) ◽  
pp. 32-33
Author(s):  
D.R. Ensor ◽  
C.G. Jensen ◽  
J.A. Fillery ◽  
R.J.K. Baker
Keyword(s):  
Correlation Analysis ◽  
Background Noise ◽  
Computer Control ◽  
Optical Diffraction ◽  
Screw Thread ◽  
Straight Line ◽  
Computer Storage ◽  
Correlation Process ◽  
Electron Microscope Image ◽  
Fixed Beam

Because periodicity is a major indicator of structural organisation numerous methods have been devised to demonstrate periodicity masked by background “noise” in the electron microscope image (e.g. photographic image reinforcement, Markham et al, 1964; optical diffraction techniques, Horne, 1977; McIntosh,1974). Computer correlation analysis of a densitometer tracing provides another means of minimising "noise". The correlation process uncovers periodic information by cancelling random elements. The technique is easily executed, the results are readily interpreted and the computer removes tedium, lends accuracy and assists in impartiality.A scanning densitometer was adapted to allow computer control of the scan and to give direct computer storage of the data. A photographic transparency of the image to be scanned is mounted on a stage coupled directly to an accurate screw thread driven by a stepping motor. The stage is moved so that the fixed beam of the densitometer (which is directed normal to the transparency) traces a straight line along the structure of interest in the image.

Freeze fracture imaging and computer simulation of liposome structure: Membrane geometry and defects

1983 ◽  
Vol 41 ◽  
pp. 646-647
Author(s):  
Joseph A. Zasadzinski
Keyword(s):  
Liquid Crystalline ◽  
Freeze Fracture ◽  
Continuum Theory ◽  
Closed Surfaces ◽  
Straight Line ◽  
Low Weight ◽  
Concentric Spheres ◽  
Membrane Geometry ◽  
Dupin Cyclides ◽  
Limiting Case

At low weight fractions, many surfactant and biological amphiphiles form dispersions of lamellar liquid crystalline liposomes in water. Amphiphile molecules tend to align themselves in parallel bilayers which are free to bend. Bilayers must form closed surfaces to separate hydrophobic and hydrophilic domains completely. Continuum theory of liquid crystals requires that the constant spacing of bilayer surfaces be maintained except at singularities of no more than line extent. Maxwell demonstrated that only two types of closed surfaces can satisfy this constraint: concentric spheres and Dupin cyclides. Dupin cyclides (Figure 1) are parallel closed surfaces which have a conjugate ellipse (r1) and hyperbola (r2) as singularities in the bilayer spacing. Any straight line drawn from a point on the ellipse to a point on the hyperbola is normal to every surface it intersects (broken lines in Figure 1). A simple example, and limiting case, is a family of concentric tori (Figure 1b).To distinguish between the allowable arrangements, freeze fracture TEM micrographs of representative biological (L-α phosphotidylcholine: L-α PC) and surfactant (sodium heptylnonyl benzenesulfonate: SHBS)liposomes are compared to mathematically derived sections of Dupin cyclides and concentric spheres.

Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

1970 ◽  
Vol 28 ◽  
pp. 360-361
Author(s):  
John W. Coleman
Keyword(s):  
Boundary Conditions ◽  
High Performance ◽  
Force Fields ◽  
Optical Design ◽  
Direct Conversion ◽  
Design Engineering ◽  
Design Data ◽  
Scalar Potentials ◽  
Geometric Elements ◽  
At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

Human Enamel Replication

1976 ◽  
Vol 34 ◽  
pp. 180-181
Author(s):  
Norman L. Dockum ◽  
John G. Dockum
Keyword(s):  
Organic Matrix ◽  
Human Teeth ◽  
Human Enamel ◽  
Straight Line ◽  
Ultrastructural Characteristics

Ultrastructural characteristics of fractured human enamel and acid-etched enamel were compared using acetate replicas shadowed with platinum and palladium. Shadowed replications of acid-etched surfaces were also obtained by the same method.Enamel from human teeth has a rod structure within which there are crystals of hydroxyapatite contained within a structureless organic matrix composed of keratin. The rods which run at right angles from the dentino-enamel junction are considered to run in a straight line perpendicular to the perimeter of the enamel, however, in many areas these enamel rods overlap, interlacing and intertwining with one another.

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