A Linkage Type Map for Spherical 4 Position Synthesis

1995 ◽  
Author(s):  
Andrew P. Murray ◽  
J. Michael McCarthy
Keyword(s):  
Two Dimensional ◽  
Planar Case ◽  
Position Synthesis ◽  
Spherical Mechanism

Abstract This paper classifies and evaluates the solutions to the four orientation synthesis of spherical 4R linkages. Burmester’s result that a one-parameter set of planar RR dyads exists that guide a body through the four planar positions has an analogous form for spherical RR dyads given four orientations. The theory provides a two dimensional set of spherical 4R linkages that can be assembled in each of the four chosen orientations. A map of linkage types is obtained by classifying each spherical mechanism at the vertices of a finite grid on this set; Erdman titles this a “Map of Solutions” for the planar case. Each mechanism is then checked for input drivability, that is, whether or not the input link can drive the coupler smoothly through all four positions. The result is a map of the spherical 4R mechanisms that the designer can use to find practical solutions to the spherical synthesis problems.

Approximate Velocities in Mixed Exact-Approximate Position Synthesis of Planar Mechanisms

1999 ◽  
Vol 123 (3) ◽  
pp. 388-394 ◽  
Author(s):  
Jennifer E. Holte ◽  
Thomas R. Chase ◽  
Arthur G. Erdman
Keyword(s):  
Two Dimensional ◽  
Computer Implementation ◽  
Motion Generation ◽  
Planar Mechanisms ◽  
Form Complex ◽  
New Approach ◽  
Realistic Representation ◽  
Velocity Constraints ◽  
Position Synthesis ◽  
Exact Positions

A new approach to the synthesis of planar linkage mechanisms with approximate velocity constraints is proposed. The paper presents the first closed-form complex-number dyad solution to the ground pivot specification problem for two precision positions with velocity specified at one of the positions. The solution is then manipulated in order to add approximate velocity constraints to design methods for two exact positions and an unlimited number of approximate positions. The approximate position and velocity constraints facilitate more realistic representation of design objectives. Solution spaces are presented using two-dimensional ground-pivot maps. Computer implementation of the proposed methodologies would allow designers with little or no knowledge of the synthesis techniques to interactively explore maps of solutions for four-bar motion generation.

Design of a Bistable Origami Reverse-Fold Using Spherical Kinematics

2017 ◽  
Author(s):  
Rami Alfattani ◽  
Craig Lusk
Keyword(s):  
Change Point ◽  
Design Concept ◽  
Dimensional Synthesis ◽  
Bistable Behavior ◽  
Spherical Mechanisms ◽  
Formal Analogy ◽  
Simple Class ◽  
Parametric Cad ◽  
Position Synthesis ◽  
Spherical Mechanism

This paper presents a new design concept for bistability that can be implemented as a reverse-fold origami mechanism or as a spherical four-bar mechanism. The design is based on the conceptual overlap between a certain simple class of origami mechanisms (the reverse-fold) and a class of spherical change-point mechanisms. Using both a partially compliant spherical mechanism and a piece of origami made with two sheets of paper, we implement the design concept for bistable behavior. The design concept consists in adapting planar two position synthesis to spherical mechanisms and in using a formal analogy between spherical mechanisms and certain simple origami folds. The dimensional synthesis of these two mechanisms is performed using parametric CAD. The design concept was successfully prototyped both as origami and as a partially compliant spherical mechanism.

scholarly journals Non-ergodicity of inviscid two-dimensional flow on a beta-plane and on the surface of a rotating sphere

1987 ◽  
Vol 184 ◽  
pp. 289-302 ◽  
Author(s):  
Theodore G. Shepherd
Keyword(s):  
Phase Space ◽  
Domain Size ◽  
Finite Amplitude ◽  
Two Dimensional ◽  
Planar Case ◽  
Rotating Sphere ◽  
Dimensional Flow ◽  
Beta Plane ◽  
Quadratic Invariants ◽  
Two Dimensional Flow

It is shown that, for a sufficiently large value of β, two-dimensional flow on a doubly-periodic beta-plane cannot be ergodic (phase-space filling) on the phase-space surface of constant energy and enstrophy. A corresponding result holds for flow on the surface of a rotating sphere, for a sufficiently rapid rotation rate Ω. This implies that the higher-order, non-quadratic invariants are exerting a significant influence on the statistical evolution of the flow. The proof relies on the existence of a finite-amplitude Liapunov stability theorem for zonally symmetric basic states with a non-vanishing absolute-vorticity gradient. When the domain size is much larger than the size of a typical eddy, then a sufficient condition for non-ergodicity is that the wave steepness ε < 1, where ε = 2√2Z/βU in the planar case and $\epsilon = 2^{\frac{1}{4}} a^{\frac{5}{2}}Z^{\frac{7}{4}}/\Omega U^{\frac{5}{2}}$ in the spherical case, and where Z is the enstrophy, U the r.m.s. velocity, and a the radius of the sphere. This result may help to explain why numerical simulations of unforced beta-plane turbulence (in which ε decreases in time) seem to evolve into a non-ergodic regime at large scales.

Singularity Free Revolute–Prismatic–Revolute and Spherical–Prismatic–Spherical Chains for Actuating Planar and Spherical Single Degree of Freedom Mechanisms

2012 ◽  
Vol 4 (1) ◽  
Author(s):  
David A. Perkins ◽  
Andrew P. Murray
Keyword(s):  
Reference Frame ◽  
Unique Fixed Point ◽  
Degree Of Freedom ◽  
Moving Frame ◽  
Dimensional Synthesis ◽  
Planar Case ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Fixed Frame ◽  
Spherical Mechanism

Given a single degree of freedom mechanism, a moving reference frame attached to any link has a motion that can be described with a single parameter. A point relative to this moving frame is sought such that it either continually increases or decreases in distance from a point in the fixed frame over the entire motion. These points can be used to define a revolute–prismatic–revolute (RPR) chain for a planar mechanism or a spherical–prismatic–spherical (SPS) chain for a spherical mechanism capable of actuating the device over its entire range of motion. Moreover, the singularities relative to the joints in the original mechanism are not a concern and the dimensional synthesis can focus on creating the set of circuit-defect free solutions. From this analysis, a unique fixed point is determined in the planar case relative to two positions and their velocities with the following characteristic. All points in the moving reference frame that are moving away from it in the first position are approaching it in the second position, and vice versa. This point is as critical to the identification of singularity-free driving chains as the centrodes or the poles.

Quasi-Precision Position Synthesis of Four-Bar Linkages

1994 ◽  
Author(s):  
John A. Mirth
Keyword(s):  
Two Dimensional ◽  
Exact Position ◽  
Planar Linkages ◽  
Position Synthesis ◽  
Exact Positions

Abstract Quasi positions describe portions of a mechanism’s motion that do not require an exact position. Quasi positions are combined with three exact positions to define a two-dimensional design plane for the synthesis of planar linkages. Quasi-precision position synthesis is based on precision position techniques. The method preserves the computational advantages of precision position synthesis with the added advantage of being able to specify a much greater number of design positions.

Spectrophotometric measurements of objective-prism spectra

1966 ◽  
Vol 24 ◽  
pp. 118-119
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Progress Report ◽  
Two Dimensional ◽  
Objective Prism ◽  
Made In

I should like to give you a very condensed progress report on some spectrophotometric measurements of objective-prism spectra made in collaboration with H. Leicher at Bonn. The procedure used is almost completely automatic. The measurements are made with the help of a semi-automatic fully digitized registering microphotometer constructed by Hög-Hamburg. The reductions are carried out with the aid of a number of interconnected programmes written for the computer IBM 7090, beginning with the output of the photometer in the form of punched cards and ending with the printing-out of the final two-dimensional classifications.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Analysis of the 9th November 1990 flare

2000 ◽  
Vol 179 ◽  
pp. 229-232
Author(s):  
Anita Joshi ◽  
Wahab Uddin
Keyword(s):  
Image Processing ◽  
Two Dimensional ◽  
Temporal Behaviour ◽  
Contour Maps ◽  
Dimensional Measurements ◽  
Processing Software ◽  
Image Processing Software

AbstractIn this paper we present complete two-dimensional measurements of the observed brightness of the 9th November 1990Hαflare, using a PDS microdensitometer scanner and image processing software MIDAS. The resulting isophotal contour maps, were used to describe morphological-cum-temporal behaviour of the flare and also the kernels of the flare. Correlation of theHαflare with SXR and MW radiations were also studied.

High Resolution Microscopy of Multi-Layered Biological Crystals

1982 ◽  
Vol 40 ◽  
pp. 80-83
Author(s):  
H.A. Cohen ◽  
T.W. Jeng ◽  
W. Chiu
Keyword(s):  
High Resolution ◽  
Low Dose ◽  
Three Dimensional ◽  
Data Interpretation ◽  
Two Dimensional ◽  
Biological Objects ◽  
Density Maps ◽  
Density Map ◽  
Complex Crystal ◽  
High Resolution Microscopy

This tutorial will discuss the methodology of low dose electron diffraction and imaging of crystalline biological objects, the problems of data interpretation for two-dimensional projected density maps of glucose embedded protein crystals, the factors to be considered in combining tilt data from three-dimensional crystals, and finally, the prospects of achieving a high resolution three-dimensional density map of a biological crystal. This methodology will be illustrated using two proteins under investigation in our laboratory, the T4 DNA helix destabilizing protein gp32*I and the crotoxin complex crystal.

Sign in / Sign up

Export Citation Format

Share Document