The Complete Solution of Alt–Burmester Synthesis Problems for Four-Bar Linkages

2016 ◽  
Vol 8 (4) ◽  
Author(s):  
Daniel A. Brake ◽  
Jonathan D. Hauenstein ◽  
Andrew P. Murray ◽  
David H. Myszka ◽  
Charles W. Wampler
Keyword(s):  
Algebraic Geometry ◽  
Rigid Body ◽  
Finite Number ◽  
Complete Solution ◽  
Numerical Algebraic Geometry ◽  
Number Of Solutions ◽  
One Dimensional ◽  
The Family ◽  
Path Synthesis ◽  
Path Point

Precision-point synthesis problems for design of four-bar linkages have typically been formulated using two approaches. The exclusive use of path-points is known as “path synthesis,” whereas the use of poses, i.e., path-points with orientation, is called “rigid-body guidance” or the “Burmester problem.” We consider the family of “Alt–Burmester” synthesis problems, in which some combination of path-points and poses is specified, with the extreme cases corresponding to the classical problems. The Alt–Burmester problems that have, in general, a finite number of solutions include Burmester's original five-pose problem and also Alt's problem for nine path-points. The elimination of one path-point increases the dimension of the solution set by one, while the elimination of a pose increases it by two. Using techniques from numerical algebraic geometry, we tabulate the dimension and degree of all problems in this Alt–Burmester family, and provide more details concerning all the zero- and one-dimensional cases.

Synthesis of Six-Bar Timed Curve Generators of Stephenson-Type Using Random Monodromy Loops

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Aravind Baskar ◽  
Mark Plecnik
Keyword(s):  
Rigid Body ◽  
Complete Solution ◽  
Numerical Algebraic Geometry ◽  
Algebraic Equations ◽  
Solution Sets ◽  
Root Finding ◽  
Rigid Body Motions ◽  
Joint Variable ◽  
Four Bar Linkage ◽  
Parameter Continuation

Abstract Synthesis of rigid-body mechanisms has traditionally been motivated by the design for kinematic requirements such as rigid-body motions, paths, or functions. A blend of the latter two leads to timed curve synthesis, the goal of which is to produce a path coordinated to the input of a joint variable. This approach has utility for altering the transmission of forces and velocities from an input joint onto an output point path. The design of timed curve generators can be accomplished by setting up a square system of algebraic equations and obtaining all isolated solutions. For a four-bar linkage, obtaining these solutions is routine. The situation becomes much more complicated for the six-bar linkages, but the range of possible output motions is more diverse. The computation of nearly complete solution sets for these six-bar design equations has been facilitated by recent root finding techniques belonging to the field of numerical algebraic geometry. In particular, we implement a method that uses random monodromy loops. In this work, we report these solution sets to all relevant six-bars of the Stephenson topology. The computed solution sets to these generic problems represent a design library, which can be used in a parameter continuation step to design linkages for different subsequent requirements.

Convexity of a discrete Carleman weighted objective functional in an inverse medium scattering problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Nguyen Trung Thành
Keyword(s):  
Finite Number ◽  
Scattering Problem ◽  
One Dimensional ◽  
Globally Convergent ◽  
Convergent Method ◽  
Inverse Medium ◽  
Inverse Medium Scattering ◽  
Objective Functional

AbstractWe investigate a globally convergent method for solving a one-dimensional inverse medium scattering problem using backscattering data at a finite number of frequencies. The proposed method is based on the minimization of a discrete Carleman weighted objective functional. The global convexity of this objective functional is proved.

scholarly journals On 2-Diffeomorphisms with One-Dimensional Basic Sets and a Finite Number of Moduli

2016 ◽  
Vol 16 (4) ◽  
pp. 727-749
Author(s):  
V. Z. Grines ◽  
Z. Grines ◽  
S. Van Strien
Keyword(s):  
Finite Number ◽  
One Dimensional ◽  
Basic Sets

Totally knotted knots are prime

1982 ◽  
Vol 91 (3) ◽  
pp. 467-472
Author(s):  
J. C. Gomez-Larran¯aga
Keyword(s):  
Finite Number ◽  
Knot Theory ◽  
Piecewise Linear ◽  
Connected Sum ◽  
Higher Dimensional ◽  
The Family ◽  
Linear Category

Throughout, the word knot means a subspace of the 3-sphere S3 homeomorphic with the 1-sphere S1. Any knot can be expressed as a connected sum of a finite number of prime knots in a unique way (13), we consider the trivial knot a non-prime knot. (For higher dimensional knots, factorization and uniqueness have been studied in (1).) However given a knot it is difficult to determine if it is prime or not. We prove that totally knotted knots, see definition in §2, are prime in theorem 1, give a class of examples in theorem 2 and investigate how the last result can be applied to the conjecture that the family Y of unknotting number one knots are prime. (See problem 2 in (5).) At the end, prime tangles as defined by W. B. R. Lickerish are used to prove that in a certain family of knots, related somewhat to Y, there is just one non-prime knot: the square knot. The paper should be interpreted as being in the piecewise linear category. Standard definitions of 3-manifolds and knot theory may be found in (6) and (11) respectively.

Isoflavones from Camphorosma lessingii Inhibit the Organic Anion Transporters OAT1 and OAT3

Planta Medica ◽  
2018 ◽  
Vol 85 (03) ◽  
pp. 225-230 ◽  
Author(s):  
Xinhui Wang ◽  
Dujuan Wang ◽  
Xue Wang ◽  
Manana Khutsishvili ◽  
Kamilla Tamanyan ◽  
...  
Keyword(s):  
Organic Anion ◽  
Inhibitory Effect ◽  
Spectroscopic Methods ◽  
Organic Anion Transporters ◽  
One Dimensional ◽  
Anion Transporters ◽  
Significant Inhibitory Effect ◽  
Phytochemical Investigation ◽  
The Family ◽  
First Time

AbstractPhytochemical investigation of Camphorosma lessingii has resulted in the isolation of four previously unreported isoflavones (1–4) and eight known compounds (5–12). Nine of these compounds (1–6, 8–10) are reported for the first time from members of the family Amaranthaceae. The structures of all isolated compounds were determined by spectroscopic methods, primarily one-dimensional and two-dimensional nuclear magnetic resonance and mass spectrometry. The absolute configuration of 6 was confirmed by circular dichroism. Inhibition of the organic anion transporters, OAT1 and OAT3, by the isolated compounds was evaluated. Among them, 7, 2′-dihydroxy- 6,8-dimethoxyisoflavone (1), 2′-hydroxy-6,7,8-trimethoxyisoflavone (2), 6,2′-dihydroxy-7,8-dimethoxyisoflavone (3), and 7-methoxyflavone (5) showed a significant inhibitory effect on 6-carboxyfluorescein uptake mediated by OAT1 and OAT3.

scholarly journals Theta Surfaces

2020 ◽  
Author(s):  
Daniele Agostini ◽  
Türkü Özlüm Çelik ◽  
Julia Struwe ◽  
Bernd Sturmfels
Keyword(s):  
Algebraic Geometry ◽  
Theta Functions ◽  
Minkowski Sum ◽  
Zero Set ◽  
Analytic Surface ◽  
Numerical Algebraic Geometry ◽  
Abelian Integrals ◽  
Space Curves ◽  
Quartic Curves ◽  
Special Plane

Abstract A theta surface in affine 3-space is the zero set of a Riemann theta function in genus 3. This includes surfaces arising from special plane quartics that are singular or reducible. Lie and Poincaré showed that any analytic surface that is the Minkowski sum of two space curves in two different ways is a theta surface. The four space curves that generate such a double translation structure are parametrized by abelian integrals, so they are usually not algebraic. This paper offers a new view on this classical topic through the lens of computation. We present practical tools for passing between quartic curves and their theta surfaces, and we develop the numerical algebraic geometry of degenerations of theta functions.

A one dimensional random space-filling problem

1968 ◽  
Vol 5 (02) ◽  
pp. 427-435 ◽  
Author(s):  
John P. Mullooly
Keyword(s):  
Asymptotic Behavior ◽  
Finite Number ◽  
Real Line ◽  
Random Variables ◽  
Random Interval ◽  
Space Filling ◽  
One Dimensional ◽  
The Real ◽  
Fixed Constant ◽  
Filling Problem

Consider an interval of the real line (0, x), x > 0; and place in it a random subinterval S(x) defined by the random variables Xx and Yx , the position of the center of S(x) and the length of S(x). The set (0, x)– S(x) consists of two intervals of length δ and η. Let a > 0 be a fixed constant. If δ ≦ a, then a random interval S(δ) defined by Xδ, Yδ is placed in the interval of length δ. If δ < a, the placement of the second interval is not made. The same is done for the interval of length η. Continue to place non-intersecting random subintervals in (0, x), and require that the lengths of all the random subintervals be ≦ a. The process terminates after a finite number of steps when all the segments of (0, x) uncovered by random subintervals are of length < a. At this stage, we say that (0, x) is saturated. Define N(a, x) as the number of random subintervals that have been placed when the process terminates. We are interested in the asymptotic behavior of the moments of N(a, x), for large x.

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