Linkage Synthesis Using Algebraic Curves

1986 ◽  
Vol 108 (4) ◽  
pp. 543-548 ◽  
Author(s):  
J. L. Blechschmidt ◽  
J. J. Uicker
Keyword(s):  
Nonlinear Equations ◽  
Algebraic Polynomial ◽  
Algebraic Curve ◽  
Algebraic Curves ◽  
Optimization Techniques ◽  
Synthesis Methods ◽  
Nonlinear Functions ◽  
Pass Through ◽  
Four Bar Linkage ◽  
Set Of Points

A method to snythesize four-bar linkages using the algebraic curve of the motion of the coupler point on the coupler link of the four-bar linkage is developed. This method is a departure from modern synthesis methods, most of which are based upon Burmester theory. This curve, which is a planar algebraic polynomial in two variables for the four-bar linkage, is a trinodal tricircular sextic (sixth order). These properties are used to determine the coefficients of the curve given a set of points that the coupler point of the coupler link is to pass through. The coefficients of this curve are nonlinear functions of the linkage parameters. The resulting set of nonlinear equations are solved using iterative/optimization techniques for the linkage parameters.

Four-Bar Linkage Synthesis Methods for Two Precision Positions Combined With N Quasi-Positions

1995 ◽  
Author(s):  
John A. Mirth
Keyword(s):  
Synthesis Method ◽  
Synthesis Methods ◽  
Bounded Motion ◽  
Transmission Angle ◽  
Pass Through ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Exact Positions ◽  
Linkage Synthesis

Abstract Mechanisms seldom need to pass through more than one or two exact positions. The method of quasi-position synthesis combines a number of approximate or “quasi” positions with two exact positions to design four-bar linkages that will produce a specified, bounded motion. Quasi-position synthesis allows for the optimization of some linkage characteristic (such as link lengths or transmission angles) by using the three variables that describe a single quasi-position. Procedures for circuit and transmission angle rectification are also easily incorporated into the quasi-position synthesis method.

Some enumerative formulae for algebraic curves

1958 ◽  
Vol 54 (4) ◽  
pp. 399-416 ◽  
Author(s):  
I. G. Macdonald
Keyword(s):  
Equivalence Relation ◽  
Algebraic Curve ◽  
Algebraic Curves ◽  
Linear Series ◽  
Set Of Points ◽  
Algebraic Correspondence

This paper is in two parts. In Part I we are concerned with one or more linear series on an algebraic curve; we consider a set of points on the curve which are contained with assigned multiplicities in a set of each of the linear series and, by persistent use of Severi's equivalence relation for the united points of an algebraic correspondence with valency, we derive formulae for the number of such sets of points when the constants involved are such as to make this number finite. All this is essentially a generalization of the formula for the number of points in the Jacobian set of a linear series of freedom 1, and the main result is Theorem 3.

A Note on the Waldron Construction for Transmission Angle Rectification

2005 ◽  
Vol 128 (2) ◽  
pp. 509-512 ◽  
Author(s):  
Thomas R. Chase
Keyword(s):  
High Probability ◽  
Synthesis Methods ◽  
Graphical Methods ◽  
Transmission Angle ◽  
Pass Through ◽  
Four Bar Linkage

Graphical methods for synthesizing planar four-bar linkage motion generators to pass through two or three precision positions are well known. However, the practicality of these methods is limited by a high probability that the resulting linkages will suffer from kinematic defects. These may include change of circuit, change of branch or poor transmission angle. This technical brief distills earlier work of Waldron and associates (Chaung, J. C, Strong, R. T., and Waldron, K. J., 1981, J. Mech. Des., 103(3), pp. 657–664, Sun, J. W. H., and Waldron, K. J., 1981, Mech. Mach. Theory, 16(4), pp. 385–397, and Waldron, K. J., 1976, ASME J. Eng. Ind., 98(1), pp. 176–182) to an approachable procedure for controlling the transmission angle of four-bar linkages during synthesis. The procedure simultaneously eliminates the branch defect. It eliminates the circuit defect for some Grashof types but not others. The procedure is integrated with the established graphical synthesis methods by the addition of a few easily implemented substeps. The procedure is simple enough to be performed manually by undergraduates. Nevertheless, it is powerful enough to substantially improve the likelihood that the synthesized linkages will perform well when constructed. The procedure is explained in reference to an application.

Planar Linkage Synthesis for Coupler Point Path Guidance Using Poles and Rotation Angles

2014 ◽  
Author(s):  
Ronald A. Zimmerman
Keyword(s):  
Analytical Solution ◽  
Nonlinear Equations ◽  
Design Problem ◽  
Graphical Solution ◽  
Design Time ◽  
Linkage Design ◽  
Pass Through ◽  
Solution Mechanism ◽  
Four Bar Linkage ◽  
Selection Of

Coupler point path guidance is a long standing linkage design problem. It is possible to design a four bar linkage with a coupler point that will pass through up to nine specified points. This paper discloses a new graphical solution to this problem. The approach is to consider the constraints imposed by the target points on the linkage through the poles and rotation angles. This approach enables the designer to explore the range of possible solutions when fewer than nine points are specified by dragging a fixed or moving pivot in the plane. The selection of free choices is made at the end of the process and the complete mechanism is visible when the choices are made. The constraints only need to be made once which eliminates the repetitive construction required by previous methods to consider multiple pivot locations. Since it is so easy to consider multiple pivot locations and the solution mechanism is always visible, the required design time is greatly reduced. A corresponding analytical solution is also developed and solved based on the same constraints. The analytical solution is defined by a system of 28 nonlinear equations with 28 unknowns.

GEOMETRIC THEORY OF MULTIDIMENSIONAL INTERPOLATION

2020 ◽  
Vol 2020 (1) ◽  
pp. 9-16
Author(s):  
Evgeniy Konopatskiy
Keyword(s):  
Response Function ◽  
Algebraic Curves ◽  
Geometric Theory ◽  
Analytical Description ◽  
Geometric Interpretation ◽  
Affine Geometry ◽  
Mathematical Apparatus ◽  
Multidimensional Interpolation ◽  
Pass Through

The paper presents a geometric theory of multidimensional interpolation based on invariants of affine geometry. The analytical description of geometric interpolants is performed within the framework of the mathematical apparatus BN-calculation using algebraic curves that pass through preset points. A geometric interpretation of the interaction of parameters, factors, and the response function is presented, which makes it possible to generalize the geometric theory of multidimensional interpolation in the direction of increasing the dimension of space. The conceptual principles of forming the tree of the geometric interpolant model as a geometric basis for modeling multi-factor processes and phenomena are described.

Towards a Dynamic Font Respecting the Arabic Calligraphy

2011 ◽  
pp. 359-388
Author(s):  
Abdelouahad Bayar ◽  
Khalid Sami
Keyword(s):  
Mathematical Model ◽  
Optimization Techniques ◽  
Plane Curves ◽  
Time Processing ◽  
Cpu Time ◽  
Dynamic Character ◽  
Context Dependent ◽  
Set Of Points ◽  
Arabic Calligraphy

To justify texts, Arabic calligraphers use to stretch some letters with small flowing curves; the kashida instead of inserting blanks among words. Of course, such stretchings are context dependent. An adequate tool to support such writing may be based on a continuous mathematical model. The model has to take into account the motion of the qalam. The characters may be represented as outlines. Among the curves composing the characters outlines, some intersections are to be determined dynamically. In the Naskh style, the qalam‘s head behaves as a rigid rectangle in motion with a constant inclination. To determine the curves delimiting the set of points to shade when writing, we have to find out a mathematical way to compare plane curves. Moreover, as the PostScript procedure to produce a dynamic character, should be repeated whenever the letter is to draw, the development of a font supporting a continuous stretching model, allowing stretchable letters with no overlapping outlines, without optimization would be of a high cost in CPU time. In this chapter, some stretching models are given and discussed. A method to compare curves is presented. It allows the determination of the character encoding with eventually overlapping outlines. Then a way to approximate the curves intersection coefficients is given. This is enough to remove overlapping outlines. Some evaluations in time processing to confirm the adopted optimization techniques are also exposed.

Synthesis of the four-bar linkage as path generation by choosing the shape of the connecting rod

2020 ◽  
Vol 234 (13) ◽  
pp. 2643-2652 ◽  
Author(s):  
SM Varedi-Koulaei ◽  
H Rezagholizadeh
Keyword(s):  
Analytical Solution ◽  
Nonlinear Equations ◽  
Linear Equations ◽  
Solution Process ◽  
Current Method ◽  
Path Generation ◽  
Connecting Rod ◽  
Complicated Process ◽  
Four Bar Linkage ◽  
Analytical Synthesis

This paper presents a method for path generation synthesis of a four-bar linkage that includes both graphical and analytical synthesis and both cases of with and without prescribed timing. The advantage of the proposed method over available techniques is that it is easier and does not need the complicated process (especially in graphical case). In an analytical solution, this method needs the solution of the linear equations, unlike the previous methods, in that they have required the solution of the nonlinear equations. Moreover, in the current method, one can choose the shape of the coupler, while, in other methods, the shape of the coupler is the result of the solution process. The proposed algorithm can be used for path generation synthesizing of a four-bar linkage for three precision points.

A Query Beehive Algorithm for Data Warehouse Buffer Management and Query Scheduling

2014 ◽  
Vol 10 (3) ◽  
pp. 34-58 ◽  
Author(s):  
Amira Kerkad ◽  
Ladjel Bellatreche ◽  
Pascal Richard ◽  
Carlos Ordonez ◽  
Dominique Geniet
Keyword(s):  
Query Optimization ◽  
Buffer Management ◽  
Optimization Techniques ◽  
Materialized Views ◽  
Star Schema ◽  
Joint Problem ◽  
Fixed Order ◽  
Pass Through ◽  
Np Hardness ◽  
Query Scheduling

Analytical queries, like those used in data warehouses and OLAP, are generally interdependent. This is due to the fact that the database is usually modeled with a denormalized star schema or its variants, where most queries pass through a large central fact table. Such interaction has been largely exploited in query optimization techniques such as materialized views. Nevertheless, such approaches usually ignore buffer management and assume queries have a fixed order and are known in advance. We believe such assumptions are too strong and thus they need to be revisited and simplified. In this paper, we study the combination of two problems: buffer management and query scheduling, in both static and dynamic scenarios. We present an NP-hardness study of the joint problem, highlighting its complexity. We then introduce a new and highly efficient algorithm inspired by a beehive. We conduct an extensive experimental evaluation on a real DBMS showing the superiority of our algorithm compared to previous ones as well as its excellent scalability.

scholarly journals DEFINABLE SETS OF BERKOVICH CURVES

2019 ◽  
pp. 1-65
Author(s):  
Pablo Cubides Kovacsics ◽  
Jérôme Poineau
Keyword(s):  
Large Class ◽  
Algebraic Curve ◽  
Analytic Geometry ◽  
Analytic Curve ◽  
Definable Sets ◽  
Set Of Points ◽  
Analytic Curves

In this article, we functorially associate definable sets to $k$ -analytic curves, and definable maps to analytic morphisms between them, for a large class of $k$ -analytic curves. Given a $k$ -analytic curve $X$ , our association allows us to have definable versions of several usual notions of Berkovich analytic geometry such as the branch emanating from a point and the residue curve at a point of type 2. We also characterize the definable subsets of the definable counterpart of $X$ and show that they satisfy a bijective relation with the radial subsets of $X$ . As an application, we recover (and slightly extend) results of Temkin concerning the radiality of the set of points with a given prescribed multiplicity with respect to a morphism of $k$ -analytic curves. In the case of the analytification of an algebraic curve, our construction can also be seen as an explicit version of Hrushovski and Loeser’s theorem on iso-definability of curves. However, our approach can also be applied to strictly $k$ -affinoid curves and arbitrary morphisms between them, which are currently not in the scope of their setting.

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