The Geometric Generation of the Joint Loci of Spatial Dyads With Axis Joints

1992 ◽  
Author(s):  
J. Keith Nisbett ◽  
T. J. Lawley
Keyword(s):  
General Procedure ◽  
Analytical Techniques ◽  
Geometric Approach ◽  
Geometric Constraints ◽  
Geometric Constraint ◽  
Physical Linkage ◽  
Four Bar Linkage ◽  
Linkage Synthesis

Abstract The geometric aspects of Burmester theory, as used in planar four-bar linkage synthesis, are examined to define a general procedure which is applied to the generation of the joint loci of spatial dyads with axis joints. The joints are geometrically related to the screw axes of the prescribed motion, by means of a screw triangle. The geometric relationships are typically separated into several geometric constraints. Each geometric constraint is considered separately to generate the loci of lines representing joint axes which satisfy the constraint. Combining the loci from each constraint produces a single loci of all the possible fixed or moving joints. The geometric approach is shown to have several benefits not obtained in numerical and pure analytical techniques, especially in relating the characteristics of the loci to the physical linkage and its required motion.

4MDS: A Geometric Constraint Based Motion Design Software for Synthesis and Simulation of Planar Four-Bar Linkages

2014 ◽  
Author(s):  
Anurag Purwar ◽  
Abhijit Toravi ◽  
Q. J. Ge
Keyword(s):  
Real Time ◽  
Geometric Constraints ◽  
Geometric Constraint ◽  
Design System ◽  
Dimensional Synthesis ◽  
Complete Control ◽  
Dimensional Changes ◽  
Design Software ◽  
Four Bar Linkage ◽  
Motion Design

This paper presents our recent work on designing and developing a geometric constraint based motion design software system for planar four-bar linkages. Given a motion task, the software computes possible four-bar linkage topologies as well as its dimensions. This capability to analyze the given task and find the best type of the linkage and the dimensions simultaneously sets it apart from any other linkage design software. The Four-Bar Motion Design System (4MDS) makes the synthesis and simulation capabilities available to mechanism designers in an intuitive graphical user interface (GUI) environment. Instead of taking a black box approach to mechanism design, wherein the user simply enters the motion requirements and the software outputs parameters of mechanisms, this software facilitates a dialog with the designer by providing various paths to simulation and synthesis in a design session. The designer has complete control over the specification of motion task, interactive tweaking of the motion, choice of linkage topology computed, dimensional changes, and their apparent effect on motion, all done in real time. This interactivity enhances designers kinematic experience. The underlying theoretical foundation of this paper is based on our earlier work on a task-driven approach to unified type and dimensional synthesis of planar four-bar linkage mechanisms. Instead of treating a planar four-bar mechanism as a set of connected rigid links and joints, we treat them as line or circle constraint generators. With that view, the synthesis problem is reduced to extracting geometric constraints hidden in a given motion task and the simulation is reduced to assembling constraints realizable by mechanical dyads. The algorithm employed is simple and efficient and permits real-time computation, and thus precludes using a limiting database-oriented approach. This tool should make innovation of mechanical motion generating devices accessible to novice and experienced designers alike.

Function Generation With Finitely Separated Precision Points Using Geometric Constraint Programming

2006 ◽  
Vol 129 (11) ◽  
pp. 1185-1190 ◽  
Author(s):  
Edward C. Kinzel ◽  
James P. Schmiedeler ◽  
Gordon R. Pennock
Keyword(s):  
Nonlinear Equations ◽  
Constraint Programming ◽  
Parametric Design ◽  
Geometric Constraints ◽  
Geometric Constraint ◽  
Function Generation ◽  
Large Numbers ◽  
Design Software ◽  
Complex Mechanisms ◽  
Four Bar Linkage

This paper extends geometric constraint programming (GCP) to function generation problems involving large numbers of finitely separated precision points and complex mechanisms. In parametric design software, GCP uses the sketching mode to graphically impose geometric constraints in kinematic diagrams and the numerical solvers to solve the relevant nonlinear equations without the user explicitly formulating them. For function generation, the same approach can be applied to any mechanism, requiring no unique algorithms. Implementation is straightforward, so the designer can quickly generate solutions for a large number of precision points and/or with complex mechanisms to accurately match the function. Examples of function generation with a four-bar linkage, a Stephenson III six-bar linkage, and a seven-bar linkage with a mobility of two are presented.

Function Generation With Finitely-Separated Precision Points Using Geometric Constraint Programming

2006 ◽  
Author(s):  
Edward C. Kinzel ◽  
James P. Schmiedeler ◽  
Gordon R. Pennock
Keyword(s):  
Constraint Programming ◽  
Computer Aided Design ◽  
Linear Equations ◽  
Geometric Constraints ◽  
Geometric Constraint ◽  
Function Generation ◽  
Design Software ◽  
Aided Design ◽  
Four Bar Linkage ◽  
Non Linear Equations

This paper explains how Geometric Constraint Programming can be applied to solve function generation problems with finitely-separated positions using a number of different mechanisms. Geometric Constraint Programming uses the sketching mode of commercial parametric computer-aided design software to create kinematic diagrams whose elements are parametrically related so that when a parameter is changed, the design is modified automatically. Geometric constraints are imposed graphically through the user interface, and the numerical solvers integrated into the software solve the relevant systems of non-linear equations without the user explicitly formulating those equations. A key advantage of using Geometric Constraint Programming for function generation is that the same approach can be applied to any mechanism, so no unique algorithms are required. Furthermore, because the implementation is relatively straightforward regardless of the chosen mechanism, the designer can quickly and easily generate solutions for a large number of precision points and/or with complex mechanisms to provide a very accurate match to the desired function. Examples of function generation with a four-bar linkage, a six-bar linkage, and a seven-bar linkage illustrate the benefits of the proposed methodology.

scholarly journals Four-Bar Linkage Synthesis Using Non-convex Optimization

2016 ◽  
pp. 618-635 ◽  
Author(s):  
Vincent Goulet ◽  
Wei Li ◽  
Hyunmin Cheong ◽  
Francesco Iorio ◽  
Claude-Guy Quimper
Keyword(s):  
Convex Optimization ◽  
Four Bar Linkage ◽  
Linkage Synthesis

Linkage Synthesis of a Four-Bar Mechanism for N Precision Points Using Simulated Annealing

1998 ◽  
Author(s):  
Horacio Martínez-Alfaro ◽  
Homero Valdez ◽  
Jaime Ortega
Keyword(s):  
Simulated Annealing ◽  
Computational Intelligence ◽  
Simulated Annealing Algorithm ◽  
Alternative Synthesis ◽  
Computational Intelligence Technique ◽  
Annealing Algorithm ◽  
Four Bar Linkage ◽  
Generation Problem ◽  
Intelligence Technique ◽  
Linkage Synthesis

Abstract This paper presents an alternative way of linkage synthesis by using a computational intelligence technique: Simulated Annealing. The technique allows to define n precision points of a desired path to be followed by a four-bar linkage (path generation problem). The synthesis problem is transformed into an optimization one in order to use the Simulated Annealing algorithm. With this approach, a path can be better specified since the user will be able to provide more “samples” than the usual limited number of five allowed by the classical methods. Several examples are shown to demonstrate the advantages of this alternative synthesis technique.

Solution Selectors: A User-Oriented Answer to the Geometric Constraint Multiple Solution Problem

2001 ◽  
Author(s):  
Bernhard Bettig ◽  
Jami Shah
Keyword(s):  
Linear Equations ◽  
Independent Solution ◽  
Solid Modeling ◽  
Multiple Solution ◽  
Parametric Modeling ◽  
Geometric Constraints ◽  
Geometric Constraint ◽  
Basic Solution ◽  
Solution Selection ◽  
Solution Problem

Abstract The development of solid modeling to represent the geometry of designed parts and the development of parametric modeling to control the size and shape have had significant impacts on the efficiency and speed of the design process. Designers now rely on parametric solid modeling, but surprisingly often are frustrated by a problem that unpredictably causes their sketches to become twisted and contorted. This problem, known as the “multiple solution problem” occurs because the dimensions and geometric constraints yield a set of non-linear equations with many roots. This situation occurs because the dimensioning and geometric constraint information given in a CAD model is not sufficient to unambiguously and flexibly specify which configuration the user desires. This paper first establishes that only explicit, independent solution selection declarations can provide a flexible mechanism that is sufficient for all situations of solution selection. The paper then describes the systematic derivation of a set of “solution selector” types by considering the occurrences of multiple solutions in combinations of mutually constrained geometric entities. The result is a set of eleven basic solution selector types and two derived types that incorporate topological information. In particular, one derived type “concave/convex” is user-oriented and thought to be very useful.

GPDOF — A FAST ALGORITHM TO DECOMPOSE UNDER-CONSTRAINED GEOMETRIC CONSTRAINT SYSTEMS: APPLICATION TO 3D MODELING

2006 ◽  
Vol 16 (05n06) ◽  
pp. 479-511 ◽  
Author(s):  
GILLES TROMBETTONI ◽  
MARTA WILCZKOWIAK
Keyword(s):  
Equation System ◽  
3D Models ◽  
General Purpose ◽  
Constrained Systems ◽  
Geometric Constraints ◽  
Geometric Constraint ◽  
Maximum Matching ◽  
Constraint System ◽  
Constraint Systems ◽  
Geometrical Constraints

Our approach exploits a general-purpose decomposition algorithm, called GPDOF, and a dictionary of very efficient solving procedures, called r-methods, based on theorems of geometry. GPDOF decomposes an equation system into a sequence of small subsystems solved by r-methods, and produces a set of input parameters.1. Recursive assembly methods (decomposition-recombination), maximum matching based algorithms, and other famous propagation schema are not well-suited or cannot be easily extended to tackle geometric constraint systems that are under-constrained. In this paper, we show experimentally that, provided that redundant constraints have been removed from the system, GPDOF can quickly decompose large under-constrained systems of geometrical constraints. We have validated our approach by reconstructing, from images, 3D models of buildings using interactively introduced geometrical constraints. Models satisfying the set of linear, bilinear and quadratic geometric constraints are optimized to fit the image information. Our models contain several hundreds of equations. The constraint system is decomposed in a few seconds, and can then be solved in hundredths of seconds.

Performance of EAs for four-bar linkage synthesis

2009 ◽  
Vol 44 (9) ◽  
pp. 1784-1794 ◽  
Author(s):  
S.K. Acharyya ◽  
M. Mandal
Keyword(s):  
Four Bar Linkage ◽  
Linkage Synthesis

Synthesis and Analysis of 4-DOF Parallel Manipulators of Computer Aided Geometry Approach

2014 ◽  
Vol 912-914 ◽  
pp. 1010-1016
Author(s):  
Yan Hua Zhang ◽  
Xiu Ju Du ◽  
Bai Yong Zhang
Keyword(s):  
Computer Simulation ◽  
Kinematic Analysis ◽  
Geometric Approach ◽  
Parallel Manipulators ◽  
Geometric Constraints ◽  
Type Synthesis ◽  
Moving Platforms ◽  
Kinematic Characteristics ◽  
Computer Aided

A novel computer aided geometry approach for type synthesis and analysis of new spatial 4-DOF parallel manipulators is put forward, and create the computer simulation mechanisms of parallel manipulators using the geometric constraints and dimension driving techniques in CAD software, Based on the computer simulation mechanisms of parallel manipulators, several new spatial 4-DOF parallel manipulators are synthesized, the kinematic characteristics of the moving platforms are analyzed by computer simulation. The results of computer simulation prove that the computer aided geometric approach for solving type synthesis and kinematic analysis is not only fairly quick and straightforward, but also has the advantages of accuracy.

A Task Driven Approach to Unified Synthesis of Planar Four-Bar Linkages Using Algebraic Fitting of a Pencil of G-Manifolds

2013 ◽  
Author(s):  
Q. J. Ge ◽  
Ping Zhao ◽  
Anurag Purwar
Keyword(s):  
Least Squares ◽  
Singular Values ◽  
Geometric Constraints ◽  
Motion Generation ◽  
Motion Approximation ◽  
Value Decomposition ◽  
Four Bar Linkage ◽  
The Given ◽  
Best Fit ◽  
Additional Constraints

This paper studies the problem of planar four-bar motion approximation from the viewpoint of extraction of geometric constraints from a given set of planar displacements. Using the Image Space of planar displacements, we obtain a class of quadrics, called Generalized- or G-manifolds, with eight linear and homogeneous coefficients as a unified representation for constraint manifolds of all four types of planar dyads, RR, PR, and PR, and PP. Given a set of image points that represent planar displacements, the problem of synthesizing a planar four-bar linkage is reduced to finding a pencil of G-manifolds that best fit the image points in the least squares sense. This least squares problem is solved using Singular Value Decomposition. The linear coefficients associated with the smallest singular values are used to define a pencil of quadrics. Additional constraints on the linear coefficients are then imposed to obtain a planar four-bar linkage that best guides the coupler through the given displacements. The result is an efficient and linear algorithm that naturally extracts the geometric constraints of a motion and leads directly to the type and dimensions of a mechanism for motion generation.

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