The Application of Geometric Constraint Programming to the Design of Stephenson III Dwell Linkages

2016 ◽  
Author(s):  
John A. Mirth
Keyword(s):  
Constraint Programming ◽  
Angular Displacement ◽  
Geometric Constraint ◽  
Link Length ◽  
Modeling Software ◽  
Dwell Position ◽  
Angular Displacements ◽  
Four Bar Linkage ◽  
Additional Constraints ◽  
Complete Specification

Stephenson III linkages provide a means to create an approximate dwell mechanism without the use of cams. The dwell cycle is created by first choosing or designing a four-bar linkage that contains a coupler path with a near circular segment. An external dyad is attached to the coupler point such that the center of the floating link of the dyad coincides with the center of the circular portion of the coupler curve. This connection produces a dwell in the external dyad as the four-bar linkage traverses the circular portion of the coupler curve. This paper demonstrates how the necessary conditions for a dwell linkage can be obtained with the use of Geometric Constraint Programming (GCP). The construction process is initiated by using GCP techniques to develop a four-bar linkage with a minimum of four path points that lie on a prescribed arc. This part of the problem also uses GCP to apply additional constraints to the four-bar linkage. These include the application of appropriate link dimensions to achieve a Grashof linkage with a crank input, and the specification of the required crank rotation angle during the dwell cycle of the mechanism. Once the four-bar is defined, an external dyad is attached to the coupler link of the four-bar to produce the specified dwell characteristics. The dwell dyad may include for its output either a rotational link whose range of angular travel is defined, or a sliding link whose range of linear motion is defined. GCP techniques are used to enforce a specified range of motion for the output dyad through the use of an instant center construction to define the limits of travel of the four-bar coupler curve relative to the dwell ground pivot. If the dwell dyad is designed for angular displacements, the construction is completed by using GCP to define the desired angular displacement of the dwell link, resulting in the specification of the link length and ground pivot location. If the dwell dyad is a linear (slider) output, the final part of the GCP construction is used to define the desired length of linear travel, which results in the complete specification of the slider path and angle. The GCP techniques are presented with the development of an example, with sample results presented for a dwell mechanism with a rotational dwell cycle, and also for a dwell mechanism with a linear (slider) dwell output. The example demonstrates the ability of GCP methods to use standard solid-modeling software to obtain Stephenson III linkages with dwells that deviate from the dwell position by less than 0.1% of total motion.

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.

A GCP Design Approach for Infinitesimally and Multiply Separated Positions Based on the Use of Velocity and Acceleration Vector Diagrams

2014 ◽  
Author(s):  
John A. Mirth
Keyword(s):  
Design Process ◽  
Constraint Programming ◽  
Parametric Modeling ◽  
Geometric Constraint ◽  
Design Approach ◽  
Powerful Method ◽  
Planar Mechanisms ◽  
Acceleration Vector ◽  
Acceleration Analysis ◽  
Four Bar Linkage

Geometric Constraint Programming (GCP) provides a powerful method for the synthesis of planar mechanisms using parametric modeling programs that are common to industry. The graphical nature of GCP allows for the ready incorporation of many existing graphical constructions into the design process. This paper examines the use of vector diagrams for velocity and acceleration analysis of a four-bar linkage and how such diagrams can be incorporated into the design process using the methods of GCP. The method is implemented by using GCP to create a mechanism at one or more design positions. Velocity and acceleration vector diagrams are added to positions of interest to allow for the inclusion of velocity and acceleration information in the design process. The result is an approach to GCP synthesis that allows a designer to create mechanisms to match requirements for infinitesimally and multiply separated positions using techniques that are commonly taught in an introductory undergraduate mechanisms course. Two examples are presented to demonstrate the utility of the methods described.

Design of Drag-Link Mechanisms With Optimum Transmission Angle

1983 ◽  
Vol 105 (2) ◽  
pp. 254-258 ◽  
Author(s):  
Lung-Wen Tsai
Keyword(s):  
Extreme Values ◽  
Angular Displacement ◽  
Output Link ◽  
Link Length ◽  
Design Charts ◽  
Link Mechanism ◽  
Transmission Angle ◽  
New Criterion ◽  
Four Bar Linkage ◽  
Drag Link

In this paper, a new criterion for the design of a drag-link mechanism with optimum transmission angle is established. The transmission angle, the angle between the coupler link and output link of a four-bar linkage, is considered to be optimized when its extreme values deviate equally from 90 deg. Based on this criterion, design equations and design charts are developed. It is shown that the optimum drag-link mechanism is a turning-block linkage. It is also shown that to displace the drag-link mechanism with optimum transmission angle from its minimum lag to its maximum lag position, the input link must always rotate 180 deg and the corresponding angular displacement of the output link depends only on the link-length ratio of the output link to the fixed-link.

Mixed Exact and Approximate Position Design of Planar Linkages via Geometric Constraint Programming (GCP) Techniques

2015 ◽  
Author(s):  
John A. Mirth
Keyword(s):  
Undergraduate Students ◽  
Constraint Programming ◽  
Parametric Modeling ◽  
Geometric Constraints ◽  
Geometric Constraint ◽  
Target Zones ◽  
Industry Standard ◽  
Modeling Software ◽  
Moving Points ◽  
Circular Target

The synthesis of mechanisms to reach multiple positions can often be satisfied by the specification of a combination of exact and approximate positions. Geometric Constraint Programming (GCP) uses industry standard parametric modeling software to obtain solutions to planar synthesis problems. This paper demonstrates the capability of GCP to solve problems that contain a combination of exact and approximate positions. The approximate positions are added to existing GCP design approaches by the application of geometric constraints to locate moving points on a mechanism within specified circular target zones. The target zones are used to guide the coupler point of a linkage along an approximate path between critical precision positions. The approach applies to the synthesis of both four-bar and complex linkages. In complex linkages, the target zones can be applied to multiple points on the linkage to better coordinate the motion of one or more floating links with the overall mechanism motion. The methods presented in the paper focus on the use of 2 exact positions plus 2–3 approximate positions. Examples are provided for the solution of rigid-body guidance problems for both four-bar and six-bar linkages. As with many GCP solutions, the graphical solutions presented are well within the capabilities and understanding of both undergraduate students and the practicing engineer.

Control of processing at multi-tool two-support setup

2020 ◽  
pp. 67-73
Author(s):  
N.D. YUsubov ◽  
G.M. Abbasova
Keyword(s):  
Degrees Of Freedom ◽  
Factor Model ◽  
Angular Displacement ◽  
Factor Models ◽  
Technological System ◽  
Displacement Control ◽  
Model Accuracy ◽  
Six Degrees Of Freedom ◽  
Angular Displacements ◽  
And Control

The accuracy of two-tool machining on automatic lathes is analyzed. Full-factor models of distortions and scattering fields of the performed dimensions, taking into account the flexibility of the technological system on six degrees of freedom, i. e. angular displacements in the technological system, were used in the research. Possibilities of design and control of two-tool adjustment are considered. Keywords turning processing, cutting mode, two-tool setup, full-factor model, accuracy, angular displacement, control, calculation [email protected]

scholarly journals Learning Optimal Decision Trees using Constraint Programming (Extended Abstract)

2020 ◽  
Author(s):  
Hélène Verhaeghe ◽  
Siegfried Nijssen ◽  
Gilles Pesant ◽  
Claude-Guy Quimper ◽  
Pierre Schaus
Keyword(s):  
Decision Trees ◽  
Constraint Programming ◽  
Greedy Algorithms ◽  
Building Blocks ◽  
Optimal Decision ◽  
Programming Approach ◽  
Learning Problem ◽  
New Approach ◽  
Good Classification ◽  
Additional Constraints

Decision trees are among the most popular classification models in machine learning. Traditionally, they are learned using greedy algorithms. However, such algorithms have their disadvantages: it is difficult to limit the size of the decision trees while maintaining a good classification accuracy, and it is hard to impose additional constraints on the models that are learned. For these reasons, there has been a recent interest in exact and flexible algorithms for learning decision trees. In this paper, we introduce a new approach to learn decision trees using constraint programming. Compared to earlier approaches, we show that our approach obtains better performance, while still being sufficiently flexible to allow for the inclusion of constraints. Our approach builds on three key building blocks: (1) the use of AND/OR search, (2) the use of caching, (3) the use of the CoverSize global constraint proposed recently for the problem of itemset mining. This allows our constraint programming approach to deal in a much more efficient way with the decompositions in the learning problem.

scholarly journals BIOMECHANICAL EFFECTS OF HYPERPRONATION ON MULTIDIRECTIONAL ANKLE ANGULAR DISPLACEMENT AND STIFFNESS

2020 ◽  
Vol 20 (09) ◽  
pp. 2040012
Author(s):  
GEON KIM ◽  
JIHEE JUNG ◽  
YOUNGJOO CHA ◽  
JOSHUA (SUNG) H. YOU
Keyword(s):  
Sagittal Plane ◽  
Angular Displacement ◽  
Three Dimensional ◽  
Frontal Plane ◽  
Neutral Group ◽  
Stiffness Reduction ◽  
Ankle Stiffness ◽  
Foot Injury ◽  
Increased Risk ◽  
Angular Displacements

Hyperpronation of the foot is believed to contribute to ankle hypermobility and associated stiffness reduction, but the underlying biomechanical mechanisms remain unknown. This study aimsed to investigate multidirectional ankle displacement and associated stiffness when a posterior–anterior impact force was applied to the posterior knee compartment. Forty healthy adults with and without foot hyperpronation were recruited. A three-dimensional motion capture system and force plates were used to acquire angular displacement and ankle joint moment data. The independent [Formula: see text]-test and Mann–Whitney [Formula: see text] test were used to compare the group differences in ankle angular displacement, moment, and stiffness. Spearman’s rho test was performed to determine the relationship between ankle angular displacement and stiffness. The hyperpronation group demonstrated significantly greater sagittal ([Formula: see text]) and frontal plane ([Formula: see text]) angular displacements and reduced sagittal plane ankle stiffness ([Formula: see text]) than the neutral group. The Spearman’s correlation analysis showed a close inverse relationship between the ankle angular displacement and stiffness, ranging from [Formula: see text] to [Formula: see text]. The biomechanical data in our study suggest that individuals with foot hyperpronation present with multidirectional hypermobility and a reduction in ankle stiffness. These factors contribute to an increased risk of ankle-foot injury in individuals with foot hyperpronation.

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.

Flow in a Toroidal Thermosyphon with Angular Displacement of Heated and Cooled Sections

1979 ◽  
Vol 101 (4) ◽  
pp. 672-676 ◽  
Author(s):  
P. S. Damerell ◽  
R. J. Schoenhals
Keyword(s):  
Steady State ◽  
Reverse Flow ◽  
Angular Displacement ◽  
Vertical Plane ◽  
Steady Condition ◽  
Steady State Flow ◽  
Flow Rates ◽  
Flow Phenomenon ◽  
Angular Displacements ◽  
Good Agreement

A toroidal thermosyphon consisting of a fluid-filled torus located in a vertical plane was studied analytically and experimentally. Good agreement was obtained between analytical predictions and measurements for large values of the angular displacement of the heated and cooled sections. For smaller angular displacements, the analytical predictions of steady state flow rates were found to exceed the corresponding experimentally observed values. The discrepancies were attributed to a reverse flow phenomenon. Some analytically predicted flows were not physically achievable. In these situations the flow would either reach a steady condition in the opposite direction, or it would oscillate indefinitely.

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