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.

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.

Kinematic Synthesis for Infinitesimally and Multiply Separated Positions Using Geometric Constraint Programming

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
James P. Schmiedeler ◽  
Barrett C. Clark ◽  
Edward C. Kinzel ◽  
Gordon R. Pennock
Keyword(s):  
Undergraduate Students ◽  
Constraint Programming ◽  
Computer Aided Design ◽  
Geometric Constraints ◽  
Geometric Constraint ◽  
Motion Generation ◽  
Planar Mechanisms ◽  
Kinematic Synthesis ◽  
Design Software ◽  
Aided Design

Geometric constraint programming (GCP) is an approach to synthesizing planar mechanisms in the sketching mode of commercial parametric computer-aided design software by imposing geometric constraints using the software's existing graphical user interface. GCP complements the accuracy of analytical methods with the intuition developed from graphical methods. Its applicability to motion generation, function generation, and path generation for finitely separated positions has been previously reported. By implementing existing, well-known theory, this technical brief demonstrates how GCP can be applied to kinematic synthesis for motion generation involving infinitesimally and multiply separated positions. For these cases, the graphically imposed geometric constraints alone will in general not provide a solution, so the designer must parametrically relate dimensions of entities within the graphical construction to achieve designs that automatically update when a defining parameter is altered. For three infinitesimally separated positions, the designer constructs an acceleration polygon to locate the inflection circle defined by the desired motion state. With the inflection circle in place, the designer can rapidly explore the design space using the graphical second Bobillier construction. For multiply separated position problems in which only two infinitesimally separated positions are considered, the designer constrains the instant center of the mechanism to be in the desired location. For example, four-bar linkages are designed using these techniques with three infinitesimally separated positions and two different combinations of four multiply separated positions. The ease of implementing the techniques may make synthesis for infinitesimally and multiply separated positions more accessible to mechanism designers and undergraduate students.

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.

Kinematic Synthesis for Infinitesimally and Multiply Separated Positions Using Geometric Constraint Programming

2011 ◽  
Author(s):  
James P. Schmiedeler ◽  
Barrett C. Clark ◽  
Edward C. Kinzel ◽  
Gordon R. Pennock
Keyword(s):  
Constraint Programming ◽  
Computer Aided Design ◽  
Geometric Constraints ◽  
Geometric Constraint ◽  
Motion Generation ◽  
Planar Mechanisms ◽  
Kinematic Synthesis ◽  
Function Generation ◽  
Design Software ◽  
Aided Design

Geometric Constraint Programming (GCP) is an approach to synthesizing planar mechanisms in the sketching mode of commercial parametric computer-aided design software by imposing geometric constraints using the software’s existing graphical user interface. GCP complements the accuracy of analytical methods with the intuition developed from graphical methods. Its applicability to motion generation, function generation, and path generation for finitely separated positions has been previously reported. This paper demonstrates how GCP can be applied to kinematic synthesis for motion generation involving infinitesimally and multiply separated positions. For these cases, the graphically imposed geometric constraints alone will in general not provide a solution, so the designer must parametrically relate dimensions of entities within the graphical construction to achieve designs that automatically update when a defining parameter is altered. For three infinitesimally separated positions, the designer constructs an acceleration polygon to locate the inflection circle defined by the desired motion state. With the inflection circle in place, the designer can rapidly explore the design space using the graphical second Bobillier construction. For multiply separated position problems in which only two infinitesimally separated positions are considered, the designer constrains the instant center of the mechanism to be in the desired location. Example four-bar linkages are designed using these techniques with three infinitesimally separated positions and two different combinations of four multiply separated positions.

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.

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.

Pier 55, NYC: A Case Study for the Future of Design, Documentation and Fabrication

2019 ◽  
Author(s):  
Yong-Wook Jo ◽  
David Farnsworth ◽  
Jacob Wiest
Keyword(s):  
New York ◽  
Design Process ◽  
Precast Concrete ◽  
Hudson River ◽  
Digital Fabrication ◽  
Parametric Modeling ◽  
Construction Technology ◽  
Surface Geometry ◽  
Structural Geometry ◽  
Design Documentation

<p>The Pier 55 project in New York City represents an achievement in design, documentation, fabrication and construction achievable only through recent advances in construction technology. Pier 55 is a new park built over the Hudson River constructed from complex precast concrete. It is a one of its kind pier with a signature design by the Heatherwick Studio that undulates in elevation and is structurally composed of tulip shaped concrete “pots”. Heatherwick's vision required significant collaborative efforts by all involved to define a geometry that satisfied the often-competing needs for prefabrication efficiency, durability, accessibility, design aesthetics and construction feasibility. Arup and Heatherwick developed parametric tools to automate much of the design process so that multiple iterations of geometry could be tested and refined to find optimal solutions. Initial scripts to define surface geometry of the “pot” structures for coordination evolved into additional scripts which created analysis models, full structural geometry, and shop drawing level documentation. As the project moved into construction, Arup and the fabrication team at Fort Miller precast concrete manufacturer and Fab3 steel fabricator utilized the models and scripts generated during the design process for direct digital input of the structural geometry to create complex CNC-milled foam formwork, 3- dimensional rebar documentation, and documentation and digital fabrication of steel components required for assembly and erection of the various pieces by Weeks Marine. This paper will discuss significant innovations including using sophisticated parametric modeling to digitally design, document, fabricate and construct geometrically complex structures.</p>

Identification of Modal Parameters of an Elastic Rotor With Oil Film Bearings

1984 ◽  
Vol 106 (1) ◽  
pp. 107-112 ◽  
Author(s):  
Rainer Nordmann
Keyword(s):  
Modal Analysis ◽  
Dynamic Behavior ◽  
Design Process ◽  
Mechanical Engineering ◽  
Mechanical Systems ◽  
Rotating Machinery ◽  
Modal Parameters ◽  
Powerful Method ◽  
Oil Film ◽  
Engineering Problems

Investigations of the dynamic behavior of structures have become increasingly important in the design process of mechanical systems. To have a better understanding of the dynamic behavior of a structure, the knowledge of the modal parameters is very important. The powerful method of experimental modal analysis has been used to measure modal parameters in many mechanical engineering problems. But the method was mainly applied to nonrotating structures. This presentation shows improvements of the classical modal analysis for a successful application in rotating machinery with nonconservative effects. An example is given, investigating the modal parameters of an elastic rotor with oil film bearings.

scholarly journals Building Capabilities Through Democratic Dialogues

Design Issues ◽  
2018 ◽  
Vol 34 (4) ◽  
pp. 80-95 ◽  
Author(s):  
Liesbeth Huybrechts ◽  
Katrien Dreessen ◽  
Ben Hagenaars
Keyword(s):  
Design Process ◽  
Participatory Design ◽  
Design Approach ◽  
Railway Track ◽  
Alternative Futures ◽  
Design Processes ◽  
Self Organized ◽  
Complex Design ◽  
Developing Strategies

Designers are increasingly involved in designing alternative futures for their cities, together with or self-organized by citizens. This article discusses the fact that (groups of) citizens often lack the support or negotiation power to engage in or sustain parts of these complex design processes. Therefore the “capabilities” of these citizens to collectively visualize, reflect, and act in these processes need to be strengthened. We discuss our design process of “democratic dialogues” in Traces of Coal—a project that researches and designs together with the citizens an alternative spatial future for a partially obsolete railway track in the Belgian city of Genk. This process is framed in a Participatory Design approach and, more specifically, in what is called “infrastructuring,” or the process of developing strategies for the long-term involvement of participants in the design of spaces, objects, or systems. Based on this process, we developed a typology of how the three clusters of capabilities (i.e., visualize, reflect, and act) are supported through democratic dialogues in PD processes, linking them to the roles of the designer, activities, and used tools.

scholarly journals Is the Linear Modeling Technique Good Enough for Optimal Form Design? A Comparison of Quantitative Analysis Models

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Yang-Cheng Lin ◽  
Chung-Hsing Yeh ◽  
Chen-Cheng Wang ◽  
Chun-Chun Wei
Keyword(s):  
Product Design ◽  
Design Process ◽  
Design Approach ◽  
Modeling Technique ◽  
Type I ◽  
Linear Modeling ◽  
Optimal Form ◽  
Product Image ◽  
Form Design ◽  
Product Forms

How to design highly reputable and hot-selling products is an essential issue in product design. Whether consumers choose a product depends largely on their perception of the product image. A consumer-oriented design approach presented in this paper helps product designers incorporate consumers’ perceptions of product forms in the design process. The consumer-oriented design approach uses quantification theory type I, grey prediction (the linear modeling technique), and neural networks (the nonlinear modeling technique) to determine the optimal form combination of product design for matching a given product image. An experimental study based on the concept of Kansei Engineering is conducted to collect numerical data for examining the relationship between consumers’ perception of product image and product form elements of personal digital assistants (PDAs). The result of performance comparison shows that the QTTI model is good enough to help product designers determine the optimal form combination of product design. Although the PDA form design is used as a case study, the approach is applicable to other consumer products with various design elements and product images. The approach provides an effective mechanism for facilitating the consumer-oriented product design process.

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