The Application of Geometric Constraint Programming to the Design of Motion Generating Six-Bar Linkages

2012 ◽  
Author(s):  
John A. Mirth
Keyword(s):  
Rigid Body ◽  
Constraint Programming ◽  
Synthesis Method ◽  
Solid Modeling ◽  
Single Step ◽  
Geometric Constraint ◽  
Motion Generation ◽  
Stepwise Manner ◽  
Planar Linkages

This paper looks at the application of Geometric Constraint Programming (GCP) to the synthesis of six-bar planar linkages. GCP is a synthesis method that relies on the built-in geometric capabilities of commercial solid-modeling programs to produce linkage designs while operating in the “sketch” mode for these programs. GCP provides the user with the opportunity to create mechanisms in their entirety at multiple design positions. The complexity of analyzing potential defects (such as circuit or branch defects) within a six-bar mechanism poses significant challenges to the user who might try to design such a mechanism in a single step. The methods presented in this paper apply GCP in a stepwise manner to create six-bar linkages that are less likely to suffer from defects than if they were created in a single step. Stepwise approaches are presented for six-bar mechanisms designed to solve a problem involving rigid-body guidance (motion generation). The linkages considered include the Stephenson I, II, and III chains, as well as the Watt I six-bar. The Watt II six-bar is not included since this mechanism’s application to rigid-body guidance can be handled by GCP methods previously developed for four-bar linkages.

Rectified Synthesis of Six-Bar Mechanisms With Well Defined Transmission Angles for Four-Position Motion Generation

1994 ◽  
Author(s):  
S. Bawab ◽  
G. L. Kinzel ◽  
Kenneth J. Waldron
Keyword(s):  
Rigid Body ◽  
Synthesis Method ◽  
Algebraic Method ◽  
Motion Generation ◽  
Pass Through

Abstract This paper describes a rectified synthesis method where a rigid body of a six-bar linkage with well-defined transmission angles is guided to pass through four precision positions. The procedure includes the elimination of circuit, branch, and order defects. This is achieved by decomposing the six-bar mechanism into groups of vector pairs called dyads and groups of three vectors called triads which are rectified using the algebraic method of synthesis. The procedure has been implemented for a Watt I crank-driven six-bar linkage in the interactive synthesis package RECSYN.

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.

Rectified Synthesis of Six-Bar Mechanisms With Well-Defined Transmission Angles for Four-Position Motion Generation

1996 ◽  
Vol 118 (3) ◽  
pp. 377-383 ◽  
Author(s):  
S. Bawab ◽  
G. L. Kinzel ◽  
K. J. Waldron
Keyword(s):  
Rigid Body ◽  
Synthesis Method ◽  
Algebraic Method ◽  
Motion Generation ◽  
The Past ◽  
Pass Through

This paper describes a rectified synthesis method where a rigid body of a six-bar linkage with well-defined transmission angles is guided to pass through four precision positions. The procedure includes the elimination of circuit, branch, and order defects. This is achieved by decomposing the six-bar mechanism into groups of vector pairs called dyads and groups of three vectors called triads. The algebraic method of synthesis can be applied to rectify those chains. Although these defects can be eliminated, it has been a challenging task in the past. The procedure has been implemented for a Watt I crank-driven six-bar linkage in the interactive synthesis package RECSYN.

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.

scholarly journals Geometric synthesis method of compliant mechanism based on similarity transformation of pole maps

2021 ◽  
Vol 12 (1) ◽  
pp. 375-391
Author(s):  
Song Lin ◽  
Yu Zhang ◽  
Hanchao Wang ◽  
Jingyu Jiang ◽  
Niels Modler
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Similarity Transformation ◽  
Compliant Mechanism ◽  
Research Work ◽  
Synthesis Method ◽  
Common Mechanism ◽  
Beam Model ◽  
Motion Generation ◽  
Euler Beam

Abstract. This paper presents a geometric synthesis method for compliant mechanisms based on similarity transformation of pole maps. Motion generation is a typical and common mechanism synthesis task, so this study takes it as the design requirement to expound the proposed method. Most of the current research work relies on numerical solution of the nonlinear Bernoulli–Euler beam model, numerical simulations or physical experiments to study the synthesis method of compliant mechanisms. There is a lack of simpler and more efficient methods to achieve motion generation of compliant mechanisms with various topologies. This study is based on pole map which is a geometric tool to describe the motion of rigid-body mechanisms. In this paper, we first demonstrate the feasibility of applying the similarity transformation of pole map to compliant mechanisms. It is proved that the pole map of compliant mechanisms has the same characteristic as rigid-body mechanisms during similarity transformation. Then we present the procedure of synthesis method in detail and expound the establishment method of function module which can avoid the functional defects of the final designed mechanism. At last, we take the compliant geared linkages and compliant four-bar linkage as examples to illustrate the novel synthesis approach. The result is an applicable and effective synthesis method for motion generation of compliant mechanisms.

Kinematic Synthesis for Finitely Separated Positions Using Geometric Constraint Programming

2005 ◽  
Vol 128 (5) ◽  
pp. 1070-1079 ◽  
Author(s):  
Edward C. Kinzel ◽  
James P. Schmiedeler ◽  
Gordon R. Pennock
Keyword(s):  
Constraint Programming ◽  
Computer Aided Design ◽  
Geometric Constraints ◽  
Geometric Constraint ◽  
Motion Generation ◽  
Robust Algorithms ◽  
Kinematic Synthesis ◽  
Synthesis Techniques ◽  
And Function ◽  
Accuracy And Repeatability

This paper presents an original approach to the kinematic synthesis of planar mechanisms for finitely separated positions. The technique, referred to here as geometric constraint programming, uses the sketching mode of commercial parametric computer-aided design software to create kinematic diagrams. The elements of these diagrams are parametrically related so that when a parameter is changed, the design is modified automatically. Geometric constraints are imposed graphically through a well-designed user interface, and numerical solvers integrated into the software solve the relevant systems of equations without the user explicitly formulating those equations. This allows robust algorithms for the kinematic synthesis of a wide variety of mechanisms to be “programmed” in a straightforward, intuitive manner. The results provided by geometric constraint programming exhibit the accuracy and repeatability achieved with analytical synthesis techniques, while simultaneously providing the geometric insight developed with graphical synthesis techniques. The key advantages of geometric constraint programming are that it is applicable to a broad range of kinematic synthesis problems, user friendly, and highly accessible. To demonstrate the utility of the technique, this paper applies geometric constraint programming to three examples of the kinematic synthesis of planar four-bar linkages: Motion generation for five finitely separated positions, path generation for nine finitely separated precision points, and function generation for four finitely separated positions.

Dynamic Analysis of Cage Stress in Tapered Roller Bearings Using Component-Mode-Synthesis Method

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Tomoya Sakaguchi ◽  
Kazuyoshi Harada
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Boundary Point ◽  
Axial Load ◽  
Synthesis Method ◽  
Load Condition ◽  
Component Mode Synthesis ◽  
Analysis Model ◽  
Tapered Roller ◽  
Tapered Roller Bearings

In order to investigate cage stress in tapered roller bearings, a dynamic analysis tool considering both the six degrees of freedom of motion of the rollers and cage and the elastic deformation of the cage was developed. Cage elastic deformation is equipped using a component-mode-synthesis (CMS) method. Contact forces on the elastically deforming surfaces of the cage pocket are calculated at all node points of finite-elements on it. The location and pattern of the boundary points required for the component-mode-synthesis method were examined by comparing cage stresses in a static condition of pocket forces and constraints calculated by using the finite-element and the CMS methods. These results indicated that one boundary point lying at the center on each bar is appropriate for the effective dynamic analysis model focusing on the cage stress, especially at the pocket corners of the cages, which are actually broken. A behavior measurement of a polyamide cage in a tapered roller bearing was conducted for validating the analysis model. It was confirmed in both the experiment and analysis that the cage whirled under a large axial load condition and the cage center oscillated in a small amplitude under a small axial load condition. In the analysis, the authors discussed the four models including elastic bodies having a normal eigenmode of 0, 8 or 22, and rigid-body. There were small differences among the cage center loci of the four models. These two cages having normal eigenmodes of 0 and rigid-body whirled with imperceptible fluctuations. At least approximately 8 normal eigenmodes of cages should be introduced to conduct a more accurate dynamic analysis although the effect of the number of normal eigenmodes on the stresses at the pocket corners was insignificant. From the above, it was concluded to be appropriate to introduce one boundary point lying at the center on each pocket bar of cages and approximately 8 normal eigenmodes to effectively introduce the cage elastic deformations into a dynamic analysis model.

Synthesis of Planar, Compliant Four-Bar Mechanisms for Compliant-Segment Motion Generation

1999 ◽  
Vol 123 (4) ◽  
pp. 535-541 ◽  
Author(s):  
L. Saggere ◽  
S. Kota
Keyword(s):  
Compliant Mechanisms ◽  
Shape Change ◽  
Synthesis Method ◽  
Elastic Equilibrium ◽  
Body Motion ◽  
Motion Generation ◽  
Generation Task ◽  
Potential Applications ◽  
Flexible Segment ◽  
Definition Of

Compliant four-bar mechanisms treated in previous works consisted of at least one rigid moving link, and such mechanisms synthesized for motion generation tasks have always comprised a rigid coupler link, bearing with the conventional definition of motion generation for rigid-link mechanisms. This paper introduces a new task called compliant-segment motion generation where the coupler is a flexible segment and requires a prescribed shape change along with a rigid-body motion. The paper presents a systematic procedure for synthesis of single-loop compliant mechanisms with no moving rigid-links for compliant-segment motion generation task. Such compliant mechanisms have potential applications in adaptive structures. The synthesis method presented involves an atypical inverse elastica problem that is not reported in the literature. This inverse problem is solved by extending the loop-closure equation used in the synthesis of rigid-links to the flexible segments, and then combining it with elastic equilibrium equation in an optimization scheme. The method is illustrated by a numerical example.

scholarly journals Synthesis of Nanotips Through Femtosecond Laser Ablation of Glass with Assisted Gas

2021 ◽  
Author(s):  
Nikunj Patel
Keyword(s):  
Femtosecond Laser ◽  
Building Materials ◽  
High Vacuum ◽  
Synthesis Method ◽  
Femtosecond Laser Ablation ◽  
Target Surface ◽  
Laser Pulses ◽  
Single Step ◽  
Femtosecond Laser Irradiation ◽  
Ambient Conditions

Nanotips are the key nanostructures for many applications. Until now, the nanotips of only the crystalline materials have been produced via various deposition methods which require sophisticated equipment, high vacuum, and clean room operations. This thesis proposes a single step, rapid synthesis method using femtosecond laser irradiation at megahertz frequency with background flow of nitrogen gas at ambient conditions. Amorphous nanotips are obtained without the use of catalyst. The nanotips grow from highly energetic plasma generated when target is irradiated with laser pulses. The vapor condensates, nanoparticles and droplets from the plasma get deposited back on to the hot target surface where they experience force imbalance due to which the stems for the nanotips growth are initiated. Once the stems are generated, the continuous deposition of vapor condensates [sic] provides building materials to the stems to complete the growth of nanotips. Further study found that the growth of the nanotips is influenced by laser parameters and gas conditions.

Computer-Aided Modelling of Cloth Deformation

1996 ◽  
Author(s):  
Y. F. Zhao ◽  
S. T. Tan ◽  
T. N. Wong ◽  
W. J. Chen
Keyword(s):  
Finite Element Method ◽  
Exact Solution ◽  
Finite Element ◽  
Rigid Body ◽  
Present Method ◽  
Geometric Constraint ◽  
Computationally Efficient ◽  
Large Rotation ◽  
Developable Surfaces ◽  
Computer Aided

Abstract A constrained finite element method for modelling cloth deformation is developed. The bending deformation and the geometric constraint of developable surfaces of the cloth objects are considered. The representation of large rotation and the motion of rigid body are described using the current coordinates with the geometric constraint. The effectiveness of the present method is verified by comparing the thread deformation with the exact solution of catenary. Several examples are given to show that the proposed method converges quickly and is thus computationally efficient.

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