The Synthesis of Dyads With One Prismatic Joint

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Chao Chen ◽  
Shaoping Bai ◽  
Jorge Angeles
Keyword(s):  
Geometric Parameters ◽  
Special Treatment ◽  
Prismatic Joint ◽  
Invariant Formulation ◽  
Underlying Geometry ◽  
Joint Center ◽  
Four Bar Linkage ◽  
Special Case ◽  
Linkage Synthesis

The classic Burmester problem aims at finding the geometric parameters of a planar four-bar linkage for a prescribed set of finitely separated poses. The synthesis related to the Burmester problem deals with revolute-revolute (RR), prismatic-revolute (PR), and revolute-prismatic (RP) dyads. A PR dyad is a special case of the RR dyad, namely, a dyad of this kind with its fixed joint center at infinity; a similar interpretation applies to the RP dyad. The special nature of dyads with one P joint warrants a special treatment, outside of the general methods of four-bar linkage synthesis, which target mainly RR dyads. In proposing robust computational means to synthesize PR and RP dyads, we adopt an invariant formulation, which, additionally, sheds light on the underlying geometry.

Some Special Cases of the Burmester Problem for Four and Five Poses

2005 ◽  
Author(s):  
Jorge Angeles ◽  
Shaoping Bai
Keyword(s):  
Synthesis Method ◽  
Geometric Parameters ◽  
Special Treatment ◽  
End Point ◽  
Displacement Vectors ◽  
Special Cases ◽  
Common Intersection ◽  
Four Bar Linkage ◽  
Special Case

The Burmester problem aims at finding the geometric parameters of a planar four-bar linkage for a prescribed set of finitely separated poses. The synthesis related to the Burmester problem deals with both revolute-revolute (RR) and prismatic-revolute (PR) dyads. A PR dyad is a special case of RR dyad, i.e., a dyad with one end-point at infinity. The special nature of PR dyads warrants a special treatment, outside of the general methods of four-bar linkage synthesis, which target mainly RR dyads. In this paper, we study the synthesis of planar four-bar linkages addressing the problem of the determination of PR dyads. The conditions for the presence of PR dyads with the prescribed poses are derived. A synthesis method is developed by resorting to the parallelism condition of the displacement vectors of the circle points of PR dyads. We show that the “circle” point of a PR dyad can be determined as one common intersection of three or four circles, depending on whether four or, correspondingly, five poses are prescribed.

A Robust Solution of the Spherical Burmester Problem

2010 ◽  
Author(s):  
Jorge Angeles ◽  
Shaoping Bai
Keyword(s):  
Solution Method ◽  
Synthesis Method ◽  
Robust Solution ◽  
Equation Solving ◽  
Prismatic Joints ◽  
Four Bar Linkage ◽  
Special Case ◽  
Robust Synthesis ◽  
Linkage Synthesis

The problem of spherical four-bar linkage synthesis is revisited in this paper. The work is aimed at developing a robust synthesis method by taking into account both the formulation and the solution method. In addition, the synthesis of linkages with spherical prismatic joints is considered by treating them as a special case of the linkages under study. A two-step synthesis method is developed, which sequentially deals with equation-solving by a semigraphical approach and branching-detection. Examples are included to demonstrate the proposed method.

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.

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

Software for the Kinematic Synthesis of Coupler-Driven Spherical Four-Bar Mechanisms

2007 ◽  
Author(s):  
Eric M. Grimm ◽  
Andrew P. Murray ◽  
Michael L. Turner
Keyword(s):  
Rigid Body ◽  
Kinematic Synthesis ◽  
Prismatic Joint ◽  
Second Stage ◽  
Typical Scheme ◽  
Four Bar Linkage

A spatial analogue of the Stephenson III six-bar mechanism can be formed by the connection of an SPS chain to the coupler of a spherical four-bar linkage. With the prismatic joint actuated, the spherical four-bar is driven via a force applied directly to the coupler. This linkage is termed the coupler-driven spherical four-bar mechanism, and defines an alternative to the typical scheme of actuating the four-bar via a torque applied at the input link. This paper presents software developed to assist in the kinematic synthesis of these mechanisms. In the first stage of the design, a circuit-defect free spherical four-bar is dimensioned with the capacity to guide a rigid body through two orientations. The second stage of the design is to locate the SPS leg such that the four-bar is smoothly drivable between the orientations.

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.

Burmester-Theory for Band-Mechanisms

1992 ◽  
Author(s):  
Kurt Luck ◽  
Karl-Heinz Modler
Keyword(s):  
Analytical Methods ◽  
Path Generation ◽  
Complex Vector ◽  
Vector Algebra ◽  
Flexible Application ◽  
Four Bar Linkage ◽  
Special Case ◽  
Better Than

Abstract A band-mechanism includes inter alia a flexible band and a disk-profile. Such a mechanism can excellent be used for path-generation, better than a four-bar-linkage. Also several plane-positions additionally can be realized. This paper investigates the synthesis of four-bar-band-mechanisms by using the complex vector-algebra. Several technical tasks demonstrate the flexible application of such mechanisms. This tasks are formulated analogous to the wellknown BURMESTER-THEORY, but with higher claims and the solution is done by analytical methods. Further it is demonstrated that a four-bar-linkage is a special case of a four-bar-band-mechanism.

A Unified Algorithm for Analysis and Simulation of Planar Four-Bar Motions Defined With R- and P-Joints

2014 ◽  
Author(s):  
Xiangyun Li ◽  
Xin Ge ◽  
Anurag Purwar ◽  
Q. J. Ge
Keyword(s):  
Linkage Analysis ◽  
Least Squares ◽  
Efficient Algorithm ◽  
Image Space ◽  
Loop Closure ◽  
Closure Equation ◽  
Unified Algorithm ◽  
Four Bar Linkage ◽  
Best Fit ◽  
Linkage Synthesis

This paper presents a single, unified and efficient algorithm for animating the motions of the coupler of all four-bar mechanisms formed with revolute (R) and prismatic (P) joints. This is achieved without having to formulate and solve the loop closure equation associated with each type of four-bar linkages separately. In our previous paper on four-bar linkage synthesis, we map the planar displacements from Cartesian to image space using planar quaternion. 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 Generalized- or G-manifolds that best fit the image points in the least squares sense. The three planar dyads associated with Generalized G-manifolds are RR, PR and RP which could construct six types of four-bar mechanisms. In this paper, we show that the same unified formulation for linkage synthesis leads to a unified algorithm for linkage analysis and simulation as well. Both the unified synthesis and analysis algorithms have been implemented on Apple’s iOS platform.

Intergroup Bias in Parliamentary Rule Enforcement

2016 ◽  
Vol 69 (4) ◽  
pp. 692-702
Author(s):  
Frederik Hjorth
Keyword(s):  
Intergroup Relations ◽  
Time Limit ◽  
Intergroup Bias ◽  
Special Treatment ◽  
Natural Setting ◽  
Political Actors ◽  
Extant Literature ◽  
Special Case

Political actors are often assigned roles requiring them to enforce rules without giving in-groups special treatment. But are such institutional roles likely to be successful? Here, I exploit a special case of exogenously assigned intergroup relations: debates in the Danish Parliament, in which Parliament chairmen drawn from parliamentary parties enforce speaking time. Analyzing 5,756 speeches scraped from online transcripts, I provide evidence that speech lengths are biased in favor of the presiding chairman’s party. On average, speakers of the same party as the presiding chairman give 5 percent longer speeches and are 5 percent more likely to exceed the speaking time limit. The paper contributes to the extant literature by demonstrating political intergroup bias in a natural setting, suggesting that group loyalties can supersede institutional obligations even in a “least likely” context of clear rules, complete observability, and a tradition of parliamentary cooperation.

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