A Method for Adjustable Planar and Spherical Four-Bar Linkage Synthesis

2004 ◽  
Vol 127 (3) ◽  
pp. 456-463 ◽  
Author(s):  
Boyang Hong ◽  
Arthur G. Erdman
Keyword(s):  
Synthesis Method ◽  
New Method ◽  
Spherical Form ◽  
Numerical Example ◽  
Input And Output ◽  
Special Cases ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Linkage Synthesis

This paper describes a new method to synthesize adjustable four-bar linkages, both in planar and spherical form. This method uses fixed ground pivots and an adjustable length for input and output links. A new application of Burmester curves for adjustable linkages is introduced, and a numerical example is discussed. This paper also compares a conventional synthesis method (nonadjustable linkage) to the new method. Nonadjustable four-bar linkages provide limited solutions for five-position synthesis. Adjustable linkages generate one infinity of solution choices. This paper also shows that the nonadjustable solutions are special cases of adjustable solutions. This new method can be extended to six position synthesis, with adjustable ground pivots locations.

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.

Planar Linkage Synthesis for Rigid Body Guidance Using Poles and Rotation Angles

2013 ◽  
Author(s):  
Ronald A. Zimmerman
Keyword(s):  
Rigid Body ◽  
Synthesis Method ◽  
Synthesis Methods ◽  
Center Point ◽  
Circle Center ◽  
Previous Solution ◽  
Design Software ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Linkage Synthesis

A graphical four bar linkage synthesis method for planar rigid body guidance is presented. This method, capable of synthesis for up to five specified coupler positions, uses the poles and rotation angles, which are constraints, to define guiding links. Faster and simpler than traditional graphical synthesis methods, this method, allows the designer to see and consider most or all the possible solutions within a few seconds before making any free choices. All of the guiding links satisfying five specified coupler positions can be obtained graphically within 30 minutes without plotting any Burmester curves and without any mechanism design software. For four positions, both the circle and center point curves are simultaneously traced by corresponding circle-center point pairs using three poles having a common subscript and the corresponding rotation angles without any additional construction. This method eliminates the iterative construction required in previous methods which were based on free choices rather than constraints. The tedious plotting of Burmester curves graphically using pole quadrilaterals is also eliminated. The simplicity of the method makes four and five position synthesis practical to do graphically. A corresponding analytical solution is presented which provides a simpler formulation than the previous solution method. This new method requires two fewer equations and provides a new way to plot Burmester curves analytically.

Kinematic Mapping Based Evaluation of Assembly Modes for Planar Four-Bar Synthesis

2005 ◽  
Author(s):  
Hans-Peter Schro¨cker ◽  
Manfred L. Husty ◽  
J. Michael McCarthy
Keyword(s):  
Image Space ◽  
Synthesis Problem ◽  
New Method ◽  
Kinematic Mapping ◽  
Position Synthesis ◽  
Four Bar Linkage

This paper presents a new method to determine if two task positions used to design a four-bar linkage lie on separate circuits of a coupler curve, known as a “branch defect.” The approach uses the image space of a kinematic mapping to provide a geometric environment for both the synthesis and analysis of four-bar linkages. In contrast to current methods of solution rectification, this approach guides the modification of the specified task positions, which means it can be used for the complete five position synthesis problem.

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.

New Angular Transmission Design Based on a Four-Bar Linkage Mechanism

2015 ◽  
Author(s):  
Jong-Won Kim ◽  
Jeongae Bak ◽  
TaeWon Seo ◽  
Jongwon Kim
Keyword(s):  
Simulation Analysis ◽  
New Method ◽  
Linkage Mechanism ◽  
Mechanical Loads ◽  
New Device ◽  
Space Efficiency ◽  
Input And Output ◽  
Linkage Design ◽  
Transmission Design ◽  
Four Bar Linkage

This paper presents a new angular transmission device based on a four-bar linkage mechanism. This mechanism consists of a four-bar linkage and an output gear similar to the Geneva drive. When the input link of the four-bar linkage is rotated once, the trajectory of the coupler point is generated. Then, the coupler point drives the motion of the output gear. To rotate the output gear by a specific angle, the design of the four-bar linkage is very important. The mechanism was generated using a new method for four-bar linkage design. Unlike some conventional methods, the new method can consider both the trajectory and the velocity of a coupler point. The new device has two advantages compared to the Geneva drive. Firstly, because the positions of the input and output axes are close to each other, the space efficiency of the new device is higher than that of the Geneva drive. Secondly, the duty factor of the new device is larger than that of the Geneva drive, and the mechanical loads applied to the output gear, such as that from acceleration, are much lower. Kinematic and dynamic simulation analysis was conducted to verify the advantages of the new device.

Solution region synthesis methodology of planar eight-bar linkage for four specified positions of a 4R chain

2020 ◽  
Vol 234 (24) ◽  
pp. 4813-4826
Author(s):  
Guangzhen Cui ◽  
Jianyou Han ◽  
Yanqiu Xiao ◽  
Caidong Wang
Keyword(s):  
Feasible Solution ◽  
Solution Curve ◽  
Defect Identification ◽  
Different Types ◽  
Practical Engineering ◽  
Solution Region ◽  
Synthesis Methodology ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Linkage Synthesis

The solution region methodology for solving the problem of four-bar linkage synthesis with four specified positions was extended to solve the problem of eight-bar linkage synthesis. The processes to build solution regions for synthesizing different types of eight-bar linkages are described, and the methods of building solution regions are divided into five types. First, the synthesis equation is derived, and the curve expressed by the synthesis equation is called the solution curve. Second, the process to build the spatial solution regions from the solution curves is detailed, and a new defect identification method is developed for building the spatial feasible solution region, which is a set of linkage solutions meeting four positions and excluding defects. Finally, linkage solutions that do not meet practical engineering requirements are eliminated from the spatial feasible solution region to obtain the useful spatial solution region. The examples demonstrate the feasibility of the proposed method. The proposed synthesis methodology is simple and easy to program, and provides reference for four specified position synthesis of other multi-bar linkages.

scholarly journals Design of regular positive and stable descriptor systems via state-feedbacks for descriptor continuous-time linear systems with singular pencils

2014 ◽  
Vol 24 (3) ◽  
pp. 289-297
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Special Form ◽  
The State ◽  
New Method ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Asymptotically Stable ◽  
Numerical Example ◽  
Time Linear

Abstract A new method is proposed of design of regular positive and asymptotically stable descriptor systems by the use of state-feedbacks for descriptor continuous-time linear systems with singular pencils. The method is based on the reduction of the descriptor system by elementary row and column operations to special form. A procedure for the design of the state-feedbacks gain matrix is presented and illustrated by a numerical example

scholarly journals L’innovation et le modèle du commerce néo-technologique dans l’espace des caractéristiques de Lancaster

2009 ◽  
Vol 55 (3) ◽  
pp. 342-359
Author(s):  
Petr Hanel
Keyword(s):  
Necessary Conditions ◽  
New Product ◽  
Efficient Production ◽  
Numerical Example ◽  
Special Cases ◽  
Welfare Implications ◽  
Efficient Consumption

Lancaster's case of innovation in consumption technology is formalized and extended to include beside of the criterion of efficient consumption also the criterion of efficient production. The two criteria has to be met before an invention can be commercialized economically. Trade provoked by an innovation in consumption technology—a new product—is analyzed on a simple numerical example. Necessary conditions and some welfare implications of the neo-technology trade are presented. The approach is sufficiently general to encompass trade based on cost reducing innovation as well as existing trade models as special cases.

A Simple Synthesis Method for Spherical 4R Linkages Reaching Four Positions

2011 ◽  
Vol 199-200 ◽  
pp. 1236-1239 ◽  
Author(s):  
Tong Yang ◽  
Jian You Han ◽  
Lai Rong Yin
Keyword(s):  
Matrix Method ◽  
Synthesis Method ◽  
Simple Synthesis ◽  
Simple Derivation ◽  
Derivation Method ◽  
Curve Equation ◽  
Linkage Synthesis

For spherical 4R linkage synthesis reaching four specified task positions, we introduce a simple derivation method of spherical Burmester curve equation by employing a displacement matrix method. Then we presented a method to calculate the coordinates of circle and center points, so the spherical Burmester curves can be drawn by the software developed.

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