Software for Investigating the Kinematics, Statics and Dynamics of Coupler-Driven Four-Bars for Two Position Synthesis

2007 ◽  
Author(s):  
Michael L. Turner ◽  
Eric M. Grimm ◽  
Daniel Debrosse ◽  
Kevin Kosmac ◽  
Andrew P. Murray
Keyword(s):  
Solution Space ◽  
Branch Points ◽  
Joint Force ◽  
Statics And Dynamics ◽  
Position Synthesis ◽  
Four Bar Linkage

The synthesis of a planar four-bar in which a point on the coupler reaches two specified points and orientations generates a six-fold space of solutions. The solution space increases if additional links are added to drive the mechanism, such as the Stephenson III. This paper presents an investigation of a coupler driven four-bar linkage, a Stephenson III six-bar with an RPR chain driving the four-bar sub-chain instead of the classically defined 3R chain. The software allows the designer to specify the problem and quickly scan the solution space. A comparison is constructed between a four-bar driven through a torque at the input link and a coupler-driven four-bar. Changes in branch points, the joint force index and the dynamics are observed.

A Generalized Performance Sensitivity Synthesis Methodology for Four-Bar Mechanisms

1992 ◽  
Author(s):  
Ming-Yih Lee ◽  
Arthur G. Erdman ◽  
Salaheddine Faik
Keyword(s):  
Solution Space ◽  
Design Solution ◽  
Link Length ◽  
Performance Sensitivity ◽  
Closed Chain ◽  
Synthesis Methodology ◽  
Position Synthesis ◽  
The Relationship ◽  
Accuracy Performance ◽  
Sensitivity Maps

Abstract A generalized accuracy performance synthesis methodology for planar closed chain mechanisms is proposed. The relationship between the sensitivity to variations of link lengths and the location of the moving pivots of four-link mechanisms is investigated for the particular objective of three and four position synthesis. In the three design positions case, sensitivity maps with isosensitivity curves plotted in the design solution space allow the designer to synthesize a planar mechanism with desired sensitivity value or to optimize sensitivity from a set of acceptable design solutions. In the case of four design positions, segments of the Burmester design curves that exhibit specified sensitivity to link length tolerance are identified. A performance sensitivity criterion is used as a convenient and a useful way of discriminating between many possible solutions to a given synthesis problem.

Synthesis of Compliant Mechanisms With Specified Equilibrium Positions

2005 ◽  
Author(s):  
Hai-Jun Su ◽  
J. Michael McCarthy
Keyword(s):  
Compliant Mechanisms ◽  
Equilibrium Constraints ◽  
Equilibrium Equations ◽  
Equilibrium Configurations ◽  
Form Design ◽  
Design Requirements ◽  
Synthesis Procedure ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Sine And Cosine Functions

This paper presents a synthesis procedure for a compliant four-bar linkage with three specified equilibrium configurations. The finite position synthesis equations are combined with equilibrium constraints at the flexure pivots to form design equations. These equations are simplified by modeling the joint angle variables in the equilibrium equations using sine and cosine functions. Solutions to these design equations were computed using a polynomial homotopy solver. In order to provide a design specification, we first compute the six equilibrium configurations of a known compliant four-bar mechanism. We use these results as design requirements to synthesize a compliant four-bar. The solver obtained eight real solutions which we refined using a Newton-Raphson technique. A numerical example is provided to verify the design methodology.

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.

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.

scholarly journals A Unified Approach to Exact and Approximate Motion Synthesis of Spherical Four-Bar Linkages Via Kinematic Mapping

2017 ◽  
Vol 10 (1) ◽  
Author(s):  
Xiangyun Li ◽  
Ping Zhao ◽  
Anurag Purwar ◽  
Q. J. Ge
Keyword(s):  
Null Space ◽  
Solution Space ◽  
Quadratic Equation ◽  
Image Space ◽  
Geometric Constraints ◽  
Design Parameters ◽  
Space Representation ◽  
Motion Synthesis ◽  
Four Bar Linkage ◽  
Spherical Motion

This paper studies the problem of spherical four-bar motion synthesis from the viewpoint of acquiring circular geometric constraints from a set of prescribed spherical poses. The proposed approach extends our planar four-bar linkage synthesis work to spherical case. Using the image space representation of spherical poses, a quadratic equation with ten linear homogeneous coefficients, which corresponds to a constraint manifold in the image space, can be obtained to represent a spherical RR dyad. Therefore, our approach to synthesizing a spherical four-bar linkage decomposes into two steps. First, find a pencil of general manifolds that best fit the task image points in the least-squares sense, which can be solved using singular value decomposition (SVD), and the singular vectors associated with the smallest singular values are used to form the null-space solution of the pencil of general manifolds; second, additional constraint equations on the resulting solution space are imposed to identify the general manifolds that are qualified to become the constraint manifolds, which can represent the spherical circular constraints and thus their corresponding spherical dyads. After the inverse computation that converts the coefficients of the constraint manifolds to the design parameters of spherical RR dyad, spherical four-bar linkages that best navigate through the set of task poses can be constructed by the obtained dyads. The result is a fast and efficient algorithm that extracts the geometric constraints associated with a spherical motion task, and leads naturally to a unified treatment for both exact and approximate spherical motion synthesis.

Determination of the Shortest Crank in Four Position Synthesis: A Numerical Apporach

1992 ◽  
Author(s):  
Shin-Min Song ◽  
Fu-Hung Lu ◽  
Ning-Xin Chen ◽  
Kenneth J. Waldron
Keyword(s):  
Numerical Stability ◽  
Search Algorithm ◽  
Solution Space ◽  
Numerical Approach ◽  
Parameter Perturbation ◽  
Spurious Solutions ◽  
Automatic Search ◽  
Position Synthesis ◽  
Parameter Perturbation Method

Abstract The shortest crank of a four position synthesis can be determined by solving a statically determinate five-bar structure and a set of seven nonlinear equations have been proposed for this purpose. In this paper a numerical method which can directly solve the shortest crank is presented. It is found that a direct implementation of the original seven equations has two problems: many spurious solutions and poor numerical stability. And the spurious solutions are of the following two types: solutions with incorrect signs of angles and solutions with incorrect geometry. In order to solve the problems, a set of ten equations is developed and parameter perturbation method is applied. Furthermore, a set of eight equations is developed for better numerical stability. Both the ten and eight equations can eliminate the spurious solutions with incorrect geometry. Yet the spurious solutions with incorrect signs of angles can only be rectified after convergence. An automatic search algorithm is included to automatically search the shortest crank in the solution space. Many examples are given to illustrate this numerical approach.

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.

Mixed Exact-Approximate Position Synthesis of Planar Mechanisms

1998 ◽  
Vol 122 (3) ◽  
pp. 278-286 ◽  
Author(s):  
Jennifer E. Holte ◽  
Thomas R. Chase ◽  
Arthur G. Erdman
Keyword(s):  
Three Dimensional ◽  
Solution Space ◽  
Motion Generation ◽  
Planar Mechanisms ◽  
Dimensional Solution ◽  
New Approach ◽  
Fuzzy Constraints ◽  
Position Synthesis ◽  
Synthesis Approach ◽  
Exact Positions

A new approach to the synthesis of planar linkage mechanisms with fuzzy constraints is proposed. Design methods for two exact positions and an unlimited number of approximate positions are presented. The use of approximate specifications allows the designer to represent design objectives more realistically. A precision position synthesis approach is used to generate a three-dimensional solution space of dyads satisfying all exact and approximate constraints. The three-dimensional solution space is reduced to a two-dimensional ground-pivot map. Computer implementation of the proposed methodologies would allow designers with little or no knowledge of the synthesis techniques to interactively explore maps of solutions for four-bar motion generation. [S1050-0472(00)00803-5]

Methods for Improving the Knuckle Boom Capacity in Truck-Mounted Cranes

1976 ◽  
Vol 98 (4) ◽  
pp. 1183-1187
Author(s):  
B. N. Sridhar
Keyword(s):  
Test Data ◽  
Close Agreement ◽  
Moment Arm ◽  
Linkage Design ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Constant Moment

Presented herein are two different concepts for improving the knuckle boom capacity of truck-mounted cranes. The first concept deals with an improved Planar four-bar linkage using the two-position synthesis, as well as with recommendations for optimizing the linkage. The linkage design employing the two-position synthesis was built as hardware with fairly close agreement between calculated and test data. The second concept is concerned with a constant moment-arm mechanism using a rack and pinion arrangement.

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