Kinematic Synthesis of a Geared Five-Bar Function Generator

1971 ◽  
Vol 93 (1) ◽  
pp. 11-16 ◽  
Author(s):  
Arthur G. Erdman ◽  
George N. Sandor
Keyword(s):  
Computer Program ◽  
Closed Form ◽  
Complex Numbers ◽  
Function Generator ◽  
Kinematic Synthesis ◽  
Numerical Examples ◽  
Function Generation ◽  
Structural Error ◽  
Dependent Variables ◽  
Angular Displacements

A general closed form method of planar kinematic synthesis, using complex numbers to represent link vectors, is applied to the synthesis of a geared five-bar linkage for function generation. Equations are derived and a computer program is developed to yield several solutions. Angular displacements of the input, a cycloidal crank, and the output, a simple follower, are used as linear analogs of the independent and the dependent variables, respectively. A method is demonstrated for six precision conditions (three first, three second-order precision conditions). Numerical examples are included, and the structural error of these geared five-bars are compared to that of optimized four-bar linkages generating the same functions.

Finite Kinematic Synthesis of a Cycloidal-Crank Mechanism for Function Generation

1970 ◽  
Vol 92 (3) ◽  
pp. 531-535 ◽  
Author(s):  
S. N. Kramer ◽  
G. N. Sandor
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Optimization Method ◽  
Gear Ratio ◽  
Form Solution ◽  
Complex Numbers ◽  
Kinematic Synthesis ◽  
Function Generation ◽  
Approximate Function ◽  
Crank Mechanism

The method of complex numbers is applied towards the kinematic synthesis of a planar geared five-bar cycloidal-crank mechanism for approximate function generation with finitely separated precision points. It is shown that up to 10 precision points can be obtained, and a closed-form solution is presented which yields up to 6 different mechanisms with a 6-point approximation. In this method, the designer has control over the design of the cycloidal crank regarding gear ratio and configuration. The method has been programmed for automatic digital computation on the IBM-360 system, and the program is made available to interested readers. An optimization method utilizing iterative application of the closed-form solution is outlined.

Kinematic Synthesis of Adjustable Mechanisms—Part 2: Path Generation

1973 ◽  
Vol 95 (2) ◽  
pp. 423-429 ◽  
Author(s):  
Joseph F. McGovern ◽  
George N. Sandor
Keyword(s):  
Closed Form ◽  
Higher Order ◽  
Complex Numbers ◽  
Path Generation ◽  
Function Generator ◽  
Kinematic Synthesis ◽  
Closed Form Solutions ◽  
Straight Line ◽  
Adjustable Mechanisms

A method utilizing complex numbers similar to that used in Part 1 for adjustable function generator synthesis is applied to the synthesis of adjustable path generators. Finitely separated path points with prescribed timing as well as higher order approximations (infinitesimally separated path points) are treated, by way of analytical and closed form solutions. Adjustment of the path generator mechanism is accomplished by moving a fixed pivot. Mechanisms adjustable for different approximate straight line motions, for various path curvatures, and path tangents as well as several arbitrary paths can be synthesized. Four-bar and geared five-bar mechanisms are considered. Examples are included describing synthesized mechanisms.

Application of Taguchi Method on the Tolerance Design of a Four-Bar Function Generation Mechanism

2005 ◽  
Author(s):  
Fu-Chen Chen ◽  
Hsing-Hui Huang
Keyword(s):  
Taguchi Method ◽  
Control Factor ◽  
Tolerance Design ◽  
Initial Value ◽  
Function Generator ◽  
Function Generation ◽  
Manufacturing Tolerance ◽  
Structural Error ◽  
Experimental Errors ◽  
The Mean

The purpose of this paper is to use the Taguchi method on the tolerance design of a four-bar function generator in order to obtain the structural error that is insensitive to variations in manufacturing tolerance and joint clearance. The contribution of each control factor to the variations was also examined to further determine if the tolerance of the factor should be tightened to improve the precision of the mechanism. From the study of the four-bar function generator, it was revealed that the control factor B had the most significant effect on the variation of the structural errors. These were closely followed by factors E, C and D. On the whole, experimental errors contributed only 2.69% to the structural errors, much smaller than the contribution by individual factors, indicating that the design of the experiments was appropriate and the results were highly reliable. By tightening the tolerance, it is apparent that the mean of structural errors is reduced by 0.227 and the change in variance is 69.81% of the initial value, i.e. a reduction of 30.19%.

Synthesis of a Geared N-Bar Linkage

1971 ◽  
Vol 93 (1) ◽  
pp. 157-164 ◽  
Author(s):  
A. D. Dimarogonas ◽  
G. N. Sandor ◽  
A. G. Erdman
Keyword(s):  
Dynamic Response ◽  
Computer Program ◽  
Structural Characteristics ◽  
Degree Of Freedom ◽  
Complex Numbers ◽  
Function Generator ◽  
Matrix Methods ◽  
Loop Function ◽  
Function Generators ◽  
Two Degree Of Freedom

For certain tasks, four-bar linkages may not provide needed accuracy and/or structural characteristics. To overcome this, one or more bars may be added to the coupler with geared pairs to maintain a “one-degree-of-freedom” system. Utilizing complex numbers and matrix methods, a general geared n-bar function generator is developed in this paper. The computer program devised synthesizes four-bar linkages to approximate the desired function and increases the number of links by one if specifications for accuracy and other requirements are not met. Synthesized linkages are analyzed and then optimized by way of minimizing a multidimensional objective function. As a practical illustration of the n-bar theory, geared five-bar, one-loop function generators are designed to simulate the dynamic response of a two-degree-of-freedom vibrating system.

Structural Error Analysis in Plane Kinematic Synthesis

1959 ◽  
Vol 81 (1) ◽  
pp. 15-21 ◽  
Author(s):  
Ferdinand Freudenstein
Keyword(s):  
Error Analysis ◽  
Digital Computer ◽  
Large Scale ◽  
Generation Mechanism ◽  
Kinematic Synthesis ◽  
Function Generation ◽  
Structural Error ◽  
Approximate Synthesis ◽  
Servo Loop

Methods are developed for estimating and obtaining minimum structural error in the approximate synthesis of plane, function, or path-generating mechanisms. The application to a four-bar function generation mechanism is worked out with the aid of a large-scale digital computer used in the manner of a servo loop.

Synthesis of Quasi-Constant Transmission Ratio Planar Linkages

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
Giorgio Figliolini ◽  
Ettore Pennestrì
Keyword(s):  
Range Of Motion ◽  
Closed Form ◽  
Optimality Criterion ◽  
Transmission Ratio ◽  
Kinematic Synthesis ◽  
Numerical Examples ◽  
First Case ◽  
Finite Displacements ◽  
Planar Linkages

The present paper deals with the formulation of novel closed-form algorithms for the kinematic synthesis of quasi-constant transmission ratio planar four-bar and slider–crank linkages. The algorithms are specific for both infinitesimal and finite displacements. In the first case, the approach is based on the use of kinematic loci, such as centrodes, inflection circle, and cubic of stationary curvature, as well as Euler–Savary equation. In the second case, the design equations follow from the application of Chebyshev min–max optimality criterion. These algorithms are aimed to obtain, within a given range of motion, a quasi-constant transmission ratio between the driving and driven links. The numerical examples discussed allow a direct comparison of structural errors for mechanisms designed with different methodologies, such as infinitesimal Burmester theory and the Chebyshev optimality criterion.

A Function Generation Synthesis Methodology for All Defect-Free Slider-Crank Solutions for Four Precision Points

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Ali Almandeel ◽  
Andrew P. Murray ◽  
David H. Myszka ◽  
Herbert E. Stumph
Keyword(s):  
Synthesis Problem ◽  
Kinematic Synthesis ◽  
Function Generation ◽  
Zero Velocity ◽  
Structural Error ◽  
Mechanical Press ◽  
Synthesis Methodology ◽  
Slide Velocity

The well-established methodology for slider-crank function generation states that five precision points can be achieved without structural error. The resulting designs, however, do not necessarily satisfy all of the kinematic requirements for designing a slider-crank linkage used in common machine applications such as driving the ram of a mechanical press. First, linkage solutions to the five precision point synthesis problem may need to change circuits to reach the precision points. Second, there is no guarantee that the input crank is fully rotatable. This paper presents a modification to the function generation synthesis methodology that reveals a continuum of defect-free, slider-crank solutions for four precision points. Additionally, the methodology allows the specification of velocity or acceleration at the precision points. Although smaller accelerations at a point of zero slide velocity are associated with longer dwell, a point having zero velocity and acceleration is shown not to be possible. Examples are included to illustrate this kinematic synthesis methodology.

Kinematic Synthesis of Adjustable Mechanisms—Part 1: Function Generation

1973 ◽  
Vol 95 (2) ◽  
pp. 417-422 ◽  
Author(s):  
Joseph F. McGovern ◽  
George N. Sandor
Keyword(s):  
Complex Number ◽  
Relative Orientation ◽  
Complex Numbers ◽  
Input Output ◽  
Kinematic Synthesis ◽  
Digital Computation ◽  
Closed Form Solutions ◽  
Function Generation ◽  
Planar Linkages ◽  
Adjustable Mechanisms

One of the major advantages of linkages over cams is the ease with which they can be adjusted to modify their output. Incorporating an adjustment into the design of a linkage makes it possible to make a selection from two, three, or more different outputs by simply making the adjustment. Adjustable mechanisms make it possible to use the same hardware for different input-output relationships. The adjustment considered in this paper is the changing of a fixed pivot location. This paper presents a method of synthesizing adjustable planar linkages for function generation with finitely separated precision points and higher order synthesis involving prescribed velocities, accelerations, and higher accelerations. The method of synthesis is analytical with closed form solutions and utilizes complex numbers. The method is programmed for automatic digital computation. The linkages considered are a four-bar, a geared five-bar, and a geared six-bar mechanism. Examples include adjustable mechanisms which have been successfully synthesized with the method developed here. Future extensions of the complex number method to include adjustment by changing the length of a link and by changing of the relative orientation of the gears in geared linkages are outlined.

Structural Error Synthesis of a Four-Bar Function Generator Using the Reliability Concept

1984 ◽  
Vol 198 (2) ◽  
pp. 87-90 ◽  
Author(s):  
A K Khare ◽  
A C Rao
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Optimization Techniques ◽  
Function Generator ◽  
New Approach ◽  
Numerical Example ◽  
Structural Error ◽  
Synthesis Of Mechanisms

Structural error synthesis of mechanisms is usually carried out either by the precision point approach or by using optimization techniques. A new approach for such problems using the reliability concept is presented in this paper. Besides being simple, this approach leads to a closed form solution and the mechanism can be designed to perform with any desired reliability. Its application is illustrated by means of a numerical example and the results are compared with those available.

scholarly journals Robustness to algorithmic singularities and sensitivity in computational kinematics

2011 ◽  
Vol 225 (4) ◽  
pp. 987-999
Author(s):  
L Gracia ◽  
J Angeles
Keyword(s):  
Original System ◽  
System Of Equations ◽  
Multivariate Polynomial ◽  
Function Generator ◽  
Numerical Examples ◽  
Function Generation ◽  
Polynomial Reduction ◽  
Exact Function ◽  
Univariate Polynomial ◽  
Computational Kinematics

A robust approach to computational kinematics intended to cope with algorithmic singularities is introduced in this article. The approach is based on the reduction of the original system of equations to a subsystem of bivariate equations, as opposed to the multivariate polynomial reduction leading to the characteristic univariate polynomial. The effectiveness of the approach is illustrated for the exact function-generation synthesis of planar, spherical, and spatial four-bar linkages. Some numerical examples are provided for the case of the spherical four-bar function generator with six precision points to show the benefits of the proposed method with respect to methods reported in the literature.

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