Direct Analytic Synthesis of Four-Bar Function Generators With Optimal Structural Error

1973 ◽  
Vol 95 (2) ◽  
pp. 563-571 ◽  
Author(s):  
Richard S. Rose ◽  
George N. Sandor
Keyword(s):  
Conventional Method ◽  
Function Generator ◽  
Arbitrary Choice ◽  
Usual Procedure ◽  
Structural Error ◽  
Function Generators ◽  
Conventional Optimization ◽  
Four Bar Linkage ◽  
Additional Constraints

This paper is a departure from the usual procedure for obtaining the optimal dimensions of a four bar function generator by iteration. In the usual procedure, the accuracy points are first chosen by means of Chebishev spacing or some other means. Using these accuracy points, a four bar linkage is synthesized and the error calculated. Freudenstein’s respacing formula may then be used to respace the accuracy points so as to minimize the errors. After the respacing of the accuracy points is calculated, a new mechanism is synthesized. The process is repeated until the magnitudes of the extreme errors occurring between accuracy points are equalized. The procedure adopted in this paper is to immediately force the extreme errors between accuracy points to be equal in magnitude by imposing additional constraints upon the problem. These constraints eliminate the arbitrary choice of the first set of accuracy points. This procedure results in a more extensive set of equations to be solved than the conventional method. However, once the equations are solved, they lead directly to equalized (and thus minimized) extrema of the magnitude of structural errors between the precision points. Thus there is no need to perform the iterative steps of conventional optimization. The proposed method is illustrated with an example.

Synthesis of Pareto Optimal Four-Bar Function Generators With Optimum Structural Error and Optimum Transmission Angles

1984 ◽  
Vol 106 (4) ◽  
pp. 437-443 ◽  
Author(s):  
J. T. Pugh
Keyword(s):  
Representative Sample ◽  
Pareto Optimal ◽  
Optimal Solutions ◽  
Function Generator ◽  
Solution Domain ◽  
Structural Error ◽  
Function Generators ◽  
Pareto Minima

The four-bar function generator solution domain is systematically searched-for mechanisms which exhibit at the same time minimum structural error and the best transmission angles. First, synthesis equations are developed. Then the boundary of the solution domain is defined in terms of the permissible angular changes of the coupler link. The concept of Pareto minima is used to identify potential optimal solutions from a representative sample generated over the solution domain. The procedure is illustrated with an example.

Synthesis of Four-Bar Linkage Function Generators by Means of Equations of Motion

1965 ◽  
Vol 87 (2) ◽  
pp. 170-176 ◽  
Author(s):  
C. K. Wojcik
Keyword(s):  
Equations Of Motion ◽  
Angular Acceleration ◽  
Input Output ◽  
Connecting Rod ◽  
Function Generator ◽  
Function Generation ◽  
Function Generators ◽  
Two Parameters ◽  
Four Bar Linkage ◽  
Selection Of

The function generation method presented in this paper is based on consideration of the equations of motion of a four-bar linkage with an assumed input of θ˙1 = 1 rad/sec. For a specified input-output relationship, the task of synthesizing an appropriate four-bar linkage is reduced by this method to a problem of selecting two parameters: θ˙2—the angular velocity and θ¨2—the angular acceleration of the connecting rod. The selection of these parameters is governed by certain conditions imposed on the performance of the four-bar linkage function generator. Using this method, two specific problems are solved and discussed in detail.

Synthesis and Balancing of Cam-Modulated Linkages

1987 ◽  
Author(s):  
P. Pracht ◽  
P. Minotti ◽  
M. Dahan
Keyword(s):  
Systematic Approach ◽  
Kinematic Chain ◽  
Path Generation ◽  
Industrial Manipulator ◽  
High Speeds ◽  
Structural Error ◽  
Mass Balancing ◽  
Four Bar Linkage ◽  
Robotic Applications ◽  
Class Of Functions

Abstract Linkages are inherently light, inexpensive, strong, adaptable to high speeds and have little friction. Moreover the class of functions suitable for linkage representation is large. For all these reasons numerous recent works deal with the problem of design mechanisms for robotic applications, but very often in terms of components such as gripper, transmission, balancing. We investigate a new application for linkages, using them to design industrial manipulator. The selected mechanism for this application is a four bar linkage with an adjustable lengh for exact path generation. This adjustment is performed by a track or cam which is substituted to a bar. By this mean, we define a cam-modulated linkage which possess superior accuracy potential and is capable of accomodating of industrial design restrictions. Such a kinematic chain is free from structural error for path generation and the presence of the track introduces the flexibility and versality in the usefull four bar chain. The synthesis technique of cam modulated linkage utilizes loop closure equations, envelop theory to find the centerline and the profile of the track. These techniques provide a systematic approach to the design of mechanism for path generation when extreme accuracy is required. In order to complete an contribution, we take in consideration the static balancing of the synthesized manipulator. To achieve static mass balancing we use the potential energy storage capabilities of linear springs, and integrated it with the non-linear motion of mechanism to provide an exact value of the desired counter loading functions. Examples are worked to demonstrate applications of these procedures and to illustrate the industrial potential of spring balancing and cam-modulated linkage.

Five Position Synthesis of a Slider-Crank Function Generator

2011 ◽  
Author(s):  
Mark M. Plecnik ◽  
J. Michael McCarthy
Keyword(s):  
Full Range ◽  
Linear Actuator ◽  
Tolerance Zone ◽  
Function Generator ◽  
Front End ◽  
Input And Output ◽  
Function Generators ◽  
Synthesis Procedure ◽  
Position Synthesis ◽  
Branching Solutions

In this paper, we present a synthesis procedure for the coupler link of a planar slider-crank linkage in order to coordinate input by a linear actuator with the rotation of an output crank. This problem can be formulated in a manner similar to the synthesis of a five position RR coupler link. It is well-known that the resulting equations can produce branching solutions that are not useful. This is addressed by introducing tolerances for the input and output values of the specified task function. The proposed synthesis procedure is then executed on two examples. In the first example, a survey of solutions for tolerance zones of increasing size is conducted. In this example we find that a tolerance zone of 5% of the desired full range results in a number of useful task functions and usable slider-crank function generators. To demonstrate the use of these results, we present an example design for the actuator of the shovel of a front-end loader.

Eliminating Structural Error in Real-Time Adjustable Four-Bar Path Generators Using Iterative Learning Control

2004 ◽  
Author(s):  
Hong-Jen Chen ◽  
Richard W. Longman ◽  
Meng-Sang Chew
Keyword(s):  
Control Systems ◽  
Real Time ◽  
Iterative Learning Control ◽  
Learning Control ◽  
Iterative Learning ◽  
Path Generation ◽  
Structural Error ◽  
Four Bar Linkage

Fundamental concepts of Iterative Learning Control (ILC) are applied to path generating problems in mechanisms. As an illustration to such class of problems, an adjustable four-bar linkage is used. The coupler point of a four-bar traces a coupler curve that will in general deviate from the desired coupler path. Except at the precision points, the coupler curve will exhibit some structural error, which is the deviation from the specified curve. The structural error will repeat itself every cycle at exactly the same points over the range of interest. Since ILC is a methodology that was developed to handle similar repetitive errors in control systems, it is believed that it will be well served to apply it to this class of problems. Results show that ILC can be simple to implement, and it is found to be very well suited for such path generation problems.

Kinematic Efficiency of Non-Circular Geared Transmissions

1981 ◽  
Vol 103 (1) ◽  
pp. 170-176 ◽  
Author(s):  
R. J. Ferguson ◽  
J. H. Kerr
Keyword(s):  
Power Flow ◽  
High Efficiency ◽  
Function Generator ◽  
Function Generators ◽  
Kinematic Efficiency

Infinitely-variable transmissions of high efficiency can be made using non-circular gears combined in function generators. The efficiency of a function generator depends on the gear parameters, the ratio of the differential, and the direction of power flow. The paper shows how the factors influence the total gear meshing losses and explain how efficiency is calculated. No-load losses are not included.

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%.

Multiply Separated Position Design of the Geared Five-Bar Function Generator

1971 ◽  
Vol 93 (1) ◽  
pp. 74-84 ◽  
Author(s):  
S. A. Oleksa ◽  
D. Tesar
Keyword(s):  
Design Parameters ◽  
Function Generator ◽  
Function Generation ◽  
Four Bar Linkage ◽  
Generation Problem ◽  
Made In

The geared five-bar linkage is the foundation for a function generation problem meeting specifications for 5 multiply separated positions and containing 4 free design parameters. The four-bar linkage is shown to be a member of this class of mechanisms. Design examples of rarely treated functions are given with the quality of the generated approximation. Suggestions are made in terms of the 4 design parameters to assist the designer in obtaining good results.

A Task Driven Approach to Unified Synthesis of Planar Four-Bar Linkages Using Algebraic Fitting of a Pencil of G-Manifolds

2013 ◽  
Author(s):  
Q. J. Ge ◽  
Ping Zhao ◽  
Anurag Purwar
Keyword(s):  
Least Squares ◽  
Singular Values ◽  
Geometric Constraints ◽  
Motion Generation ◽  
Motion Approximation ◽  
Value Decomposition ◽  
Four Bar Linkage ◽  
The Given ◽  
Best Fit ◽  
Additional Constraints

This paper studies the problem of planar four-bar motion approximation from the viewpoint of extraction of geometric constraints from a given set of planar displacements. Using the Image Space of planar displacements, we obtain a class of quadrics, called Generalized- or G-manifolds, with eight linear and homogeneous coefficients as a unified representation for constraint manifolds of all four types of planar dyads, RR, PR, and PR, and PP. 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 G-manifolds that best fit the image points in the least squares sense. This least squares problem is solved using Singular Value Decomposition. The linear coefficients associated with the smallest singular values are used to define a pencil of quadrics. Additional constraints on the linear coefficients are then imposed to obtain a planar four-bar linkage that best guides the coupler through the given displacements. The result is an efficient and linear algorithm that naturally extracts the geometric constraints of a motion and leads directly to the type and dimensions of a mechanism for motion generation.

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