Least-Square Optimization of Planar and Spherical Four-Bar Function Generator Under Mobility Constraints

1992 ◽  
Vol 114 (4) ◽  
pp. 569-573 ◽  
Author(s):  
Zheng Liu ◽  
J. Angeles
Keyword(s):  
Orthogonal Decomposition ◽  
Least Square ◽  
Optimization Scheme ◽  
Function Generator ◽  
Design Error ◽  
Slack Variables ◽  
Constrained Minimization Problem ◽  
Function Generators ◽  
Original Objective ◽  
Output Equation

An optimization scheme for four-bar function generators under mobility constraints, which can be applied to both planar and spherical four bar linkages, is presented in this paper. The design error, defined as the residual in the input-output equation, is minimized over the vector of linkage parameters. The mobility constraints, given as a set of inequalities, are converted into equalities by introducing slack variables. The problem is thus formulated as an equality-constrained minimization problem, which is then solved using the orthogonal-decomposition algorithm, an iterative numerical method introduced elsewhere. To reduce the dimensional unbalance, which often occurs in solving a synthesis problem, a penalty function is combined with the original objective function, whose minimization leads to dimensionally balanced linkages. A numerical example is included.

The Constrained Least-Square Optimization of Spherical Four-Bar Path Generators

1992 ◽  
Vol 114 (3) ◽  
pp. 394-405 ◽  
Author(s):  
J. Angeles ◽  
Z. Liu
Keyword(s):  
Numerical Procedure ◽  
Orthogonal Decomposition ◽  
Least Square ◽  
System Of Nonlinear Equations ◽  
Overdetermined System ◽  
Optimization Scheme ◽  
Numerical Examples ◽  
Speed Up ◽  
General Basis ◽  
Four Bar Linkage

In this paper, the optimization of the spherical RRRR four-bar linkage for the problem of path generation is addressed. The problem is formulated as a two-loop minimization of the error between the path-generating point in the coupler curve and the prescribed position, while decoupling the linkage parameters from the configuration variables, namely, the input angles. The synthesis problem consists of evaluating a set of input angles {ψk}1m defining m linkage configurations and the linkage parameters independently. This leads to a constrained overdetermined system of nonlinear equations. The orthogonal decomposition algorithm, introduced elsewhere, is employed to solve the problem. Continuation and damping techniques are used in the numerical procedure to ensure convergence and speed up its rate. The optimization scheme is developed on a general basis and can handle the problem for any number of given path points. Three numerical examples are included.

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.

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.

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.

THE CONSTRAINED LEAST-SQUARE OPTIMIZATION OF SPHERICAL FOUR-BAR LINKAGES FOR RIGID-BODY GUIDANCE

1992 ◽  
Vol 16 (1) ◽  
pp. 47-60 ◽  
Author(s):  
Zheng Liu ◽  
J. Angeles
Keyword(s):  
Rigid Body ◽  
Numerical Procedure ◽  
Optimization Procedure ◽  
Least Square ◽  
Optimization Scheme ◽  
Loop Optimization ◽  
Linkage Error ◽  
General Basis ◽  
Set Up ◽  
Guidance Problem

The synthesis of spherical four-bar linkages for rigid-body guidance consists of the computation of the relevant dimensions of this type of linkage so that it can guide its coupler link to attain a set of prescribed orientations, Generalized coupler curves are used to describe the specified orientations and to evaluate the linkage error, defined as the sum of the errors between the corresponding computed and prescribed orientations. A two-loop optimization procedure is set up to minimize this error, results being obtained resorting to the orthogonal decomposition algorithm, an iterative numerical scheme introduced elsewhere. Continuation and damping techniques are used in the numerical procedure to enhance the convergence likelihood and its rate. The optimization scheme is developed on a general basis and can handle the spherical rigid-body guidance problem for any number of prescribed orientations. A numerical example is included in the paper.

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.

The Influencing Factors of Transfer of Training among the Academic Staff of UiTM

2018 ◽  
Vol 7 (4.34) ◽  
pp. 417
Author(s):  
N. S. Nik Md Salleh ◽  
W. A. A. Wan Mohd Amin ◽  
I. Mamat ◽  
S. Mat Zin ◽  
M. Mamat ◽  
...  
Keyword(s):  
Work Environment ◽  
Transfer Of Training ◽  
Academic Staff ◽  
Partial Least Square ◽  
Least Square ◽  
Error Management ◽  
Training Design ◽  
Design Work ◽  
Design Error ◽  
Motivation To Transfer

This study examined the relationships between employee readiness (attitude, organisational commitment, abilities and motivation to learn), training design (error management and perceived importance), work environment (supervisor’s role and opportunity to use) and transfer of training among the academic staff of UiTM. This study also aimed to determine if motivation to transfer mediates the relationships between employee readiness, training design, work environment and transfer of training. By using the Structural Equation Model – Partial Least Square (SEM-PLS) for the final analysis, the results found that abilities, error management, supervisor’s role and opportunity to use had significant and positive relationships with transfer of training. The study also confirmed the mediating effects of motivation to transfer between error management, opportunity to use and transfer of training.  

A General Theory for Synthesizing Crank-Type Four-Bar Function Generators With Transmission Angle Control

1978 ◽  
Vol 45 (2) ◽  
pp. 415-421 ◽  
Author(s):  
Krishna C. Gupta
Keyword(s):  
General Theory ◽  
Least Square ◽  
Angle Variation ◽  
Numerical Examples ◽  
Transmission Angle ◽  
Function Generators

In this paper, the author proposes a general theory for synthesizing crank-type (i.e., crank-rocker and double-crank) four-bar function generators in which the transmission angle variation over a full crank revolution is in a specified range. Precision point as well as least-square designs have been considered in the paper. Applications of the theory are illustrated by means of numerical examples.

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