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.

Finding All Solutions to Approximate Synthesis of Planar Linkages for Function Generation, Rigid-Body Guidance and Path Generation

1996 ◽  
Author(s):  
An-Xin Liu ◽  
Ting-Li Yang
Keyword(s):  
Rigid Body ◽  
Continuation Method ◽  
Optimization Method ◽  
Global Optimum ◽  
Path Generation ◽  
Kinematic Synthesis ◽  
Function Generation ◽  
All Solutions ◽  
Approximate Synthesis ◽  
Optimum Solution

Abstract Generally, approximate kinematic synthesis of planar linkage is studied using optimization method. But this method has two defects: i) the initial guesses are hard to determine and ii) the global optimum solution is difficult to find. In this paper, a new method which can find all solutions to approximate kinematic synthesis of planar linkage is proposed. Firstly, we reduce the approximate synthesis problem to finding all solutions to polynomial equations. Polynomial continuation method is then used to find all solutions. Finally, all possible linkages can be obtained. Approximate syntheses of planar four-bar linkage for function generation, rigid-body guidance and path generation are studied in detail and 3 examples are given to illustrate the advantages of the proposed method.

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 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.

The logical design of a digital computer for a large-scale real-time application

1956 ◽  
Author(s):  
M. M. Astrahan ◽  
B. Housman ◽  
J. F. Jacobs ◽  
R. P. Mayer ◽  
W. H. Thomas
Keyword(s):  
Real Time ◽  
Digital Computer ◽  
Large Scale ◽  
Logical Design ◽  
Real Time Application

Large-scale spatial angle measurement and the pointing error analysis

2016 ◽  
Vol 12 (3) ◽  
pp. 229-232 ◽  
Author(s):  
Wen-jian Xiao ◽  
Zhi-bin Chen ◽  
Dong-xi Ma ◽  
Yong Zhang ◽  
Xian-hong Liu ◽  
...  
Keyword(s):  
Error Analysis ◽  
Large Scale ◽  
Angle Measurement ◽  
Pointing Error

Finding All Solutions to Unconstrained Nonlinear Optimization for Approximate Synthesis of Planar Linkages Using Continuation Method

1999 ◽  
Vol 121 (3) ◽  
pp. 368-374 ◽  
Author(s):  
A.-X. Liu ◽  
T.-L. Yang
Keyword(s):  
Continuation Method ◽  
Optimization Method ◽  
Global Optimum ◽  
Kinematic Synthesis ◽  
All Solutions ◽  
Approximate Synthesis ◽  
Unconstrained Nonlinear Optimization ◽  
Optimum Solution ◽  
Planar Linkages ◽  
Four Bar Linkage

Generally, approximate kinematic synthesis of planar linkage is studied using optimization method. But this method has two defects: i) the suitable initial guesses are hard to determine and ii) the global optimum solution is difficult to find. In this paper, a new method which can find all solutions to approximate kinematic synthesis of planar linkage is proposed. Firstly, we reduce the approximate synthesis problem to finding all solutions to polynomial equations. Polynomial continuation method is then used to find all solutions. Finally, all possible linkages can be obtained. Approximate syntheses of planar four-bar linkage for function generation, rigid-body guidance and path generation are studied in detail and three examples are given to illustrate the advantages of the proposed method.

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