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.

Defect-Free Slider-Crank Function Generation for 4.5 Precision Points

2000 ◽  
Author(s):  
Herbert E. Stumph ◽  
Andrew P. Murray
Keyword(s):  
Synthesis Problem ◽  
Point Function ◽  
Function Generation ◽  
Structural Error ◽  
Mechanical Press

Abstract The well-established methodology for slider-crank function generation states that 5 precision points can be achieved with no structural error. The resulting designs, however, do not necessarily satisfy all of the kinematic requirements for designing the slider-crank linkages used to drive the ram of a mechanical press. First, solutions to the 5 precision point synthesis problem may not have the precision points on one circuit. Additionally, there is no guarantee of a fully rotatable input crank. In this paper we present 4.5 precision point synthesis, a modification to the 5 precision point methodology for designing slider-cranks with fully rotatable input links and all precision points on the same circuit. The 4.5 precision point function generation methodology is illustrated with an example.

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.

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.

SDAMP: Software for the Design and Analysis of Mechanical Presses

2000 ◽  
Author(s):  
Herbert E. Stumph ◽  
Andrew P. Murray
Keyword(s):  
Kinematic Analysis ◽  
Kinematic Synthesis ◽  
Link Mechanism ◽  
Mechanical Press ◽  
Analysis And Synthesis ◽  
Drag Link ◽  
Mechanism Kinematic ◽  
Functioning Mechanism

Abstract In this paper we introduce the MATLAB-based SDAMP (pronounced stamp) software for the analysis and synthesis of several mechanical press linkages. These linkages include the slider-crank and the four six-bar mechanisms formed by attaching a drag-link, crank-rocker, crank-shaper or Whitworth mechanism to a slider-crank. SDAMP performs four basic tasks: guided layout, kinematic analysis, mechanism refine and kinematic synthesis. Guided layout leads the user through joint selection to ensure a functioning mechanism. Kinematic analysis displays the position, velocity, acceleration and jerk of the sliding output versus the rotation of the input link. Mechanism refine allows the user to vary the geometry of an existing mechanism towards the goal of achieving a desired kinematic analysis. Lastly, kinematic synthesis determines the set of defect-free slider-cranks capable of achieving four precision points. All of these capabilities are integrated through a host of GUI driven MATLAB files in SDAMP.

Kinematic Synthesis and Analysis of the Rack and Pinion Multi-Purpose Mechanism

1992 ◽  
Vol 114 (3) ◽  
pp. 428-432 ◽  
Author(s):  
G. K. Ananthasuresh ◽  
S. N. Kramer
Keyword(s):  
General Procedure ◽  
Full Range ◽  
Mechanism Synthesis ◽  
Kinematic Synthesis ◽  
Function Generation ◽  
Monotonic Functions ◽  
Transmission Angle ◽  
Velocity Condition ◽  
Method Of Solution ◽  
Design Requirements

The general procedure for synthesizing the rack and pinion mechanism up to seven precision conditions is developed. To illustrate the method, the mechanism has been synthesized in closed form for three precision conditions of path generation, two positions of function generation, and a velocity condition at one of the precision points. This mechanism has a number of advantages over conventional four bar mechanisms. First, since the rack is always tangent to the pinion, the transmission angle is always 90 deg minus the pressure angle of the rack. Second, with both translation and rotation of the rock occurring, multiple outputs are available. Other advantages include the generation of monotonic functions for a wide variety of motion and nonmonotonic functions for a full range of motion as well as nonlinear amplified motions. In this work the mechanism is made to satisfy a number of amplified motions. In this work the mechanism is made to satisfy a number of practical design requirements such as completely rotatable input crank and others. By including the velocity specification, the designer has considerably more control of the output motion. The method of solution developed in this work uses the complex number method of mechanism synthesis. A numerical example is 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%.

Kinematic Synthesis of Geared Spherical Five Bar Mechanisms for Function Generation

1975 ◽  
Vol 97 (2) ◽  
pp. 723-730 ◽  
Author(s):  
D. L. Riddle ◽  
D. Tesar ◽  
J. Duffy
Keyword(s):  
Gear Train ◽  
Kinematic Synthesis ◽  
Design Procedures ◽  
Function Generation ◽  
Complete Formulation ◽  
Generation Problem

The synthesis of geared spherical five-bar mechanisms with application to the function generation problem is considered for multiply separated position specifications. Special gear train values reduce the geared five-bar to the elementary spherical four-bar. The planar four- and five-bar become a design subset to the spherical five-bar. Design procedures with complete formulation are outlined in detail.

scholarly journals Finding Only Finite Roots to Large Kinematic Synthesis Systems

2017 ◽  
Vol 9 (2) ◽  
Author(s):  
Mark M. Plecnik ◽  
Ronald S. Fearing
Keyword(s):  
Polynomial Systems ◽  
Synthesis Problem ◽  
New Method ◽  
Homotopy Continuation ◽  
Kinematic Synthesis ◽  
Root Finding ◽  
Large Polynomial Systems ◽  
Path Synthesis

In this work, a new method is introduced for solving large polynomial systems for the kinematic synthesis of linkages. The method is designed for solving systems with degrees beyond 100,000, which often are found to possess quantities of finite roots that are orders of magnitude smaller. Current root-finding methods for large polynomial systems discover both finite and infinite roots, although only finite roots have meaning for engineering purposes. Our method demonstrates how all infinite roots can be precluded in order to obtain substantial computational savings. Infinite roots are avoided by generating random linkage dimensions to construct startpoints and start systems for homotopy continuation paths. The method is benchmarked with a four-bar path synthesis problem.

Optimisation Design of Six-Bar Double Dwell Mechanisms: A New Approach

2011 ◽  
Vol 110-116 ◽  
pp. 5216-5222 ◽  
Author(s):  
Mohan Jagannath
Keyword(s):  
Genetic Algorithm ◽  
Synthesis Problem ◽  
Simple Manner ◽  
Nsga Ii ◽  
Recent Contribution ◽  
New Approach ◽  
Constrained Optimisation ◽  
Function Generation ◽  
Concept Of Function ◽  
Single Objective

This paper introduces a new approach for me-chanical design of planar six-bar linkages with rotary joints which produce two dwells in each cycle of the input crank. The approach builds on the concept of function generation in a simple manner. The synthesis problem is posed as a single-objective constrained optimisation problem. A genetic algorithm-based optimisation scheme, namely the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) has been used for solving the optimisation problem. The proposed method has been illustrated by means of an example problem from a recent contribution to literature. It is seen that the results compare favourably with the existing work.

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