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.

The Kinematic Synthesis of Toggle Clamps

1998 ◽  
Vol 120 (3) ◽  
pp. 648-655 ◽  
Author(s):  
Pei-Lum Tso
Keyword(s):  
Quadratic Equation ◽  
Function System ◽  
Implicit Function ◽  
Kinematic Synthesis ◽  
Mechanical Advantage ◽  
Function Generation ◽  
Different Types ◽  
Almost All ◽  
Generation Problem

The toggle clamp is one of the most common forms of clamps used throughout industry. They are commercially available in different types and models satisfying almost all ordinary fixture clamping requirements. Based on the theorem of implicit function system existence and the concept of solution plane, computers have been employed to generate planar four-bar mechanisms for three position function generation problem at the toggle positions. A quadratic equation which defines the locus can be plotted in the plane of solutions which have toggle at first, second, or third positions. Additionally this approach offers control over the mechanical advantage at clamping position, and defect free solutions. A vertical acting toggle clamp has been worked for illustrative purposes. This methodology has also been applied to generate slider-crank at toggle position for push-pull type toggle clamps.

Multiply Separated Synthesis of Six-Link Mechanisms Using Parallel Homotopy With M-Homogenization

1998 ◽  
Author(s):  
A. K. Dhingra ◽  
M. Zhang
Keyword(s):  
Group Theory ◽  
Matrix Method ◽  
Parallel Implementation ◽  
Homotopy Methods ◽  
Numerical Work ◽  
Function Generation ◽  
Connection Machine ◽  
The Matrix ◽  
Generation Problem ◽  
Complete Solutions

Abstract This paper presents complete solutions to the function generation problem of six-link Watt and Stephenson mechanisms, with multiply separated precision positions (PP), using homotopy methods with m-homogenization. It is seen that using the matrix method for synthesis, applying m-homogeneous group theory and by defining auxiliary equations in addition to the synthesis equations, the number of homotopy paths to be tracked in obtaining all possible solutions to the synthesis problem can be drastically reduced. Numerical work dealing with the synthesis of Watt and Stephenson mechanisms for 6 and 9 multiply separated precision points is presented. For both mechanisms, it is seen that complete solutions for 6 and 9 precision points can be obtained by tracking 640 and 286,720 paths, respectively. A parallel implementation of homotopy methods on the Connection Machine on which several thousand homotopy paths can be tracked concurrently is also discussed.

Elimination of Branch, Grashof, and Order Defects in Path-Angle Generation and Function Generation Synthesis

1979 ◽  
Vol 101 (3) ◽  
pp. 428-437 ◽  
Author(s):  
K. J. Waldron ◽  
E. N. Stevensen
Keyword(s):  
Motion Generation ◽  
Function Generation ◽  
And Function ◽  
Generation Problem

Path-Angle Generation and Function Generation synthesis problems are restated as Plane-Position (or Motion Generation) problems, enabling the use of the classical Burmester technique and recent extensions that permit the avoidance of Branch, Grashof, and Order defects. An example of the solution of a Path-Angle Generation problem is given.

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.

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.

Characteristic Surfaces for Three-Position Function Generation With Planar Four-Bar Mechanisms

1989 ◽  
Vol 111 (1) ◽  
pp. 104-109 ◽  
Author(s):  
C. R. Barker ◽  
P.-L. Tso
Keyword(s):  
Design Problem ◽  
Solution Space ◽  
Function Generation ◽  
Numerical Example ◽  
All Solutions ◽  
The Relationship ◽  
Generation Problem

This paper considers the relationship between the three-position function-generation problem and the solution space for planar four-bar mechanisms. The two infinities of solutions possible are mapped in a plane to determine the locations where particular types of mechanisms occur. It is possible to generate a contour in the mapping plane which joins together all solutions which possess a common characteristic in regard to their link lengths. This same contour can be displayed in the solution space to ascertain the overall characteristics of potential solutions to the design problem. A numerical example is used for illustrative purposes, but the results can be applied to any three-position function-generation problem.

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.

Synthesis of Linkages to Generate Specified Histories of Forces and Torques: The Planar Slider-Crank Mechanism

1987 ◽  
Author(s):  
C. Bagci
Keyword(s):  
Elementary Function ◽  
Synthesis Methods ◽  
Function Generation ◽  
Optimum Synthesis ◽  
Output Force ◽  
Torque Generation ◽  
Position Synthesis ◽  
Solution Mechanism ◽  
Generation Problem ◽  
Crank Mechanism

Abstract The first part of the article presented analytical precision and optimum synthesis methods for linkages for the generation of specified torque histories and applied to the planar 4R four-bar mechanism. This article presents analytical mechanical advantage method (MAM) and integration of power equilibrium method (IPEM) for the synthesis of the planar slider-crank mechanism for the generation of specified input-output force and torque histories. Design equations for one, two, three, and four precision position synthesis are given. They are used to formulate the optimum synthesis technique, which requires no iteration to reach a solution mechanism. Slider-crank mechanisms synthesized also replace pinion-rack drives with noncircular and circular pinions to generate non-uniform and uniform velocity ratios, respectively. The MAM can be applied for discretely defined and continuous force-torque relationships, while IPEM is used with continuous relationships which reduces the force-torque generation into an elementary function generation problem. Application examples are included.

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.

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