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.

Synthesis of Linkages to Generate Specified Histories of Forces and Torques: The Planar 4R Four-Bar Mechanism

1987 ◽  
Author(s):  
C. Bagci
Keyword(s):  
Return Time ◽  
Synthesis Process ◽  
Synthesis Methods ◽  
Multiplication Factor ◽  
Optimum Synthesis ◽  
Torque Generation ◽  
Gear Drives ◽  
Position Synthesis ◽  
Internal Gear ◽  
Generation Problem

Abstract Analytical precision position and optimum synthesis methods for linkages to generate specified force and torque histories are presented and applied to the planar four-bar mechanism. Mechanical advantage method (MAM) and integration of power equilibrium method (IPEM) are used to develop design equations. MAM yields design equations to use when the torque multiplication factor is defined at discrete number of design positions, as well as in continuous forms. IPEM requires continuous forms, but it reduces the torque generation problem into a function generation problem. Design equations with one, two, three, and four unknowns are developed for precision position synthesis; and they are used to formulate optimum synthesis process using many design positions that requires no iteration. Generation of infinite torque multiplication factor and synthesis of quick-return four-bar mechanism to generate specified advance-to-return time ratio are also considered. The synthesized four-bar mechanisms replace circular and non-circular external and internal gear drives. Several industrial application examples are included. The second part of the article considers the slider-crank mechanism.

Discussion of Hwang and Chen's constraint equations to eliminate order, circuit and branch defects for the paper: Defect-free synthesis of Stephenson-III motion generators, published in Journal of Mechanical Engineering Science, 2008; 222: 2485–2494

2019 ◽  
Vol 234 (5) ◽  
pp. 1130-1134
Author(s):  
Wen-Yi Lin
Keyword(s):  
Mechanical Engineering ◽  
Optimization Algorithms ◽  
Synthesis Method ◽  
Synthesis Methods ◽  
Engineering Science ◽  
Function Generation ◽  
Constraint Equations ◽  
Optimum Synthesis

Many studies to find solutions for the optimum synthesis problems of linkage mechanisms for path, motion or function generation have appeared in the literature. However, their main focus has been on the development of optimization algorithms or synthesis methods without the handling of the defect problems or only with consideration of the same assembly mode. Hwang and Chen's pioneering work proposed a defect-free optimum synthesis method with constraint equations to eliminate order, circuit and branch defects for Stephenson III six-bar motion generators. However, their proposed constraint equations for the three types of defects are incomplete or not clear enough. In this discussion, we not only examine these faults but also offer the correct and complete constraints to eliminate the three types of defects.

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.

Finite Position Synthesis of 5-SS Platform Linkages Including Partially Specified Joint Locations

2017 ◽  
Author(s):  
Xin Ge ◽  
Anurag Purwar ◽  
Q. J. Ge
Keyword(s):  
Linear Structure ◽  
Motion Generation ◽  
Numerical Examples ◽  
Moving Points ◽  
Unified Algorithm ◽  
Moving Platform ◽  
Position Synthesis ◽  
Partial Specification ◽  
Generation Problem ◽  
Novel Algorithm

A 5-SS platform linkage generates a one-degree-of-freedom motion of a moving platform such that each of five moving points on the platform is constrained on a sphere, or in its degenerated case, on a plane. It has been well established a 5-SS platform linkage can be made to guide though seven positions exactly. This paper investigates the cases when the number of given positions are less than seven that allows for partial specification of locations of the moving points. A recently developed novel algorithm with linear structure in the design equations has been extended for the solution of the problem. The formulation of this expanded motion generation problem unifies the treatment of the input positions and constraints on the moving and fixed joints associated with the 5-SS platform linkage. Numerical examples are provided to show the effectiveness of the unified algorithm.

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.

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.

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