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.

scholarly journals The Synthesis of Planar Four-Bar Linkage for Mixed Motion and Function Generation

Sensors ◽  
2021 ◽  
Vol 21 (10) ◽  
pp. 3504
Author(s):  
Bin Wang ◽  
Xianchen Du ◽  
Jianzhong Ding ◽  
Yang Dong ◽  
Chunjie Wang ◽  
...  
Keyword(s):  
Complex Plane ◽  
Path Generation ◽  
Motion Generation ◽  
Numerical Examples ◽  
Function Generation ◽  
Long Time ◽  
Synthesis Procedure ◽  
And Function ◽  
Four Bar Linkage ◽  
Numerical Synthesis

The synthesis of four-bar linkage has been extensively researched, but for a long time, the problem of motion generation, path generation, and function generation have been studied separately, and their integration has not drawn much attention. This paper presents a numerical synthesis procedure for four-bar linkage that combines motion generation and function generation. The procedure is divided into two categories which are named as dependent combination and independent combination. Five feasible cases for dependent combination and two feasible cases for independent combination are analyzed. For each of feasible combinations, fully constrained vector loop equations of four-bar linkage are formulated in a complex plane. We present numerical examples to illustrate the synthesis procedure and determine the defect-free four-bar linkages.

Synthesis of Harmonic Motion Generating Linkages: Part II — Path and Motion Generation

1987 ◽  
Author(s):  
K. Farhang ◽  
A. Midha ◽  
A. S. Hall
Keyword(s):  
Companion Paper ◽  
Higher Order ◽  
Rate Of Change ◽  
Connecting Rod ◽  
Motion Generation ◽  
Harmonic Motion ◽  
Function Generation ◽  
Synthesis Techniques ◽  
General Synthesis

Abstract This paper, a sequel to a companion paper on function generation, discusses the path and motion generation problems in the synthesis of linages with relatively small input cranks. The point on the floating link (i.e., the coupler of a crank-rocker linkage point on connecting rod in a slider-crank linkage) traces an approximate ellipse. This fact serves as a major distinction between the method described herein and the conventional, more general, synthesis techniques. In other words, only elliptical paths may be generated by the path (or coupler) points in the synthesis of linkages with small cranks. Higher order path and motion generation, in which velocity, acceleration, slope and the rate of change of slope of the coupler path may be specified, are also addressed in this paper.

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.

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.

Planar Linkage Synthesis for Mixed Motion, Path and Function Generation Using Poles and Rotation Angles

2017 ◽  
Author(s):  
Ronald A. Zimmerman
Keyword(s):  
Sufficient Conditions ◽  
Motion Path ◽  
Engineering Practice ◽  
Function Generation ◽  
Problem Types ◽  
The Family ◽  
And Function ◽  
Necessary And Sufficient ◽  
Four Bar Linkage ◽  
Selection Of

The kinematic synthesis of planar linkage mechanisms has traditionally been broken into the categories of motion, path and function generation. Each of these categories of problems has been solved separately. Many problems in engineering practice require some combination of these problem types. For example, a problem requiring coupler points and/or poses in addition to specific input and/or output link angles that correspond to those positions. A limited amount of published work has addressed some specific underconstrained combinations of these problems. This paper presents a general graphical method for the synthesis of a four bar linkage to satisfy any combination of these exact synthesis problems that is not over constrained. The approach is to consider the constraints imposed by the target positions on the linkage through the poles and rotation angles. These pole and rotation angle constraints are necessary and sufficient conditions to meet the target positions. After the constraints are made, free choices which may remain can be explored by simply dragging a fixed pivot, a moving pivot or a pole in the plane. The designer can thus investigate the family of available solutions before making the selection of free choices to satisfy other criteria. The fully constrained combinations for a four bar linkage are given and sample problems are solved for several of them.

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.

Planar Linkage Synthesis for Mixed Motion, Path, and Function Generation Using Poles and Rotation Angles1

2018 ◽  
Vol 10 (2) ◽  
Author(s):  
Ronald A. Zimmerman
Keyword(s):  
Sufficient Conditions ◽  
Motion Path ◽  
Engineering Practice ◽  
Function Generation ◽  
Problem Types ◽  
The Family ◽  
And Function ◽  
Necessary And Sufficient ◽  
Four Bar Linkage ◽  
Selection Of

The kinematic synthesis of planar linkage mechanisms has traditionally been broken into the categories of motion, path, and function generation. Each of these categories of problems has been solved separately. Many problems in engineering practice require some combination of these problem types. For example, a problem requiring coupler points and/or poses in addition to specific input and/or output link angles that correspond to those positions. A limited amount of published work has addressed some specific underconstrained combinations of these problems. This paper presents a general graphical method for the synthesis of a four bar linkage to satisfy any combination of these exact synthesis problems that is not overconstrained. The approach is to consider the constraints imposed by the target positions on the linkage through the poles and rotation angles. These pole and rotation angle constraints (PRCs) are necessary and sufficient conditions to meet the target positions. After the constraints are made, free choices which may remain can be explored by simply dragging a fixed pivot, a moving pivot, or a pole in the plane. The designer can thus investigate the family of available solutions before making the selection of free choices to satisfy other criteria. The fully constrained combinations for a four bar linkage are given and sample problems are solved for several of them.

Sign in / Sign up

Export Citation Format

Share Document