Closure to “Discussion of ‘Analysis and Design of Basic Linkages for Harmonic Motion Generation’” (1985, ASME J. Mech. Transm. Autom. Des., 107, p. 507)

1985 ◽  
Vol 107 (4) ◽  
pp. 507-507
Author(s):  
A. Midha ◽  
R. J. Cipra ◽  
K. Farhang
Keyword(s):  
Motion Generation ◽  
Analysis And Design ◽  
Harmonic Motion

Analysis and Design of Basic Linkages for Harmonic Motion Generation

1985 ◽  
Vol 107 (4) ◽  
pp. 499-506 ◽  
Author(s):  
A. Midha ◽  
R. J. Cipra ◽  
K. Farhang
Keyword(s):  
Order Of Approximation ◽  
Motion Generation ◽  
Small Motion ◽  
Analysis And Design ◽  
Harmonic Motion ◽  
Simple Harmonic Motion ◽  
Transmission Angle ◽  
Unique Approach ◽  
Planar Linkages

This paper deals with basic planar linkages driven by relatively small cranks, and as a consequence generating approximate simple harmonic motion at the output members. A unique approach is presented to yield the kinematic equations, as exemplified by planar crank-rocker and offset slider-crank linkages. The method involves the presumption of a mean linkage configuration and a small motion excursion therefrom. Its validity is demonstrated by means of several error plots, generated for varying, nondimensional linkage parameters and a constant mean transmission angle. These plots also serve to illustrate the order of approximation involved for a particular combination of parameters. Finally, the synthesis of a crank-rocker linkage for a representative set of requirements is exemplified using the equations developed herein.

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.

A Higher-Order Analysis of Basic Linkages for Harmonic Motion Generation

1987 ◽  
Vol 109 (3) ◽  
pp. 301-307 ◽  
Author(s):  
K. Farhang ◽  
A. Midha ◽  
A. Bajaj
Keyword(s):  
Perturbation Technique ◽  
Motion Generation ◽  
Link Length ◽  
Small Motion ◽  
Harmonic Motion ◽  
Order Analysis ◽  
Modified Equations ◽  
Crank Angle ◽  
The Mean ◽  
Definition Of

In an earlier work, a perturbation technique was first presented to obtain approximate simple harmonic equations for describing the output motions of rudimentary linkages, i.e., a crank-rocker and a slider-crank, with relativley small input cranks. The technique involved consideration of a small motion excursion about a so-called “mean linkage configuration.” These equations were facilitated through truncation of the binomial series expansion of the output motions, expressed in terms of the input crank angle. Assuming a small crank to ground link length ratio, terms containing second or higher powers of this ratio were neglected. This paper retains terms containing higher powers in an effort to improve upon (i) the definition of the mean linkage configuration, and (ii) the harmonic motion content representation of the output motions. The improvements made due to the “modified” equations, relative to the “original” ones, are pictorially presented as being significant.

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

1988 ◽  
Vol 110 (1) ◽  
pp. 22-27 ◽  
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

This paper, a sequel to a companion paper on function generation, discusses the path and motion generation problems in the synthesis of linkages with relatively small input cranks. The point on the floating link (i.e., the coupler of a crank-rocker linkage or the 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.

Discussion following the presentation by F. Deubner

1977 ◽  
Vol 36 ◽  
pp. 69-74
Keyword(s):  
List Type ◽  
The Sun ◽  
Type Number ◽  
Harmonic Motion ◽  
Locally Excited ◽  
Long Period ◽  
Coherent Wave ◽  
Short Period ◽  
Global Modes

The discussion was separated into 3 different topics according to the separation made by the reviewer between the different periods of waves observed in the sun :1) global modes (long period oscillations) with predominantly radial harmonic motion.2) modes with large coherent - wave systems but not necessarily global excitation (300 s oscillation).3) locally excited - short period waves.

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