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.

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.

TPT NOTES: Damped Simple Harmonic Motion on a Linear Air Track

1969 ◽  
Vol 7 (7) ◽  
pp. 395-396
Author(s):  
Thomas B. Greenslade
Keyword(s):  
Harmonic Motion ◽  
Simple Harmonic Motion

Response characteristics of electromagnetic seismographs and their dependence on the instrumental constants

1949 ◽  
Vol 39 (3) ◽  
pp. 205-218
Author(s):  
S. K. Chakrabarty
Keyword(s):  
General Solution ◽  
Equation Of Motion ◽  
Harmonic Motion ◽  
Response Characteristics ◽  
Local Earthquakes ◽  
Simple Harmonic Motion ◽  
The Earth ◽  
Electromagnetic Seismograph ◽  
Different Types ◽  
Proper Values

Summary The equation of motion of the seismometer and the galvanometer in an electromagnetic seismograph has been derived in the most general form taking into consideration all the forces acting on the system except that produced by hysteresis. A general solution has been derived assuming that the earth or the seismometer frame is subjected to a sustained simple harmonic motion, and expressions for both the transient and the steady term in the solution have been given. The results for the particular case when the seismograph satisfies the Galitzin conditions can easily be deduced from the results given in the present paper. The results can now be used to study the response characteristics of all electromagnetic seismographs, whether they satisfy the Galitzin conditions or not, and will thus give an accurate theoretical picture of the response also of seismographs used for the study of “local earthquakes” and “microseisms” which do not in general obey the Galitzin conditions. The results obtained can also be used to get analytically the response of the seismographs for different types of earth motion from the very beginning, and not only after the transient term has disappeared. The theory of the response to simple tests used to determine the dynamic magnification of any seismograph and also to determine and check regularly the instrumental constants of the seismographs has been worked out. The results obtained can also be used for ascertaining the proper values of the instrumental constants suitable for the various purposes for which the seismographs are to be used.

Simple harmonic motion

2019 ◽  
pp. 262-268
Author(s):  
John Bird ◽  
Carl Ross
Keyword(s):  
Harmonic Motion ◽  
Simple Harmonic Motion

An Arduino Investigation of Simple Harmonic Motion

2014 ◽  
Vol 52 (3) ◽  
pp. 157-159 ◽  
Author(s):  
Calin Galeriu ◽  
Scott Edwards ◽  
Geoffrey Esper
Keyword(s):  
Harmonic Motion ◽  
Simple Harmonic Motion
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