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.

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.

Synthesis of Harmonic Motion Generating Linkages—Part I: Function Generation

1988 ◽  
Vol 110 (1) ◽  
pp. 16-21 ◽  
Author(s):  
K. Farhang ◽  
A. Midha ◽  
A. K. Bajaj
Keyword(s):  
Harmonic Functions ◽  
Higher Order ◽  
Order Function ◽  
Harmonic Motion ◽  
Function Generation ◽  
Synthesis Techniques ◽  
Input Motion

This paper deals with the first and higher-order function-generation problems in the synthesis of linkages with relatively small input cranks. Such linkages tend to produce nearly simple harmonic motions at the output members. Owing to this distinction, the generality of the conventional synthesis techniques is no longer applicable. Thus, in function generation, only harmonic functions of the input motion may be expected to be synthesized for output motions.

Synthesis of Harmonic Motion Generating Linkages: Part I — Function Generation

1987 ◽  
Author(s):  
K. Farhang ◽  
A. Midha ◽  
A. K. Bajaj
Keyword(s):  
Harmonic Functions ◽  
Higher Order ◽  
Order Function ◽  
Harmonic Motion ◽  
Function Generation ◽  
Synthesis Techniques ◽  
Input Motion

Abstract This paper deals with the first- and higher-order function generation problems in the synthesis of linkages with relatively small input cranks. Such linkages tend to produce nearly simple harmonic motions at the output members. Owing to this distinction, the generality of the conventional synthesis techniques is no longer applicable. Thus, in function generation, only harmonic functions of the input motion may be expected to be synthesized for output motions.

An Integral Method of Liapunov Function Generation for Nonlinear Autonomous Systems

1965 ◽  
Vol 32 (3) ◽  
pp. 569-575 ◽  
Author(s):  
J. A. Walker ◽  
L. G. Clark
Keyword(s):  
Asymptotic Stability ◽  
Integral Method ◽  
Autonomous Systems ◽  
Liapunov Function ◽  
Higher Order ◽  
Phase Variable ◽  
Variable Form ◽  
Function Generation ◽  
Liapunov Functions

A method is developed for generating Liapunov functions with which to determine the domain of asymptotic stability for nonlinear autonomous systems of any order, so long as these systems may be represented in phase variable form. The method is illustrated by several examples of higher order.

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 General synthesis techniques for coupled resonator networks

2007 ◽  
Vol 8 (5) ◽  
pp. 98-104 ◽  
Author(s):  
Fabien Seyfert ◽  
Stephane Bila
Keyword(s):  
Synthesis Techniques ◽  
General Synthesis ◽  
Coupled Resonator

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.

On a General Method of Spatial Kinematic Synthesis by Means of a Stretch-Rotation Tensor

1969 ◽  
Vol 91 (1) ◽  
pp. 115-121 ◽  
Author(s):  
G. N. Sandor ◽  
K. E. Bisshopp
Keyword(s):  
Mathematical Model ◽  
Kinematic Chain ◽  
Higher Order ◽  
Motion Generation ◽  
Rotation Tensor ◽  
Kinematic Synthesis ◽  
Rotation Operator ◽  
Key Concepts ◽  
The Mathematical Model ◽  
General Method

One of the key concepts in a general method of spatial kinematic synthesis is a stretch-rotation operator applied to members of a general spatial kinematic chain. The latter consists of one or more interconnected loops of successively ball-jointed bar-slideball members. Each member is represented by a vector free to stretch-rotate with the motion of the chain. In the mathematical model of the general chain, displacement is simulated by means of stretch-rotation tensors operating on each member vector. Appropriate mathematical constraints render the general chain and its mathematical model equivalent to a particular mechanism. With this approach and by taking derivatives, first, second, and higher-order loop equations can be developed which form the basis for a general method of spatial kinematic synthesis, applicable to path, function and motion generation (body guidance) with first, second, and higher-order as well as for combined “point-order” approximations.

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