Displacement Analysis of the Generalized Clemens Coupling, The R-R-S-R-R Spatial Linkage

1975 ◽  
Vol 97 (2) ◽  
pp. 575-580 ◽  
Author(s):  
D. M. Wallace ◽  
F. Freudenstein
Keyword(s):  
Fourth Order ◽  
Constant Velocity ◽  
Degrees Of Freedom ◽  
Input Output ◽  
Closed Form Solutions ◽  
Input And Output ◽  
Order Polynomial ◽  
Special Case ◽  
Output Equation ◽  
Fourth Order Polynomial

The Clemens Coupling is a constant-velocity, universal-type joint for nonparallel intersecting shafts. This mechanism is a spatial linkage with five links connected by four revolute pairs, R, and one spherical pair (ball-and-socket joint), S, which is located symmetrically with respect to the input and output shafts. The Clemens Coupling is a special case of the R-R-S-R-R spatial linkage with general proportions, which will, therefore, be called the Generalized Clemens Coupling. This paper gives the algebraic derivation of the input-output equation for the general R-R-S-R-R linkage and demonstrates that it is a fourth-order polynomial in the half tangents of the crank angles. The effect of housing-error tolerances on the displacements of the Clemens Coupling has also been considered. The results demonstrate feasibility of closed-form solutions for five-link mechanisms with kinematic pairs having more than two degrees of freedom.

Kinematic Analysis of Spatial Six-Link 3R-2P-C Mechanisms

1976 ◽  
Vol 4 (2) ◽  
pp. 71-76
Author(s):  
M.O.M. Osman ◽  
R. V. Dukkipati
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Input Output ◽  
Variable Parameters ◽  
Output Displacement ◽  
Loop Equation ◽  
Dual Number ◽  
Input And Output ◽  
Order Polynomial ◽  
Output Equation

Using (3 x 3) matrices with dual-number elements, closed-form displacement relationships are derived for a spatial six-link R-C-P-R-P-R mechanism. The input-output closed form displacement relationship is obtained as a second order polynomial in the output displacement. For each set of the input and output displacements obtained from the equation, all other variable parameters of the mechanism are uniquely determined. A numerical illustrative example is presented. Using the dual-matrix loop equation, with proper arrangement of terms and following a procedure similar to that presented, the closed-form displacement relationships for other types of six-link 3R + 2P + 1C mechanisms can be obtained. The input-output equation derived may also be used to generate the input-output functions for five-link 2R + 2C + 1P mechanisms and four-link mechanisms with one revolute and three cylinder pairs.

Manufacturing Process for Circular-Arc Curvilinear Cylindrical Gears with Predesigned Fourth Order Transmission Error

2010 ◽  
Vol 37-38 ◽  
pp. 623-627 ◽  
Author(s):  
Jin Zhan Su ◽  
Zong De Fang
Keyword(s):  
Fourth Order ◽  
Gear Tooth ◽  
Transmission Error ◽  
Circular Arc ◽  
Cylindrical Gears ◽  
Polynomial Curve ◽  
Order Polynomial ◽  
Tooth Surfaces ◽  
The Stability ◽  
Fourth Order Polynomial

A fourth order transmission error was employed to improve the stability and tooth strength of circular-arc curvilinear cylindrical gears. The coefficient of fourth order polynomial curve was determined, the imaginary rack cutter which formed by the rotation of a head cutter and the imaginary pinion were introduced to determine the pinion and gear tooth surfaces, respectively. The numerical simulation of meshing shows: 1) the fourth order transmission error can be achieved by the proposed method; 2) the stability transmission can be performed by increasing the angle of the transfer point of the cycle of meshing; 3) the tooth fillet strength can be enhanced.

scholarly journals An Improved Analysis for the Harmonic Distortion of MOS Voltage-Controlled-Resistors

1997 ◽  
Vol 19 (4) ◽  
pp. 253-260
Author(s):  
Muhammad Taher Abuelma'atti
Keyword(s):  
Fourth Order ◽  
Harmonic Distortion ◽  
Voltage Characteristic ◽  
Current Voltage Characteristic ◽  
Mos Transistor ◽  
Current Voltage ◽  
Order Polynomial ◽  
Polynomial Expression ◽  
Analytical Expressions ◽  
Fourth Order Polynomial

In this paper, a fourth-order polynomial expression is obtained for the nonlinear current-voltage characteristic of a MOS transistor operating in the triode region. Using this expression, closed-form expressions are obtained for the second-, third- and fourth-harmonic distortion of a MOS voltage-controlled- resistors. The analytical expressions obtained in this paper can be used for a quantitative study of the effect of different parameters of the performance of MOS voltage-controlled-resistors.

On the Motion Characteristics of Tripode Joints. Part 1: General Case

1984 ◽  
Vol 106 (2) ◽  
pp. 228-234 ◽  
Author(s):  
E. Akbil ◽  
T. W. Lee
Keyword(s):  
Constant Velocity ◽  
Analytical Study ◽  
Orbital Motion ◽  
Analytical Investigation ◽  
Rigorous Proof ◽  
Input Output ◽  
Arbitrary Position ◽  
Motion Parameters ◽  
Motion Characteristics ◽  
Output Equation

This paper is concerned with the analytical investigation of the motion characteristics of tripode joints with general proportions and arbitrary position of shafts. It provides a rigorous proof that the tripode joint is not a true constant velocity joint except in ideal cases, and this is due to the inherent orbital motion of the output spider shaft. Algebraic derivations of the input-output equation and explicit relations for motion parameters are presented. From this general analytical study, some insights into the behavior of the tripode joint are observed and interpreted.

ENERGY-LIKE FUNCTIONS FOR SOME DISSIPATIVE CHAOTIC SYSTEMS

2005 ◽  
Vol 15 (08) ◽  
pp. 2507-2521 ◽  
Author(s):  
C. SARASOLA ◽  
A. D'ANJOU ◽  
F. J. TORREALDEA ◽  
A. MOUJAHID
Keyword(s):  
Phase Space ◽  
Dynamic Behavior ◽  
Fourth Order ◽  
Chaotic Systems ◽  
Quantitative Measure ◽  
Energy Functions ◽  
Dissipation Of Energy ◽  
Rossler System ◽  
Order Polynomial ◽  
Fourth Order Polynomial

Functions of the phase space variables that can considered as possible energy functions for a given family of dissipative chaotic systems are discussed. This kind of functions are interesting due to their use as an energy-like quantitative measure to characterize different aspects of dynamic behavior of associated chaotic systems. We have calculated quadratic energy-like functions for the cases of Lorenz, Chen, Lü–Chen and Chua, and show the patterns of dissipation of energy on their respective attractors. We also show that in the case of the Rössler system at least a fourth-order polynomial is required to properly represent its energy.

Displacement Analysis of a Special Case of the 7R, Single-Loop, Spatial Mechanism

1983 ◽  
Vol 105 (1) ◽  
pp. 78-87
Author(s):  
Hiram Albala ◽  
David Pessen
Keyword(s):  
Input Output ◽  
Fourth Degree ◽  
Displacement Analysis ◽  
Single Loop ◽  
Spatial Mechanism ◽  
Rotation Axes ◽  
Successive Rotation ◽  
Special Case ◽  
Output Equation

Based on the displacement equations for the general n-bar, single-loop spatial linkage, obtained elsewhere, the displacement analysis for a special case of the 7R spatial mechanism is carried out. In this mechanism the successive rotation axes are perpendicular to each other, the distances between axes 3-4, 4-5, 5-6, are equal and the offsets along axes 4 and 5 are zero, when input axis is labeled axis 1. In this fashion, there still remain nine free linkage parameters. Input-output equation is of the eighth-degree in the tangent of half the output angle. A particular case of this one, where all the distances between axes are equal and all the offsets along axes are zero, leads to an input-output equation of the fourth-degree in the same quantity, with a maximum of four closures. This mechanism resulted to be a double-rocker.

scholarly journals Parasupersymmetric Quantum Mechanics and Indices of Fredholm Operators

1997 ◽  
Vol 12 (15) ◽  
pp. 2725-2739 ◽  
Author(s):  
Ali Mostafazadeh
Keyword(s):  
Quantum Mechanics ◽  
Fourth Order ◽  
Classification Scheme ◽  
Algebraic Expression ◽  
Topological Invariants ◽  
Square Root ◽  
Fredholm Operators ◽  
Compatibility Conditions ◽  
Order Polynomial ◽  
Fourth Order Polynomial

The general features of the degeneracy structure of (p = 2) parasupersymmetric quantum mechanics are employed to yield a classification scheme for the form of the parasupersymmetric Hamiltonians. The method is applied to parasupersymmetric systems whose Hamiltonian is the square root of a fourth order polynomial in the generators of the parasupersymmetry. These systems are interesting to study for they lead to the introduction of a set of topological invariants very similar to the Witten indices of ordinary supersymmetric quantum mechanics. The topological invariants associated with parasupersymmetry are shown to be related to a pair of Fredholm operators satisfying two compatibility conditions. An explicit algebraic expression for the topological invariants of a class of parasupersymmetric systems is provided.

Some Intriguing Results Pertaining to Functionally Graded Columns

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
Isaac Elishakoff ◽  
Yohann Miglis
Keyword(s):  
Inverse Method ◽  
Vibration Mode ◽  
Flexural Rigidity ◽  
Axial Loading ◽  
Functionally Graded ◽  
Concentrated Load ◽  
Closed Form Solutions ◽  
Order Polynomial ◽  
Governing Differential Equation ◽  
Fourth Order Polynomial

Some intriguing results are reported in conjunction with closed form solutions obtained for a clamped-free vibrating inhomogeneous column under an axial concentrated load using the semi-inverse method. Fourth order polynomial is postulated for both the vibration mode shape and buckling displacement. Solution is provided for the flexural rigidity and the natural frequency. It is shown that, for each level of axial loading, there may exist up to five flexural rigidities satisfying the governing differential equation and boundary conditions.

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