Singularity Analysis of Spatial Mechanisms Using Dual Polynomials and Complex Dual Numbers

1999 ◽  
Vol 121 (2) ◽  
pp. 200-205 ◽  
Author(s):  
H. H. Cheng ◽  
S. Thompson
Keyword(s):  
Numerical Solutions ◽  
Polynomial Equation ◽  
Singularity Analysis ◽  
Polynomial Equations ◽  
Dual Numbers ◽  
Output Displacement ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
Physical Insight ◽  
Language Environment

Complex dual numbers wˇ = x + iy + εu + iεv which form a commutative ring are introduced in this paper to solve dual polynomial equations numerically. It is shown that the singularities of a dual input-output displacement polynomial equation of a mechanism correspond to its singularity positions. This new method of identifying singularities provides clear physical insight into the geometry of the singular configurations of a mechanism, which is illustrated through analysis of special configurations of the RCCC spatial mechanism. Numerical solutions for dual polynomial equations and complex dual numbers are conveniently implemented in the CH language environment for analysis of the RCCC spatial mechanism.

Dual Polynomials and Complex Dual Numbers for Analysis of Spatial Mechanisms

1996 ◽  
Author(s):  
Harry H. Cheng ◽  
Sean Thompson
Keyword(s):  
Numerical Solutions ◽  
Polynomial Equation ◽  
Mathematical Tool ◽  
Polynomial Equations ◽  
Dual Numbers ◽  
Output Displacement ◽  
Spatial Mechanism ◽  
Dual Number ◽  
Spatial Mechanisms ◽  
Language Environment

Abstract Complex dual numbers w̌1=x1+iy1+εu1+iεv1 which form a commutative ring are for the first time introduced in this paper. Arithmetic operations and functions of complex dual numbers are defined. Complex dual numbers are used to solve dual polynomial equations. It is shown that the singularities of a dual input-output displacement polynomial equation of a mechanism correspond to its singularity positions. This new method of identifying singularities provides clear physical insight into the geometry of the singular configurations of a mechanism, which is illustrated through analysis of special configurations of the RCCC spatial mechanism. Numerical solutions for dual polynomial equations and complex dual numbers are conveniently implemented in the CH language environment for analysis of the RCCC spatial mechanism. Like the dual number, the complex dual number is a useful mathematical tool for analytical and numerical treatment of spatial mechanisms.

Computer-Aided Displacement Analysis of Spatial Mechanisms

1994 ◽  
Author(s):  
Sean Thompson ◽  
Harry H. Cheng
Keyword(s):  
Programming Languages ◽  
Design Automation ◽  
Data Type ◽  
Complex Numbers ◽  
Dual Numbers ◽  
Displacement Analysis ◽  
Spatial Mechanism ◽  
Programming Paradigm ◽  
Spatial Mechanisms ◽  
Programming Techniques

Abstract Recently, Cheng (1993) introduced the CH programming language. CH is designed to be a superset of ANSI C with all programming features of FORTRAN. Many programming features in CH are specifically designed and implemented for design automation. Handling dual number as a basic built-in data type in the language is one example. Formulas with dual numbers can be translated into CH programming statements as easily as formulas with real and complex numbers. In this paper we will show that both formulation and programming with dual numbers are remarkably simple for analysis of complicated spatial mechanisms within the programming paradigm of CH. With computational capabilities for dual formulas in mind, formulas for analysis of spatial mechanisms are derived differently from those intended for implementation in computer programming languages without dual data type. We will demonstrate some formulation and programming techniques in the programming paradigm of CH through a displacement analysis of the RCRCR five-link spatial mechanism. A CH program that can obtain both numerical and graphical results for complete displacement analysis of the RCRCR mechanism will be presented.

On the shaft locations of two contra-rotating counterweights for balancing spatial mechanisms

1997 ◽  
Vol 211 (8) ◽  
pp. 567-578 ◽  
Author(s):  
S-T Chiou ◽  
J-C Tzou
Keyword(s):  
Root Mean Square ◽  
Mean Square ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
Crank Mechanism ◽  
Frequency Term ◽  
Shaking Moment

It has been shown in a previous work that a frequency term of the shaking force of spatial mechanisms, whose hodograph is proved to be an ellipse, can be eliminated by a pair of contrarotating counterweights. In this work, it is found that the relevant frequency term of the shaking moment is minimized if the balancing shafts are coaxial at the centre of a family of ellipsoids, called isomomental ellipsoids, with respect to (w.r.t.) any point on an ellipsoid, as is also the root mean square (r.m.s.) of the relevant frequency term of the shaking moment. It can also be minimized even though the location of either shaft, but not both, is chosen arbitrarily on a plane. The location of the second shaft is then determinate. In order to locate the centre, a derivation for the theory of isomomental ellipsoids of a frequency term of the shaking moment of spatial mechanisms is given. It is shown that the r.m.s. of a frequency term shaking moment of a spatial mechanism w.r.t. the concentric centre of the isomomental ellipsoids is the minimum. Examples of a seven-link 7-R spatial linkage and a spatial slider-crank mechanism are included.

Closed-Form Displacement Relations of a Five-Link R-R-C-C-R Spatial Mechanism

1971 ◽  
Vol 93 (1) ◽  
pp. 221-226 ◽  
Author(s):  
A. H. Soni ◽  
P. R. Pamidi
Keyword(s):  
Closed Form ◽  
Polynomial Equation ◽  
Input Output ◽  
Degree Polynomial ◽  
Spatial Mechanism ◽  
Dual Number ◽  
Numerical Example

Using (3 × 3) matrices with dual-number elements, closed form displacement relationships are derived for a spatial five-link R-R-C-C-R mechanism. The input-output closed form displacement relationship is an eighth degree polynomial equation. A numerical example is presented.

Kinematic Analysis of Spatial Mechanisms by Means of Screw Coordinates. Part 2—Analysis of Spatial Mechanisms

1971 ◽  
Vol 93 (1) ◽  
pp. 67-73 ◽  
Author(s):  
M. S. C. Yuan ◽  
F. Freudenstein ◽  
L. S. Woo
Keyword(s):  
Computer Program ◽  
Kinematic Analysis ◽  
Static Force ◽  
Single Degree Of Freedom ◽  
Numerical Examples ◽  
Spatial Mechanism ◽  
Single Degree ◽  
Spatial Mechanisms ◽  
Torque Analysis ◽  
Basic Concepts

The basic concepts of screw coordinates described in Part I are applied to the numerical kinematic analysis of spatial mechanisms. The techniques are illustrated with reference to the displacement, velocity, and static-force-and-torque analysis of a general, single-degree-of-freedom spatial mechanism: a seven-link mechanism with screw pairs (H)7. By specialization the associated computer program is capable of analyzing many other single-loop spatial mechanisms. Numerical examples illustrate the results.

Integrated Kinematic and Dynamic Optimal Synthesis of Spatial Mechanisms

1987 ◽  
Author(s):  
A. J. Kakatsios ◽  
S. J. Tricamo
Keyword(s):  
Nonlinear Programming ◽  
Simultaneous Optimization ◽  
Programming Formulation ◽  
Joint Torques ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
Structural Error ◽  
Integrated Technique ◽  
Driving Torque ◽  
Shaking Moment

Abstract A novel integrated technique permitting the simultaneous optimization of kinematic and dynamic characteristics in the synthesis of spatial mechanisms is shown. The nonlinear programming formulation determines mechanism variables which simultaneously minimize the maximum values of bearing reactions, joint torques, driving torque, shaking moment, and shaking force while constraining the maximum kinematic structural error to a prescribed bound. The method is applied to the design of a path generating RRSS spatial mechanism with prescribed input link timing. Dynamic reactions in the mechanisms synthesized using the integrated technique were substantially reduced when compared to those of a mechanism synthesized to satisfy only the specified kinematic conditions.

A PHIGS-Based Graphics Input Interface for Spatial Mechanism Design

1987 ◽  
Author(s):  
B. R. Thatch ◽  
A. Myklebust
Keyword(s):  
Data Entry ◽  
Interactive Graphics ◽  
Mechanism Synthesis ◽  
Spatial Mechanism ◽  
Input Interface ◽  
New Methods ◽  
Spatial Mechanisms ◽  
Six Dof ◽  
Device Independence ◽  
Definition Of

Abstract Creation of input specifications for synthesis or analysis of spatial mechanisms can be a significant problem. A graphics preprocessor which interactively assists in the definition of spatial mechanism problems is described. New methods of depth cucing and six DOF data entry are presented. To achieve graphics device-independence, the proposed graphics standard PHIGS (Programmer’s Hierarchical Interactive Graphics System) is used. Examples of application are presented including generation of input commands for Integrated Mechanisms Program (IMP) and generation of input for spatial mechanism synthesis routines.

THE KINEMATIC SYNTHESIS OF STEERING MECHANISMS

2000 ◽  
Vol 24 (3-4) ◽  
pp. 453-476 ◽  
Author(s):  
Jin Yao ◽  
Jorge Angeles
Keyword(s):  
Polynomial Equation ◽  
Global Optimum ◽  
Polynomial Equations ◽  
Kinematic Synthesis ◽  
Local Optima ◽  
Speed Reduction ◽  
Design Variables ◽  
Transmission Quality ◽  
Four Bar Linkage ◽  
Maximum Transmission

We propose a computational-kinematics approach based on elimination procedures to synthesize a steering four-bar linkage. In this regard, we aim at minimizing the root-mean square error of the synthesized linkage in meeting the steering condition over a number of linkage configurations within the linkage range of motion. A minimization problem is thus formulated, whose normality conditions lead to two polynomial equations in two unknown design variables. Upon eliminating one of these two variables, a monovariate polynomial equation is obtained, whose roots yield all locally-optimum linkages. From these roots, the global optimum, as well as unfeasible local optima, are readily identified. The global optimum, however, turns out to be impractical because of the large differences in its link lengths, which we refer to as dimensional unbalance. To cope with this drawback, we use a kinematically-equivalent focal mechanism, i.e., a six-bar linkage with an input-output function identical to that of the four-bar linkage. Given that the synthesized linkage requires a rotational input, as opposed to most existing steering linkages, which require a translational input, we propose a spherical four-bar linkage to drive the steering linkage. The spherical linkage is synthesized so as to yield a speed reduction as close as possible to 2:1 and to have a maximum transmission quality.

ANALYTICAL MODELING OF DRAIN CURRENT, CAPACITANCE AND TRANSCONDUCTANCE IN SYMMETRIC DOUBLE-GATE MOSFETs CONSIDERING QUANTUM EFFECTS

2013 ◽  
Vol 12 (01) ◽  
pp. 1350005 ◽  
Author(s):  
VIMALA PALANICHAMY ◽  
N. B. BALAMURUGAN
Keyword(s):  
Numerical Solutions ◽  
Inversion Layer ◽  
Drain Current ◽  
Quantum Effects ◽  
Schrodinger Equations ◽  
Double Gate ◽  
Schrödinger Equations ◽  
Inversion Charge ◽  
Physical Insight ◽  
Quantum Mechanical Effects

An analytical model for double-gate (DG) MOSFETs considering quantum mechanical effects is proposed in this paper. Schrödinger and Poisson's equations are solved simultaneously using a variational approach. Solving the Poisson and Schrödinger equations simultaneously reveals quantum effects (QME) that influence the performance of DG MOSFETs. This model is developed to provide an analytical expression for inversion charge distribution function for all regions of device operation. This expression is used to calculate the other important parameters like inversion layer centroid, inversion charge, gate capacitance, drain current and transconductance. We systematically evaluate and analyze the parameters of DG MOSFETs considering QME. The analytical solutions are simple, accurate and provide good physical insight into the quantization caused by quantum confinement under various gate biases. The analytical results of this model are verified by comparing the data obtained with one-dimensional self-consistent numerical solutions of Poisson and Schrödinger equations known as SCHRED.

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