Numerical Algorithms for Mapping Boundaries of Manipulator Workspaces

1994 ◽  
Author(s):  
Edward J. Haug ◽  
Chi-Mei Luh ◽  
Frederick A. Adkins ◽  
Jia-Yi Wang
Keyword(s):  
Computer Program ◽  
Continuation Method ◽  
Initial Point ◽  
Numerical Algorithms ◽  
Stewart Platform ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Bifurcation Points ◽  
Input And Output ◽  
Computational Implementation

Abstract Broadly applicable numerical algorithms for mapping boundaries of manipulator accessible output sets are developed and illustrated. Accessible output sets for planar and spatial manipulators are defined and analytical criteria determining their boundaries are stated, for both manipulators having the same number of input and output coordinates and redundantly controlled manipulators with a larger number of inputs than outputs. A method is presented for finding an initial point on the boundary of the accessible output set. From this point, a continuation method is used to map a family of one dimensional solution curves on the boundary. A method for finding tangents to solution curves at bifurcation points of continuation equations is presented and a computational implementation in the form of an experimental computer program is outlined. A planar redundantly controlled serial manipulator, a planar Stewart platform, and a spatial Stewart platform are analyzed, determining both the exterior boundary of the accessible output set and interior curves that represent local impediments to motion or controllability.

Numerical Algorithms for Mapping Boundaries of Manipulator Workspaces

1996 ◽  
Vol 118 (2) ◽  
pp. 228-234 ◽  
Author(s):  
E. J. Haug ◽  
Chi-Mei Luh ◽  
F. A. Adkins ◽  
Jia-Yi Wang
Keyword(s):  
Continuation Method ◽  
Initial Point ◽  
Numerical Algorithms ◽  
Companion Paper ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Bifurcation Points ◽  
Input And Output ◽  
Taylor Expansions ◽  
Tangent Calculation

Numerical algorithms for mapping boundaries of manipulator workspaces are developed and illustrated. Analytical criteria for boundaries of workspaces for both manipulators having the same number of input and output coordinates and redundantly controlled manipulators with a larger number of inputs than outputs are well known, but reliable numerical methods for mapping them have not been presented. In this paper, a numerical method is first developed for finding an initial point on the boundary. From this point, a continuation method that accounts for simple and multiple bifurcation of one-dimensional solution curves is developed. Second order Taylor expansions are derived for finding tangents to solution curves at simple bifurcation points of continuation equations and for characterizing barriers to control of manipulators. A recently developed method for tangent calculation at multiple bifurcation points is employed. A planar redundantly controlled serial manipulator is analyzed, determining both the exterior boundary of the accessible output set and interior curves that represent local impediments to motion control. Using these methods, more complex planar and spatial Stewart platform manipulators are analyzed in a companion paper.

Development of Method and Computer Program for Multistage Axial Compressor Design: Part II — Two-Dimensional Design and Validation Using CFD

2018 ◽  
Author(s):  
Milan Banjac ◽  
Milan V. Petrovic
Keyword(s):  
Computer Program ◽  
Pressure Ratio ◽  
Axial Compressor ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Initial Flow ◽  
One Dimensional ◽  
Compressor Design ◽  
Two Dimensional Flow ◽  
Line Design

Part I of this paper presents a method and a computer program for the mean design of multistage axial compressors. This second part describes a method and an additional computer routine that use the basic mean line design to create a fully two-dimensional flow solution and a compressor design. The two-dimensional solution according to a selected swirl vortex function is calculated using streamline curvature throughflow equations and spanwise distribution of losses. An iterative calculation procedure slightly reshapes the initial flow path in order to retain the desired input flow coefficients. Other variables such as stage loading parameters are changed in order to obtain the desired overall pressure ratio. A spanwise distribution of certain stage parameters can then be adjusted to achieve desired radial flow field variations. The basic one-dimensional input data can be varied at any moment to obtain a new one-dimensional result and the corresponding two-dimensional solution. A new output is created instantaneously and can be used for further CFD analysis, external throughflow, blade-to-blade flow computations or mechanical and vibration analysis.

Corrosion initiation time of steel reinforcement in a chloride environment—A one dimensional solution

1997 ◽  
Vol 39 (4) ◽  
pp. 739-759 ◽  
Author(s):  
P. Arora ◽  
B.N. Popov ◽  
B. Haran ◽  
M. Ramasubramanian ◽  
S. Popova ◽  
...  
Keyword(s):  
Steel Reinforcement ◽  
Initiation Time ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Corrosion Initiation ◽  
Corrosion Initiation Time ◽  
Chloride Environment

Mathematical Analysis for Off-Design Performance of Cryogenic Turboexpander

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Subrata K. Ghosh ◽  
R. K. Sahoo ◽  
Sunil K. Sarangi
Keyword(s):  
Pressure Ratio ◽  
Expansion Ratio ◽  
Flow Conditions ◽  
Flow Properties ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Design Performance ◽  
Fluid Properties ◽  
The Mean ◽  
Inlet Conditions

A study has been conducted to determine the off-design performance of cryogenic turboexpander. A theoretical model to predict the losses in the components of the turboexpander along the fluid flow path has been developed. The model uses a one-dimensional solution of flow conditions through the turbine along the mean streamline. In this analysis, the changes of fluid and flow properties between different components of turboexpander have been considered. Overall, turbine geometry, pressure ratio, and mass flow rate are input information. The output includes performance and velocity diagram parameters for any number of given speeds over a range of turbine pressure ratio. The procedure allows any arbitrary combination of fluid species, inlet conditions, and expansion ratio since the fluid properties are properly taken care of in the relevant equations. The computational process is illustrated with an example.

scholarly journals CALCULATION OF A JET ENGINE IN A COMPLEX PLANE USING A ONE-DIMENSIONAL SOLUTION OF THE NAVIER-STOKES EQUATION

2021 ◽  
Vol 7 (1(37)) ◽  
pp. 9-22
Author(s):  
E.G. Yakubovsky
Keyword(s):  
Speed Of Sound ◽  
Added Mass ◽  
Navier Stokes ◽  
Speed Of Light ◽  
Attached Mass ◽  
Additional Mass ◽  
Navier Stokes Equation ◽  
Dimensional Solution ◽  
Jet Engine ◽  
One Dimensional

This article proposes an algorithm to describe the motion of a body in the atmosphere using the added mass. Attached mass is the property of a medium to form additional mass, as I assume with a relativistic denominator at the speed of sound instead of the speed of light. Newton’s second law for added mass assumes two terms with the same speed, one is relativistic at the speed of light, and the other is attached mass with a relativistic denominator at the speed of sound. The use of a relativistic denominator with the speed of sound is a new idea that allows, according to well-known formulas with added mass, which is valid at low speeds of a body, to describe

First Paper: A General Approach to Hydraulic Lock

1967 ◽  
Vol 182 (1) ◽  
pp. 595-602 ◽  
Author(s):  
P. Dransfield ◽  
D. M. Bruce ◽  
M. Wadsworth
Keyword(s):  
Reynolds Equation ◽  
Lateral Force ◽  
Hydraulic Control ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Particular Solutions ◽  
Piston Cylinder ◽  
The One ◽  
Hydraulic Control System ◽  
General Method

The present state of knowledge on the hydraulic lock phenomena of oil hydraulic control system components is reviewed briefly. A general one-dimensional solution of the Reynolds equation which governs hydraulic lock is presented. The solution embraces the particular solutions of past workers, and allows ready solution for piston-cylinder configurations for which a one-dimensional solution is adequate. A general method for making full solutions of the Reynolds equation is presented, requiring the use of a digital computer for particular solutions. Pressure distribution, the lateral force on the piston which produces hydraulic lock, and the location of the lateral force can be obtained. The commonly occurring case of a single-land piston lying tilted in its bore is examined in detail. The limit of accuracy of a one-dimensional solution is clearly shown by illustrating the discrepancies between the one-dimensional and two-dimensional solutions for several configurations.

Approaches to the Numerical Estimates of Grid Convergence of NSE in the Presence of Singularities

2018 ◽  
Vol 19 (3-4) ◽  
pp. 281-287
Author(s):  
Chenguang Zhang ◽  
Krishnaswamy Nandakumar
Keyword(s):  
Numerical Algorithms ◽  
Nonlinear Problems ◽  
Order Of Accuracy ◽  
One Dimensional ◽  
Accuracy Order ◽  
Uniform Grids ◽  
Grid Convergence ◽  
The Common ◽  
Spatial Grid ◽  
Different Levels

AbstractEvaluating the order of accuracy (order) is an integral part of the development and application of numerical algorithms. Apart from theoretical functional analysis to place bounds on error estimates, numerical experiments are often essential for nonlinear problems to validate the estimates in a reliable answer. The common workflow is to apply the algorithm using successively finer temporal/spatial grid resolutions ${\delta _i}$, measure the error ${\isin _i}$ in each solution against the exact solution, the order is then obtained as the slope of the line that fits $(\log {\isin _i}, \log {\delta _i})$. We show that if the problem has singularities like divergence to infinity or discontinuous jump, this common workflow underestimates the order if solution at regions around the singularity is used. Several numerical examples with different levels of complexity are explored. A simple one-dimensional theoretical model shows it is impossible to numerically evaluate the order close to singularity on uniform grids.

The backward problem of parabolic equations with the measurements on a discrete set

2020 ◽  
Vol 28 (1) ◽  
pp. 137-144 ◽  
Author(s):  
Jin Cheng ◽  
Yufei Ke ◽  
Ting Wei
Keyword(s):  
Parabolic Equations ◽  
Numerical Approximation ◽  
Cross Validation ◽  
Continuation Method ◽  
Measurement Data ◽  
Initial Value ◽  
One Dimensional ◽  
Backward Problem ◽  
The One ◽  
Validation Rule

AbstractThe backward problems of parabolic equations are of interest in the study of both mathematics and engineering. In this paper, we consider a backward problem for the one-dimensional heat conduction equation with the measurements on a discrete set. The uniqueness for recovering the initial value is proved by the analytic continuation method. We discretize this inverse problem by a finite element method to deduce a severely ill-conditioned linear system of algebra equations. In order to overcome the ill-posedness, we apply the discrete Tikhonov regularization with the generalized cross validation rule to obtain a stable numerical approximation to the initial value. Numerical results for three examples are provided to show the effect of the measurement data.

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