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.

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.

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 The faint young Sun problem revisited with a 3-D climate–carbon model – Part 1

2014 ◽  
Vol 10 (2) ◽  
pp. 697-713 ◽  
Author(s):  
G. Le Hir ◽  
Y. Teitler ◽  
F. Fluteau ◽  
Y. Donnadieu ◽  
P. Philippot
Keyword(s):  
Radiative Forcing ◽  
General Circulation ◽  
Freezing Point ◽  
Climatic Factors ◽  
General Circulation Models ◽  
Companion Paper ◽  
One Dimensional ◽  
Carbon Dioxide Concentrations ◽  
Wide Range ◽  
High Concentrations

Abstract. During the Archaean, the Sun's luminosity was 18 to 25% lower than the present day. One-dimensional radiative convective models (RCM) generally infer that high concentrations of greenhouse gases (CO2, CH4) are required to prevent the early Earth's surface temperature from dropping below the freezing point of liquid water and satisfying the faint young Sun paradox (FYSP, an Earth temperature at least as warm as today). Using a one-dimensional (1-D) model, it was proposed in 2010 that the association of a reduced albedo and less reflective clouds may have been responsible for the maintenance of a warm climate during the Archaean without requiring high concentrations of atmospheric CO2 (pCO2). More recently, 3-D climate simulations have been performed using atmospheric general circulation models (AGCM) and Earth system models of intermediate complexity (EMIC). These studies were able to solve the FYSP through a large range of carbon dioxide concentrations, from 0.6 bar with an EMIC to several millibars with AGCMs. To better understand this wide range in pCO2, we investigated the early Earth climate using an atmospheric GCM coupled to a slab ocean. Our simulations include the ice-albedo feedback and specific Archaean climatic factors such as a faster Earth rotation rate, high atmospheric concentrations of CO2 and/or CH4, a reduced continental surface, a saltier ocean, and different cloudiness. We estimated full glaciation thresholds for the early Archaean and quantified positive radiative forcing required to solve the FYSP. We also demonstrated why RCM and EMIC tend to overestimate greenhouse gas concentrations required to avoid full glaciations or solve the FYSP. Carbon cycle–climate interplays and conditions for sustaining pCO2 will be discussed in a companion paper.

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.

scholarly journals Action minimization and macroscopic interface motion under forced displacement

2018 ◽  
Vol 24 (2) ◽  
pp. 765-792 ◽  
Author(s):  
Panagiota Birmpa ◽  
Dimitrios Tsagkarogiannis
Keyword(s):  
Stochastic Process ◽  
Evolution Equation ◽  
Fixed Time ◽  
Companion Paper ◽  
The Other ◽  
Final Position ◽  
Dimensional Model ◽  
Interface Motion ◽  
One Dimensional ◽  
Non Local

We study an one dimensional model where an interface is the stationary solution of a mesoscopic non local evolution equation which has been derived by a microscopic stochastic spin system. Deviations from this evolution equation can be quantified by obtaining the large deviations cost functional from the underlying stochastic process. For such a functional, derived in a companion paper, we investigate the optimal way for a macroscopic interface to move from an initial to a final position distant by R within fixed time T. We find that for small values of R∕T the interface moves with a constant speed, while for larger values there appear nucleations of the other phase ahead of the front.

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