scholarly journals A Task-Driven Approach to Optimal Synthesis of Planar Four-Bar Linkages for Extended Burmester Problem

2017 ◽  
Vol 9 (6) ◽  
Author(s):  
Shrinath Deshpande ◽  
Anurag Purwar
Keyword(s):  
Geometric Constraints ◽  
Nonlinear Constraints ◽  
Unified Approach ◽  
Revolute Joints ◽  
Special Cases ◽  
Approximate Synthesis ◽  
Linear And Nonlinear Constraints ◽  
Linear And Nonlinear ◽  
The One ◽  
Fitting Error

The classic Burmester problem is concerned with computing dimensions of planar four-bar linkages consisting of all revolute joints for five-pose problems. We define extended Burmester problem as the one where all types of planar four-bars consisting of dyads of type RR, PR, RP, or PP (R: revolute, P: prismatic) and their dimensions need to be computed for n-geometric constraints, where a geometric constraint is an algebraically expressed constraint on the pose, pivots, or something equivalent. In addition, we extend it to linear, nonlinear, exact, and approximate constraints. This extension also includes the problems when there is no solution to the classic Burmester problem, but designers would still like to design a four-bar that may come closest to capturing their intent. Machine designers often grapple with such problems while designing linkage systems where the constraints are of different varieties and usually imprecise. In this paper, we present (1) a unified approach for solving the extended Burmester problem by showing that all linear and nonlinear constraints can be handled in a unified way without resorting to special cases, (2) in the event of no or unsatisfactory solutions to the synthesis problem, certain constraints can be relaxed, and (3) such constraints can be approximately satisfied by minimizing the algebraic fitting error using Lagrange multiplier method. We present a new algorithm, which solves new problems including optimal approximate synthesis of Burmester problem with no exact solutions.

scholarly journals Incorporating User Input Into Optimal Constraining Procedures for Survey Estimates

2013 ◽  
Vol 29 (3) ◽  
pp. 375-396 ◽  
Author(s):  
Matthew Williams ◽  
Emily Berg
Keyword(s):  
First Principles ◽  
Contingency Table ◽  
Nonlinear Constraints ◽  
Constrained Estimation ◽  
Data Set ◽  
User Input ◽  
Optimal Estimates ◽  
Linear And Nonlinear Constraints ◽  
Linear And Nonlinear ◽  
Survey Estimates

Abstract We examine the incorporation of analyst input into the constrained estimation process. In the calibration literature, there are numerous examples of estimators with “optimal” properties. We show that many of these can be derived from first principles. Furthermore, we provide mechanisms for injecting user input to create user-constrained optimal estimates. We include derivations for common deviance measures with linear and nonlinear constraints and we demonstrate these methods on a contingency table and a simulated survey data set. R code and examples are available at https://github.com/mwilli/Constrained-estimation.git.

Robust Constrained Optimization of Short- and Long-Term Net Present Value for Closed-Loop Reservoir Management

SPE Journal ◽  
2012 ◽  
Vol 17 (03) ◽  
pp. 849-864 ◽  
Author(s):  
C.. Chen ◽  
G.. Li ◽  
A.C.. C. Reynolds
Keyword(s):  
Life Cycle ◽  
Net Present Value ◽  
Production Optimization ◽  
Nonlinear Constraints ◽  
Present Value ◽  
Short Term ◽  
Linear And Nonlinear Constraints ◽  
Linear And Nonlinear ◽  
Reservoir Description

Summary In this paper, we develop an efficient algorithm for production optimization under linear and nonlinear constraints and an uncertain reservoir description. The linear and nonlinear constraints are incorporated into the objective function using the augmented Lagrangian method, and the bound constraints are enforced using a gradient-projection trust-region method. Robust long-term optimization maximizes the expected life-cycle net present value (NPV) over a set of geological models, which represent the uncertainty in reservoir description. Because the life-cycle optimal controls may be in conflict with the operator's objective of maximizing short-time production, the method is adapted to maximize the expectation of short-term NPV over the next 1 or 2 years subject to the constraint that the life-cycle NPV will not be substantially decreased. The technique is applied to synthetic reservoir problems to demonstrate its efficiency and robustness. Experiments show that the field cannot always achieve the optimal NPV using the optimal well controls obtained on the basis of a single but uncertain reservoir model, whereas the application of robust optimization reduces this risk significantly. Experimental results also show that robust sequential optimization on each short-term period is not able to achieve an expected life-cycle NPV as high as that obtained with robust long-term optimization.

A Task-Driven Approach to Optimal Synthesis of Planar Four-Bar Linkages for Extended Burmester Problem

2017 ◽  
Author(s):  
Shrinath Deshpande ◽  
Anurag Purwar
Keyword(s):  
Linear Constraints ◽  
Image Space ◽  
Geometric Constraints ◽  
Motion Generation ◽  
Quadratic Constraints ◽  
Special Cases ◽  
Non Linear ◽  
Approximate Synthesis ◽  
Step Algorithm ◽  
Value Decomposition

The classic Burmester problem is concerned with computing dimensions of planar four-bar linkages consisting of all revolute joints for five-pose problems. In the context of motion generation, each pose can be seen as a constraint that the coupler of a planar four-bar mechanism needs to interpolate or approximate through. We define extended Burmester problem as the one where all types of planar four-bars consisting of dyads of type RR, PR, RP, or PP (R: revolute, P: prismatic) and their dimensions need to be computed for n-geometric-constraints, where a geometric constraint can be an algebraically expressed constraint on the pose, or location of the fixed or moving pivots or something equivalent. In addition, we include both linear and non-linear and exact and approximate constraints. This extension also includes the problems where there is no solution to the classic Burmester problem, but designers would still like to design a four-bar that may come closest to capturing their intent. Such problems are representative of the problems that machine designers grapple with while designing linkage systems for a variety of constraints, which are not merely a set of poses. Recently, we have derived a unified form of geometric constraints of all types of dyads (RR, RP, PR, and PP) in the framework of kinematic mapping and planar quaternions, which map to generalized manifolds (G-manifolds) in the image space of planar displacements. The given poses map to points in the image space. Thus, the problem of synthesis is reduced to minimizing the algebraic error of fitting between the image points and the G-manifolds. We have also created a simple, two-step algorithm using Singular Value Decomposition (SVD) for the least-squares fitting of the manifolds, which yields a candidate space of solution. By imposing two fundamental quadratic constraints on the candidate solutions, we are able to simultaneously determine both the type and dimensions of the planar four-bar linkages. In this paper, we present 1) a unified approach for solving the extended Burmester problem by showing that all linear- and non-linear constraints can be handled in a unified way without resorting to special cases, 2) in the event of no or unsatisfactory solutions to the synthesis problem certain constraints can be relaxed, and 3) such constraints can be approximately satisfied by minimizing the algebraic fitting error using Lagrange Multiplier method. In doing so, we generalize our earlier formulation and present a new algorithm, which solves new problems including optimal approximate synthesis of Burmester problem with no exact solutions.

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