Motion Analysis of Manipulators With Uncertainty in Kinematic Parameters

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Vahid Nazari ◽  
Leila Notash
Keyword(s):  
Exact Solution ◽  
Motion Analysis ◽  
Parametric Method ◽  
Coefficient Matrix ◽  
Linear Functions ◽  
Kinematic Parameters ◽  
Interval Linear ◽  
Novel Method ◽  
Motion Performance ◽  
Interval Linear Systems

In this article, a novel method for characterizing the exact solution for interval linear systems is presented. In the proposed method, the entries of the interval coefficient matrix and interval right-hand side vector are formulated as linear functions of two or three parameters. The parameter groups for two- and three-parameter cases are identified. The exact solution is characterized using the solution sets corresponding to the parameter groups. The parametric method is then employed in the motion analysis of manipulators considering the uncertainty in kinematic parameters. Example manipulators are used to show the implementation of the method and the effect of uncertainty in the motion performance.

Investigation of Wrench Accuracy for Parallel Manipulators

2016 ◽  
Author(s):  
Leila Notash
Keyword(s):  
Parallel Manipulators ◽  
Coefficient Matrix ◽  
Solution Set ◽  
Output Vector ◽  
Discrete Method ◽  
Interval Linear ◽  
Closed Line ◽  
Interval Linear Systems ◽  
Real Linear ◽  
The Given

In this paper, the wrench accuracy for parallel manipulators is examined and the solution sets of actuator forces/torques are investigated under variations in parameters and data. The subset of solution set that produces platform wrenches within the required lower and upper bounds are modeled using discrete and analytical methods. In addition, the formulation of the solutions that provide any platform wrench within the defined interval is examined. Intersection of these two sets, if any, results in the given interval platform wrench. Moreover, the dependency among the entries of the interval linear systems and its effect on the solution set is considered. The discrete method is based on the discretization of solution set enclosure and validation at each increment, or the collection of the solutions of real linear relations for the discretized interval coefficient matrix and output vector. The analytical method for each solution set is based on the intersection of the pertinent closed half-spaces or the assembly of closed line segments that encompass the solution. Implementation of the methods to identify the solution for actuator forces/torques is presented on example parallel manipulators.

Farkas-type theorems for interval linear systems

2014 ◽  
Vol 63 (7) ◽  
pp. 1390-1400 ◽  
Author(s):  
Mengxue Xia ◽  
Wei Li ◽  
Haohao Li
Keyword(s):  
Linear Systems ◽  
Interval Linear ◽  
Interval Linear Systems

On the Solutions of Interval Systems for Under-Constrained and Redundant Parallel Manipulators

2017 ◽  
Vol 9 (6) ◽  
Author(s):  
Leila Notash
Keyword(s):  
Least Squares ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Constrained Systems ◽  
Solution Set ◽  
Least Squares Solution ◽  
Interval Linear ◽  
Interval Linear Systems ◽  
Parameter Dependency ◽  
Interval Systems

For under-constrained and redundant parallel manipulators, the actuator inputs are studied with bounded variations in parameters and data. Problem is formulated within the context of force analysis. Discrete and analytical methods for interval linear systems are presented, categorized, and implemented to identify the solution set, as well as the minimum 2-norm least-squares solution set. The notions of parameter dependency and solution subsets are considered. The hyperplanes that bound the solution in each orthant characterize the solution set of manipulators. While the parameterized form of the interval entries of the Jacobian matrix and wrench produce the minimum 2-norm least-squares solution for the under-constrained and over-constrained systems of real matrices and vectors within the interval Jacobian matrix and wrench vector, respectively. Example manipulators are used to present the application of methods for identifying the solution and minimum norm solution sets for actuator forces/torques.

scholarly journals Exact Solution for Viscoelastic Flow in Pipe and Experimental Validation

Polymers ◽  
2022 ◽  
Vol 14 (2) ◽  
pp. 334
Author(s):  
Ekaterina Vachagina ◽  
Nikolay Dushin ◽  
Elvira Kutuzova ◽  
Aidar Kadyirov
Keyword(s):  
Experimental Data ◽  
Exact Solution ◽  
Analytical Methods ◽  
Experimental Validation ◽  
Parametric Method ◽  
Fluid Flows ◽  
Parametric Representation ◽  
Viscoelastic Flow ◽  
Exponential Form ◽  
Image Velocimetry

The development of analytical methods for viscoelastic fluid flows is challenging. Currently, this problem has been solved for particular cases of multimode differential rheological equations of media state (Giesekus, the exponential form of Phan-Tien-Tanner, eXtended Pom-Pom). We propose a parametric method that yields solutions without additional assumptions. The method is based on the parametric representation of the unknown velocity functions and the stress tensor components as a function of coordinate. Experimental flow visualization based on the SIV (smoke image velocimetry) method was carried out to confirm the obtained results. Compared to the Giesekus model, the experimental data are best predicted by the eXtended Pom-Pom model.

Motion Analysis in Delirium: A Novel Method of Clarifying Motoric Subtypes

Neurocase ◽  
2007 ◽  
Vol 13 (4) ◽  
pp. 272-277 ◽  
Author(s):  
Maeve Leonard ◽  
Alan Godfrey ◽  
Martin Silberhorn ◽  
Marion Conroy ◽  
Sinead Donnelly ◽  
...  
Keyword(s):  
Motion Analysis ◽  
Novel Method
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