Singularity Analysis of an Extensible Kinematic Architecture: Assur Class N, Order N−1

2008 ◽  
Vol 1 (1) ◽  
Author(s):  
David H. Myszka ◽  
Andrew P. Murray ◽  
James P. Schmiedeler
Keyword(s):  
Singularity Analysis ◽  
Closed Contour ◽  
Rigid Link ◽  
Contour Shape ◽  
Condensed Form

This paper presents an analysis to create a general singularity condition for a mechanism that contains a deformable closed contour. This kinematic architecture is particularly relevant to rigid-link, shape-changing mechanisms. Closed contour shape-changing mechanisms will be shown to belong to the Assur classification because of the pattern of interconnections among the links. The general singularity equations are reduced to a condensed form, which allows geometric relationships to be readily detected. The analysis is repeated for alternative input links. A method for formulating the singularity condition for an Assur Class N, knowing the condition for a Class N−1 mechanism, is given. This approach is illustrated with several examples.

Singularity Analysis of Rigid-Body, Closed-Loop, Shape-Changing Mechanisms

2008 ◽  
Author(s):  
David Myszka ◽  
Andrew Murray ◽  
James Schmiedeler
Keyword(s):  
Rigid Body ◽  
Body Shape ◽  
Closed Loop ◽  
Singularity Analysis ◽  
Closed Contour ◽  
Condensed Form ◽  
Loop Shape

This paper presents an analysis to create a general singularity condition for a mechanism that contains a deformable closed contour. This kinematic architecture is widely used in rigid-body shape changing mechanisms. The general singularity equation is reduced to a condensed form, which allows geometric relationships to be readily detected. A method for formulating the singularity condition for a mechanism with N links in the closed contour, knowing the condition for the N − 1 mechanism, is also given.

scholarly journals Cues to closed-contour shape revealed using visual search.

2015 ◽  
Vol 15 (12) ◽  
pp. 1024
Author(s):  
David Badcock ◽  
Krystle Haley ◽  
Edwin Dickinson
Keyword(s):  
Visual Search ◽  
Closed Contour ◽  
Contour Shape

scholarly journals Singularity analysis and analytic solutions for the Benney–Gjevik equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Genly Leon ◽  
P. G. L. Leach
Keyword(s):  
Evolution Equations ◽  
Singularity Analysis ◽  
Analytic Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Painlevé Test ◽  
Wave Solutions ◽  
Algebraic Solutions

Abstract We apply the Painlevé test for the Benney and the Benney–Gjevik equations, which describe waves in falling liquids. We prove that these two nonlinear 1 + 1 evolution equations pass the singularity test for the travelling-wave solutions. The algebraic solutions in terms of Laurent expansions are presented.

scholarly journals Task-space regulation of rigid-link electrically-driven robots with uncertain kinematics using neural networks

2021 ◽  
Vol 54 (1-2) ◽  
pp. 102-115
Author(s):  
Wenhui Si ◽  
Lingyan Zhao ◽  
Jianping Wei ◽  
Zhiguang Guan
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Control Method ◽  
Joint Space ◽  
Robot Kinematics ◽  
Rbf Neural Networks ◽  
Task Space ◽  
Actuator Dynamics ◽  
Rigid Link ◽  
On Line

Extensive research efforts have been made to address the motion control of rigid-link electrically-driven (RLED) robots in literature. However, most existing results were designed in joint space and need to be converted to task space as more and more control tasks are defined in their operational space. In this work, the direct task-space regulation of RLED robots with uncertain kinematics is studied by using neural networks (NN) technique. Radial basis function (RBF) neural networks are used to estimate complicated and calibration heavy robot kinematics and dynamics. The NN weights are updated on-line through two adaptation laws without the necessity of off-line training. Compared with most existing NN-based robot control results, the novelty of the proposed method lies in that asymptotic stability of the overall system can be achieved instead of just uniformly ultimately bounded (UUB) stability. Moreover, the proposed control method can tolerate not only the actuator dynamics uncertainty but also the uncertainty in robot kinematics by adopting an adaptive Jacobian matrix. The asymptotic stability of the overall system is proven rigorously through Lyapunov analysis. Numerical studies have been carried out to verify efficiency of the proposed method.

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