scholarly journals Geometric Approach to the Realization of Planar Elastic Behaviors With Mechanisms Having Four Elastic Components

2018 ◽  
Vol 10 (4) ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Sufficient Conditions ◽  
Geometric Approach ◽  
Necessary And Sufficient Conditions ◽  
Elastic Component ◽  
Elastic Behavior ◽  
Parallel Mechanisms ◽  
Compliant Joints ◽  
Necessary And Sufficient ◽  
Selection Of

This paper addresses the passive realization of any selected planar elastic behavior with redundant elastic manipulators. The class of manipulators considered are either serial mechanisms having four compliant joints or parallel mechanisms having four springs. Sets of necessary and sufficient conditions for mechanisms in this class to passively realize an elastic behavior are presented. The conditions are interpreted in terms of mechanism geometry. Similar conditions for nonredundant cases are highly restrictive. Redundancy yields a significantly larger space of realizable elastic behaviors. Construction-based synthesis procedures for planar elastic behaviors are also developed. In each, the selection of the mechanism geometry and the selection of joint/spring stiffnesses are completely decoupled. The procedures require that the geometry of each elastic component be selected from a restricted space of acceptable candidates.

scholarly journals Geometric Construction-Based Realization of Planar Elastic Behaviors With Parallel and Serial Manipulators

2017 ◽  
Vol 9 (5) ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Elastic Properties ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Geometric Construction ◽  
Elastic Component ◽  
Elastic Behavior ◽  
Serial Manipulators ◽  
New Construction ◽  
Necessary And Sufficient ◽  
Serial Mechanism

This paper addresses the passive realization of any selected planar elastic behavior with a parallel or a serial manipulator. Sets of necessary and sufficient conditions for a mechanism to passively realize an elastic behavior are presented. These conditions completely decouple the requirements on component elastic properties from the requirements on mechanism kinematics. The restrictions on the set of elastic behaviors that can be realized with a mechanism are described in terms of acceptable locations of realizable elastic behavior centers. Parallel–serial mechanism pairs that realize identical elastic behaviors (dual elastic mechanisms) are described. New construction-based synthesis procedures for planar elastic behaviors are developed. Using these procedures, one can select the geometry of each elastic component from a restricted space of kinematically allowable candidates. With each selection, the space is further restricted until the desired elastic behavior is achieved.

On the Preservation of Root Numbers and the Behavior of Weil Characters under Reciprocity Equivalence

1997 ◽  
Vol 40 (4) ◽  
pp. 402-415
Author(s):  
Jenna P. Carpenter
Keyword(s):  
Number Field ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Witt Ring ◽  
Root Numbers ◽  
Local Root ◽  
Necessary And Sufficient ◽  
Selection Of ◽  
Local Root Numbers

AbstractThis paper studies how the local root numbers and the Weil additive characters of the Witt ring of a number field behave under reciprocity equivalence. Given a reciprocity equivalence between two fields, at each place we define a local square class which vanishes if and only if the local root numbers are preserved. Thus this local square class serves as a local obstruction to the preservation of local root numbers. We establish a set of necessary and sufficient conditions for a selection of local square classes (one at each place) to represent a global square class. Then, given a reciprocity equivalence that has a finite wild set, we use these conditions to show that the local square classes combine to give a global square class which serves as a global obstruction to the preservation of all root numbers. Lastly, we use these results to study the behavior of Weil characters under reciprocity equivalence.

scholarly journals Bipartite Consensus for Multiagent Systems via Event-Based Control

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Cui-Qin Ma ◽  
Wei-Guo Sun
Keyword(s):  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Balance Case ◽  
Control Gain ◽  
New Type ◽  
Bipartite Consensus ◽  
Necessary And Sufficient ◽  
Event Based ◽  
Selection Of

This paper studies bipartite consensus for first-order multiagent systems. To improve resource utilization, event-based protocols are considered for bipartite consensus. A new type of control gain is designed in the proposed protocols. By appropriate selection of control gains, the convergence rate of the closed-loop system can be adjusted. Firstly, for structural balance case, necessary and sufficient conditions are given on communication relations and consensus gains to achieve bipartite consensus. Secondly, for structural unbalance case, necessary and sufficient conditions are proposed to ensure the stabilizing of the system. It can be found that the system will not show Zeno behavior. Numerical simulations are used to demonstrate the theoretical results.

Synthesis of Point Planar Elastic Behaviors Using Three-Joint Serial Mechanisms of Specified Construction

2016 ◽  
Vol 9 (1) ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Elastic Behavior ◽  
Compliance Matrix ◽  
Revolute Joint ◽  
Redundant Mechanism ◽  
Compliance Matrices ◽  
Necessary And Sufficient ◽  
Serial Mechanism

This paper presents methods for the realization of 2 × 2 translational compliance matrices using serial mechanisms having three joints, each either revolute or prismatic and each with selectable compliance. The geometry of the mechanism and the location of the compliance frame relative to the mechanism base are each arbitrary but specified. Necessary and sufficient conditions for the realization of a given compliance with a given mechanism are obtained. We show that, for an appropriately constructed serial mechanism having at least one revolute joint, any single 2 × 2 compliance matrix can be realized by properly choosing the joint compliances and the mechanism configuration. For each type of three-joint combination, requirements on the redundant mechanism geometry are identified for the realization of every point planar elastic behavior at a given location, just by changing the mechanism configuration and the joint compliances.

scholarly journals Solutions to Lyapunov stability problems: nonlinear systems with continuous motions

1994 ◽  
Vol 17 (3) ◽  
pp. 587-596 ◽  
Author(s):  
Ljubomir T. Grujic
Keyword(s):  
Lyapunov Function ◽  
Nonlinear Dynamical System ◽  
Sufficient Conditions ◽  
Stability Domain ◽  
Necessary And Sufficient Conditions ◽  
Nonlinear Dynamical ◽  
Bounded Set ◽  
Necessary And Sufficient ◽  
Bounded Sets ◽  
Selection Of

The necessary and sufficient conditions for accurate construction of a Lyapunov function and the necessary and sufficient conditions for a set to be the asymptotic stability domain are algorithmically solved for a nonlinear dynamical system with continuous motions. The conditions are established by utilizing properties of o-uniquely bounded sets, which are explained in the paper. They allow arbitrary selection of an o-uniquely bounded set to generate a Lyapunov function.Simple examples illustrate the theory and its applications.

scholarly journals Optimal Versus Equal Dimensions of Round Bales of Agricultural Materials Wrapped with Plastic Film—Conflict or Compliance?

2021 ◽  
Vol 11 (21) ◽  
pp. 10246
Author(s):  
Anna Stankiewicz
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Integer Number ◽  
Agricultural Practice ◽  
Plastic Film ◽  
Algebraic Equations ◽  
Overlap Ratio ◽  
Agricultural Materials ◽  
Necessary And Sufficient ◽  
Selection Of

For the assumed bale volume, its dimensions (diameter, height), minimizing the consumption of the plastic film used for bale wrapping with the combined 3D method, depend on film and wrapping parameters. Incorrect selection of these parameters may result in an optimal bale diameter, which differs significantly from its height, while in agricultural practice bales with diameters equal or almost equal to the height dominate. The aim of the study is to formulate and solve the problem of selecting such dimensions of the bale with a given volume that the film consumption is minimal and, simultaneously, the bale diameter is equal or almost equal to its height. Necessary and sufficient conditions for such equilibria of the optimal bale dimensions are derived in the form of algebraic equations and inequalities. Four problems of the optimal bale dimension design guaranteeing assumed equilibrium of diameter and height are formulated and solved; both free and fixed bale volume are considered. Solutions of these problems are reduced to solving the sets of simple algebraic equations and inequalities with respect to two variables: integer number of film layers and continuous overlap ratio in bottom layers. Algorithms were formulated and examples regarding large bales demonstrate that they can handle the optimal dimensions' equilibria problems.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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