Detection of Improper General Spatial Kinematic Chains With Different Types of Pairs

1994 ◽  
Author(s):  
Xian-Wen Kong ◽  
Ting-Li Yang
Keyword(s):  
Unsolved Problem ◽  
Degree Of Freedom ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Single Degree Of Freedom ◽  
Kinematic Chains ◽  
Single Degree ◽  
Different Types ◽  
Necessary And Sufficient ◽  
Topological Synthesis

Abstract Improper general spatial kinematic chains (GSKCs) due to the effect of pair types may be generated during the process of topological synthesis of GSKCs with different types of pairs. Thus, detection of improper GSKCs is necessary in topological synthesis of GSKCs with different types of pairs. Unfortunately, it is still an unsolved problem. In this paper, a method for detecting improper GSKCs is presented. Both a necessary and sufficient condition and a sufficient condition for proper GSKCs with R, P, H, T and C pairs are introduced at first. Based on these two conditions, an algorithm to detect improper GSKCs is then developed which is very efficient and suitable for topological synthesis of GSKCs with R, P, H, T and C pairs. The proposed algorithm has been applied to topological synthesis of 1- and 2-loop, single degree of freedom GSKCs with R, P, H, T and C pairs and the corresponding atlas is obtained.

Stability of On-Line Bin Packing with Random Arrivals and Long-Run-Average Constraints

1990 ◽  
Vol 4 (4) ◽  
pp. 447-460 ◽  
Author(s):  
Coastas Courcobetis ◽  
Richard Weber
Keyword(s):  
Bin Packing ◽  
Random Processes ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Expected Number ◽  
Long Run ◽  
Different Types ◽  
On Line ◽  
Necessary And Sufficient ◽  
Uniformly Bounded

Items of various types arrive at a bin-packing facility according to random processes and are to be combined with other readily available items of different types and packed into bins using one of a number of possible packings. One might think of a manufacturing context in which randomly arriving subassemblies are to be combined with subassemblies from an existing inventory to assemble a variety of finished products. Packing must be done on-line; that is, as each item arrives, it must be allocated to a bin whose configuration of packing is fixed. Moreover, it is required that the packing be managed in such a way that the readily available items are consumed at predescribed rates, corresponding perhaps to optimal rates for manufacturing these items. At any moment, some number of bins will be partially full. In practice, it is important that the packing be managed so that the expected number of partially full bins remains uniformly bounded in time. We present a necessary and sufficient condition for this goal to be realized and describe an algorithm to achieve it.

The Response of Nonlinear Systems to Modulated High-Frequency Input

1993 ◽  
Author(s):  
S. A. Nayfeh ◽  
A. H. Nayfeh
Keyword(s):  
Nonlinear Systems ◽  
Natural Frequency ◽  
Amplitude Modulation ◽  
Carrier Frequency ◽  
High Frequency ◽  
Degree Of Freedom ◽  
Resonant Excitation ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Different Types

Abstract We study the response of a single-degree-of-freedom system with cubic nonlinearities to an amplitude-modulated excitation whose carrier frequency is much higher than the natural frequency of the system. The only restriction on the amplitude modulation is that it contain frequencies much lower than the carrier frequency of the excitation. We apply the theory to different types of amplitude modulation and find that resonant excitation of the system may occur under some conditions.

The Virtual Cam – Hexagon Method Authentication on Locating Key Instant Centers of All Planar Single Degree of Freedom Kinematically Indeterminate Linkages up to Ten-Bar

2018 ◽  
Author(s):  
Zhengqi Liu ◽  
Yin-ping Chang
Keyword(s):  
Degree Of Freedom ◽  
Universal Method ◽  
Single Degree Of Freedom ◽  
Graphical Approach ◽  
Single Degree ◽  
Wide Range ◽  
Different Types ◽  
Limited Application ◽  
Complete Sets ◽  
Improved Technique

At this moment all the methods which had been proposed have extremely limited application to only several specific constructions of kinematically indeterminate linkages, i.e. their complete sets of instant centers cannot be obtained simply from Kennedy Theorem due to lack of enough four-bar loop information in their constructions. Planar single degree of freedom linkages up to ten-bar include two different types of mechanisms, i.e. pure bar linkages, such as four-, six-, eight-, and ten-bar; and geared-bar linkages, i.e. geared-five, seven, and nine-bar. The huge varieties of different types and constructions can serve as great testbeds for these methods. This research systematically investigates and modifies the graphical approach, i.e. virtual cam method, whose employment will show it to be an almost-universal method which can be compliantly applied on very wide range of kinematically indeterminate linkages. The procedures and criteria of the methodology are proposed and examined thoroughly to help locate key instant centers of all planar single degree of freedom kinematically indeterminate linkages up to ten-bar so that their complete sets of instant centers can be located successfully. We call this modified and improved technique as Virtual Cam – Hexagon Method. The results are verified carefully against traditional Kennedy Theorem approach and CAD modeling.

Analysis on Degree of Freedom and Singularity of Mechanism Based on Topological Graph Theory

2011 ◽  
Vol 393-395 ◽  
pp. 20-23
Author(s):  
Jian Guo Luo ◽  
Mao Yan He
Keyword(s):  
Graph Theory ◽  
Degree Of Freedom ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Topological Graph ◽  
Topological Graph Theory ◽  
Hybrid Mechanism ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Case Number

Based on the analysis of current developing state of graph theory, define the description of spacial moving capability of common couples and translation base and rotation base of mechanism, based on the new description method in topological graph theory. DOF(degree of freedom) of hybrid mechanism analysised with example based on the definition of dimensionity of branch spacial moving capability and mechanism spacial moving capability, necessary and sufficient condition of nonsingularity of mechanism presented, as well as the necessary and sufficient condition of singularity of mechanism deduced , in-phase and assimilation condition and in-phase and dissimilarity condition and asynchronism condition of limitation of input base of branch adopted, case number of position singularity and pose singularity and position and pose singularity obtained then, still the way of founding the combination and case number of common serial mechanism and parallel mechanism and hybrid mechanism mentioned.

Normal Modal Vibrations for Some Damped n-Degree-of-Freedom Nonlinear Systems

1966 ◽  
Vol 33 (4) ◽  
pp. 877-880 ◽  
Author(s):  
George W. Morgenthaler
Keyword(s):  
Nonlinear Systems ◽  
Normal Mode ◽  
Nonlinear Vibrations ◽  
Normal Modes ◽  
Degree Of Freedom ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Damping Matrix ◽  
Necessary And Sufficient ◽  
Do So

T. K. Caughey1 has shown that a necessary and sufficient condition that a damped, linear, n-degree-of-freedom system possess classical linear normal modes is that the damping matrix be diagonalized by the same transformation which uncouples the undamped system. Rosenberg2 has defined normal modes for nonlinear n-degree-of-freedom undamped systems and has shown the existence of such modes for various classes of nonlinear systems. In linear systems, the frequency is independent of the amplitude and, if a set of masses is vibrating in unison, it is not surprising that in some cases they continue to do so as the motion damps out. In nonlinear vibrations, however, frequency depends upon amplitude so that a series of masses vibrating at different amplitudes in a Rosenberg normal mode might generally be expected to lose synchronization as their amplitudes damp out. Two classes of systems are discussed here in which normal modes are preserved under damping, and several examples are given.

Active Absorption of Viscously Damped System With Time Delay

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
Yitshak M. Ram ◽  
Kumar Vikram Singh
Keyword(s):  
Time Delay ◽  
Passive Control ◽  
Degree Of Freedom ◽  
Sufficient Condition ◽  
Total Absorption ◽  
Necessary And Sufficient Condition ◽  
Controlled System ◽  
Damped System ◽  
Necessary And Sufficient ◽  
System With Time Delay

In general, it is not possible to obtain total motion absorption of a certain degree of freedom in a harmonically excited damped system by passive control. This paper presents a method of obtaining total absorption in viscously damped system by active control, including time delay, which is unavoidable in digital controlled system. The control is applied on one degree of freedom and the absorption is achieved at another point. This study is carried out by both complex and real analyses. The necessary and sufficient condition for obtaining total absorption is given. Examples demonstrate the various results.

On the Flexibility of Spatial Kinematic Chains

1986 ◽  
Vol 10 (4) ◽  
pp. 213-218
Author(s):  
A.C. Rao
Keyword(s):  
Graph Theory ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Structural Arrangement ◽  
Kinematic Chains ◽  
Single Degree ◽  
A Chain ◽  
Space Mechanisms

A number of distinct or non-isomorphic kinematic chains exist for a specified number of links and joints. For example, sixteen distinct chains can be obtained with eight links and two hundred and thirty chains with ten links having a single degree of freedom. Similarly, many space mechanisms can be formed with four links and joints having different degrees of freedom. So far no measure is available to know which of these possesses greater mobility or flexibility. Flexibility is not to be confused with the degree of freedom. Intuitively one feels that a six-link chain has greater flexibility than a four-bar chain both having the same degrees of freedom. Though the mobility of a chain increases with the number of links one is not sure how the structural arrangement, type of links and joints, their numbers and sequence etc. influence the same. Combining graph theory with the concepts of probability, simple formulae are developed to investigate the relative merits of spatial and planar kinematic chains. The greater the flexibility or mobility of the chain, the higher is the ability to meet the motion requirements, i.e., a chain having greater entropy can be expected, say, to reproduce a given function more accurately.

Analysis on Degree of Freedom and Singularity of Mechanism Based on Topological Graph Theory

2012 ◽  
Vol 430-432 ◽  
pp. 1943-1946
Author(s):  
Jian Guo Luo ◽  
Mao Yan He
Keyword(s):  
Graph Theory ◽  
Degree Of Freedom ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Topological Graph ◽  
Topological Graph Theory ◽  
Hybrid Mechanism ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Case Number

Based on the analysis of current developing state of graph theory, define the description of spacial moving capability of common couples and translation base and rotation base of mechanism, based on the new description method in topological graph theory. DOF(degree of freedom) of hybrid mechanism analysised with example based on the definition of dimensionity of branch spacial moving capability and mechanism spacial moving capability, necessary and sufficient condition of nonsingularity of mechanism presented, as well as the necessary and sufficient condition of singularity of mechanism deduced , in-phase and assimilation condition and in-phase and dissimilarity condition and asynchronism condition of limitation of input base of branch adopted, case number of position singularity and pose singularity and position and pose singularity obtained then, still the way of founding the combination and case number of common serial mechanism and parallel mechanism and hybrid mechanism mentioned.

Aspects of creep buckling II. The effects of small deflexion approximations on predicted behaviour

1978 ◽  
Vol 364 (1718) ◽  
pp. 415-433 ◽  
Keyword(s):  
Constant Load ◽  
Buckling Analysis ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Creep Buckling ◽  
Different Types ◽  
Post Buckling

In creep buckling analysis, small deflexion approximations generally influence the calculated displacement‒time relations and may also result in the prediction of different phenomena from those indicated by exact analyses. Part II examines the nature of these approximations and the effects of using them. As in Part I, much significance is attached to the link between a structure’s creep buckling behaviour at constant load and its instantaneous buckling and post-buckling behaviour under varying load. Analyses of simple single degree of freedom models are used for illustration. Some general conclusions are drawn which permit a better understanding of the relationships between the different types of analysis that have been used in previous creep buckling studies.

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