On the Integrability of Screw Spaces

1992 ◽  
Vol 114 (2) ◽  
pp. 251-256 ◽  
Author(s):  
S. W. Peterson
Keyword(s):  
Tangent Space ◽  
Screw Theory ◽  
Joint Space ◽  
Rigid Bodies ◽  
Joint Contact ◽  
A Chain ◽  
Configuration Manifold ◽  
Relationship Of ◽  
The Relationship ◽  
Line Space

In the development of a method for generating the dynamic equations of a chain of rigid bodies in elliptic line space, it has been discovered that the joint freedom spaces from the tangent space of the system’s joint space, called the configuration manifold by dynamicists. The freedom space of a joint can be calculated from the joint contact geometry using reciprocal screw theory. The present paper describes the relationship of the joint freedom spaces to the tangent space of the configuration manifold, and determines the integrability conditions which must be satisfied if the freedom space represents a valid configuration manifold. The paper also shows that the integrability of the tangent space of a chain of rigid bodies is established once the integrability of each joint freedom space has been demonstrated. These conditions are used to define valid generalized coordinates for describing the chain’s configuration. Cylindrical and spherical joints are treated as examples.

The Geometry of Virtual Work Dynamics in Screw Space

1992 ◽  
Vol 59 (2) ◽  
pp. 411-417 ◽  
Author(s):  
Steven Peterson
Keyword(s):  
Tangent Space ◽  
Screw Theory ◽  
Virtual Work ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Coordinate Space ◽  
Dynamical Equations ◽  
Least Action ◽  
System Of Rigid Bodies ◽  
Configuration Manifold

In this paper, screw theory is employed to develop a method for generating the dynamic equations of a system of rigid bodies. Exterior algebra is used to derive the structure of screw space from projective three space (homogeneous coordinate space). The dynamic equation formulation method is derived from the parametric form of the principle of least action, and it is shown that a set of screws exist which serves as a basis for the tangent space of the configuration manifold. Equations generated using this technique are analogs of Hamilton’s dynamical equations. The freedom screws defining the manifold’s tangent space are determined from the contact geometry of the joint using the virtual coefficient, which is developed from the principle of virtual work. This results in a method that eliminates all differentiation operations required by other virtual work techniques, producing a formulation method based solely on the geometry of the system of rigid bodies. The procedure is applied to the derivation of the dynamic equations for the first three links of the Stanford manipulator.

From “Fiscal-Military” State to Laissez-faire State, 1760–1850

1993 ◽  
Vol 32 (1) ◽  
pp. 44-70 ◽  
Author(s):  
Philip Harling ◽  
Peter Mandler
Keyword(s):  
Eighteenth Century ◽  
Industrial Revolution ◽  
Early Nineteenth Century ◽  
Government Growth ◽  
Regressive Tax ◽  
Central Apparatus ◽  
A Chain ◽  
British State ◽  
Relationship Of ◽  
The Relationship

The recent historiographical revolution in our understanding of the eighteenth-century state has broad implications, analytical as well as empirical, that are only beginning to be plumbed. Due largely to the work of Patrick O'Brien and John Brewer, the old picture—of a small, amateurish, corrupt central apparatus largely maintained (between sporadic wars) to dignify the crown and assist gentlemanly (i.e., parliamentary) plunder—has been pretty completely effaced. We now see that by the end of the French wars the British state was one of the largest and most efficient in Europe; certainly it engorged the largest proportion of national product by means of a ruthlessly regressive tax system. The French wars were the climax, not the sole begetters of this system, which had been spawned by a chain of wars mounting in scope and sophistication since the late seventeenth century and requiring commensurate improvements in fiscal policy: thus Brewer's memorable naming of the system as the “fiscal-military state.”For historians of the early nineteenth century, this revision raises a host of questions about the relationship of social change and social class to government growth. Particularly, it casts doubt on the customary association made between growth in the size or scope of government and the rise in the Industrial Revolution of new social and economic questions and a bourgeoisie to answer them; that is, it casts doubt on the implicit “modernization” model that hitches together economic growth, government growth, bureaucracy, professionalism, and embourgeoisement.

A Kirigami-Inspired 8R Linkage and Its Evolved Overconstrained 6R Linkages With the Rotational Symmetry of Order Two

2014 ◽  
Vol 6 (2) ◽  
Author(s):  
Ketao Zhang ◽  
Jian S. Dai
Keyword(s):  
Screw Theory ◽  
Rotational Symmetry ◽  
Structural Evolution ◽  
Joint Space ◽  
Geometric Characteristics ◽  
Constraint Analysis ◽  
Motion Parameters ◽  
Motion Characteristics ◽  
The Relationship

This paper presents a novel metamorphic 8R linkage extracted from a kirigami-fold with pregrooved creases and two overconstrained 6R linkages evolved from the 8R linkage by taking the concept of metamorphosis in the sense of structural evolution. The geometric characteristics and the parametric constraints of the evolved 6R linkages are identified following the structural evolution of the 8R linkage. The paper reveals that the evolved 6R linkages are special line-symmetric Bricard 6R loops characterized by the rotational symmetry of order two. The joint space of the overconstrained 6R linkages is analyzed and the relationship between motion parameters of the evolved 6R linkages and reconfiguration parameters of the metamorphic 8R linkage are derived. The motion characteristics of the overconstrained 6R linkages are further verified in terms of screw theory. The bifurcation and trifurcation associated with various transitory positions of the evolved 6R linkages having distinct parametric constraints are consequently identified based on constraint analysis.

On the influence of the time factor on the correlation between the barometric heights at stations more than 1000 miles apart.

1905 ◽  
Vol 74 (497-506) ◽  
pp. 403-413 ◽  
Author(s):  
F. E. Cave-Browne-Cave ◽  
Karl Pearson
Keyword(s):  
Nova Scotia ◽  
Atlantic Ocean ◽  
Time Factor ◽  
East Side ◽  
The West ◽  
Preliminary Note ◽  
A Chain ◽  
Extreme North ◽  
Relationship Of ◽  
The Relationship

1. An investigation of the relationship of the daily barometric heights on both sides of the Atlantic Ocean has been in progress for some years, and in a preliminary note by Professor Pearson and myself some account was given of the contemporaneous relationship of a chain of stations from the extreme north of Norway down the west coasts of Europe and Africa. Observations for this east side of the Atlantic have now been copied for twenty years, as far as stations are available from Norway to the Cape, and the only need here is more aid in the very laborious reductions necessary before any inferences can be drawn. A similar chain of stations from Nova Scotia to the Falkland Isles has been completed, with the exception of Brazil, from which, so far, we have been able to obtain no data whatever.

The Jacobian Matrix Structure of the Barrier Arm of Inspection Robot

2013 ◽  
Vol 706-708 ◽  
pp. 1183-1186
Author(s):  
Yu Yan ◽  
Gong Ping Wu
Keyword(s):  
Jacobian Matrix ◽  
Space Velocity ◽  
Joint Space ◽  
Transformation Method ◽  
Linear Mapping ◽  
Real Time Control ◽  
Inspection Robot ◽  
Time Control ◽  
Relationship Of ◽  
The Relationship

The Jacobian matrix represents the relationship of the linear mapping between the space velocity of robot operation and joint space velocity, which is the important link in the process of robot control. According to analyzing the gesture character of the inspection robot when it gets over the obstacles. This paper sets up the dynamitic model of robot by utilizing D-H. Based on that, it builds the Jacobian matrix by adopting differential transformation method, which establishes the foundation of the robots motion planning and real-time control.

Intertextual networks in the correspondence of Lady Katherine Paston

2004 ◽  
Vol 5 (2) ◽  
pp. 255-269
Author(s):  
Sanna-Kaisa Tanskanen
Keyword(s):  
Intertextual Connections ◽  
A Chain ◽  
Relationship Of ◽  
The Relationship

In the dialogue of correspondence, letters both respond to previous letters and anticipate new ones. The intertextuality existing between letters in a chain of correspondence can be made explicit, and it is these manifest intertextual connections that are explored in this paper. More specifically, the study focuses on the use of references to other letters as intertextual links. The analysis reveals that other letters, previous, future, and even some that were planned but never written, are explicitly present in the majority of the letters passing between Lady Katherine Paston and her fellow correspondents. Some types of references to other letters are constrained by the relationship of the correspondents and the frequency of the correspondence, while others function independently of such factors.

The relationship between the saphenopopliteal junction and the common peroneal nerve: a cada-veric study

2009 ◽  
Vol 24 (2) ◽  
pp. 67-73 ◽  
Author(s):  
R Balasubramaniam ◽  
R Rai ◽  
D C Berridge ◽  
D J A Scott ◽  
R W Soames
Keyword(s):  
Peroneal Nerve ◽  
Anatomic Variation ◽  
Common Peroneal Nerve ◽  
Joint Space ◽  
Anatomical Landmarks ◽  
Fibula Head ◽  
Increased Risk ◽  
The Common ◽  
Relationship Of ◽  
The Relationship

Objectives The variable anatomy of the short saphenous vein (SSV) and the potential failure to identify the saphenopopliteal junction (SPJ) contribute to an increased risk of damage to the common peroneal nerve (CPN) during surgical exploration. The aim of the present study was to determine the variation of the SPJ, its relationship to the CPN, and the relationship of both SPJ and CPN to defined anatomical landmarks. Methods Measurements of the distance between the SPJ and CPN, and the defined anatomical landmarks (fibula head, lateral joint space, lateral femoral epicondyle), were undertaken on 30 cadaveric limbs following careful dissection of the popliteal fossa. Results The level of SPJ termination was classified as low (below), normal (within 100 mm above) and high (more than 100 mm above), the lateral femoral epicondyle. Of the 30 limbs dissected, 70% of SPJs were normal, 23% low and 7% high. Direct measurement from the SPJ to anatomical landmarks showed a higher interquartile range (IQR) in low compared with normal terminations; however, the vertical distance from the SPJ to the fibula head showed an increase in IQR from low to normal terminations (7.1–14.2). The mean distances between the SPJ and CPN in low and normal terminations were 23.3 and 16.7 mm, respectively. Comparison of the IQR showed values very similar to low terminations having a slightly higher IQR compared with normal terminations (7.15–6.0). Conclusion Significant anatomic variation was observed in the termination of the SSV, with 67% located within 66 mm above the lateral femoral epicondyle. The risk of damaging the CPN during saphenopopliteal ligation may be higher for SPJs located above the lateral femoral epicondyle because of the proximity of the two structures and variability of SPJ.

Hierarchical Heteroclinics in Dynamical Model of Cognitive Processes: Chunking

2014 ◽  
Vol 24 (10) ◽  
pp. 1450132 ◽  
Author(s):  
Valentin S. Afraimovich ◽  
Todd R. Young ◽  
Mikhail I. Rabinovich
Keyword(s):  
Cognitive Processes ◽  
Mathematical Object ◽  
Brain Network ◽  
Temporal Organization ◽  
Cognitive Activities ◽  
Information Chain ◽  
A Chain ◽  
Network Functionality ◽  
Relationship Of ◽  
The Relationship

Combining the results of brain imaging and nonlinear dynamics provides a new hierarchical vision of brain network functionality that is helpful in understanding the relationship of the network to different mental tasks. Using these ideas it is possible to build adequate models for the description and prediction of different cognitive activities in which the number of variables is usually small enough for analysis. The dynamical images of different mental processes depend on their temporal organization and, as a rule, cannot be just simple attractors since cognition is characterized by transient dynamics. The mathematical image for a robust transient is a stable heteroclinic channel consisting of a chain of saddles connected by unstable separatrices. We focus here on hierarchical chunking dynamics that can represent several cognitive activities. Chunking is the dynamical phenomenon that means dividing a long information chain into shorter items. Chunking is known to be important in many processes of perception, learning, memory and cognition. We prove that in the phase space of the model that describes chunking there exists a new mathematical object — heteroclinic sequence of heteroclinic cycles — using the technique of slow–fast approximations. This new object serves as a skeleton of motions reflecting sequential features of hierarchical chunking dynamics and is an adequate image of the chunking processing.

scholarly journals The relationship of three‐dimensional joint space width on weight‐bearing CT with pain and physical function

2020 ◽  
Vol 38 (6) ◽  
pp. 1333-1339
Author(s):  
Mayank D. Kothari ◽  
Kaitlin G. Rabe ◽  
Donald D. Anderson ◽  
Michael C. Nevitt ◽  
John A. Lynch ◽  
...  
Keyword(s):  
Physical Function ◽  
Weight Bearing ◽  
Three Dimensional ◽  
Joint Space Width ◽  
Joint Space ◽  
Relationship Of ◽  
The Relationship ◽  
Space Width
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