Dynamics of Chain of Flexible Links

1988 ◽  
Vol 110 (4) ◽  
pp. 410-415 ◽  
Author(s):  
M. Benati ◽  
A. Morro
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Lagrangian Approach ◽  
The Other ◽  
Dynamic Equations ◽  
Flexible Links ◽  
A Chain

A Lagrangian approach is developed for the dynamics of a chain with flexible links. Each link is modeled as a system with a finite number of degrees of freedom, one of them describing the rotation, the other ones the flexibility. While the approach is developed for chains with any numbers of links, the dynamic equations are written explicitly for a chain with two links and a payload.

Formulation of Equations of Motion for a Chain of Flexible Links Using Hamilton’s Principle

1994 ◽  
Vol 116 (1) ◽  
pp. 81-88 ◽  
Author(s):  
M. Benati ◽  
A. Morro
Keyword(s):  
Boundary Conditions ◽  
Finite Number ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Dynamic Equations ◽  
Relative Deformation ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Flexible Links ◽  
A Chain

The dynamic equations of a chain of flexible links are determined by means of Hamilton’s principle. First a continuous model is adopted and the boundary conditions are determined, along with the partial differential equations of motion. Then a model with a finite number of degrees of freedom is set up. The configuration of each link is described through the line which joins the end points and the relative deformation is described in terms of appropriate trial functions. The boundary conditions are incorporated into a set of basic trial functions. The time-dependent coefficients of the remaining shape functions play the role of Lagrangian coordinates. The dynamic equations are then derived and the procedure is contrasted with other methods for reduction of a system of links to a system with a finite number of degrees of freedom.

Explicit dynamic equations for a chain of flexible links

1992 ◽  
Vol 9 (8) ◽  
pp. 1083-1094
Author(s):  
Zhongping Deng ◽  
Liping Wang
Keyword(s):  
Dynamic Equations ◽  
Flexible Links ◽  
A Chain ◽  
Explicit Dynamic

Two-Degree-of-Freedom Decoupled Non-Redundant Cable-Loop-Driven Parallel Mechanism

2012 ◽  
Author(s):  
Hanwei Liu ◽  
Clément Gosselin ◽  
Thierry Laliberté
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
The Other ◽  
Dynamic Equations ◽  
End Effector ◽  
Actuation Redundancy ◽  
Rigid Link ◽  
Force Closure ◽  
Two Degree Of Freedom

A novel two-degree-of-freedom cable-loop slider-driven parallel mechanism is introduced in this paper. The two degrees of freedom of the mechanism are decoupled and only two actuators are needed to control the motion. There are two cable loops for each direction of motion: one acts as the actuating loop while the other is the constraint loop. Due to the simple geometric design, the kinematic and static equations of the mechanism are very compact. The stiffness of the mechanism is also analyzed in the paper. It can be observed that the mechanism’s stiffness is much higher than the stiffness of the cables. Finally, the dynamic equations of the mechanism, including the compliance and the damping of the cables are obtained. The proposed mechanism’s workspace is essentially equal to its footprint and there are no singularities. The mechanism does not require the use of a rigid-link passive bridge and trolley (only cables are connected to the end-effector). Sliders located on the edges of the workspace are used and actuation redundancy is eliminated while providing force closure everywhere in the workspace.

scholarly journals On the positioning error of a 2-DOF spherical parallel wrist with flexible links and joints – an FEM approach

2015 ◽  
Vol 6 (1) ◽  
pp. 9-14 ◽  
Author(s):  
G. Palmieri
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fixed Point ◽  
Degrees Of Freedom ◽  
The Other ◽  
Mobile Platform ◽  
Positioning Error ◽  
Flexible Links ◽  
Continuous Maps ◽  
Base Platform

Abstract. This paper deals with an elasto-static analysis of a 2-DOF (degrees of freedom) spherical parallel wrist where the links and the joints are considered flexible. Theoretically, the mobile platform of the wrist rotates around a fixed point which is the intersection of all the joint axes. However, if the flexibility of the limbs is taken into account, while the base platform (BP) and the mobile platform (MP) are assumed rigid, two centers can be identified: one for the BP and the other for the MP. In general such points are not coincident; as a result, the positioning of the MP is affected by inaccuracies, which can be evaluated in terms of displacement and orientation errors. A finite-element method (FEM) approach is used to analyze the problem in a series of configurations of the wrist; the results are elaborated in order to obtain continuous maps of the errors over the workspace of the machine.

Study of some rheological models with a finite number of degrees of freedom

2000 ◽  
Vol 19 (2) ◽  
pp. 277-307 ◽  
Author(s):  
Jérôme Bastien ◽  
Michelle Schatzman ◽  
Claude-Henri Lamarque
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Rheological Models

CRYSTALLINE GRAVITY

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3243-3255 ◽  
Author(s):  
GERARD 't HOOFT
Keyword(s):  
Finite Number ◽  
Lorentz Group ◽  
Degrees Of Freedom ◽  
Holonomy Group ◽  
Discrete Subgroup ◽  
Analytic Solutions ◽  
Space Time ◽  
Exact Analytic Solutions ◽  
Finite Domains ◽  
Dimensional Crystal

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate a theory that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Next, we suggest replacing in the string holonomy group, the Lorentz group by a discrete subgroup, which turns space-time into a 4-dimensional crystal with defects.

scholarly journals XXIII.—On the Disruptive Discharge of Electricity: An Experimental Thesis for the Degree of Doctor of Science, Department A

1878 ◽  
Vol 28 (2) ◽  
pp. 633-671 ◽  
Author(s):  
Alexander Macfarlane
Keyword(s):  
Copper Wire ◽  
Late Summer ◽  
The Other ◽  
Straight Line ◽  
Summer Session ◽  
The Difference ◽  
A Chain ◽  
The One ◽  
Metallic Parts ◽  
The University

The experiments to which I shall refer were carried out in the physical laboratory of the University during the late summer session. I was ably assisted in conducting the experiments by three students of the laboratory,—Messrs H. A. Salvesen, G. M. Connor, and D. E. Stewart. The method which was used of measuring the difference of potential required to produce a disruptive discharge of electricity under given conditions, is that described in a paper communicated to the Royal Society of Edinburgh in 1876 in the names of Mr J. A. Paton, M. A., and myself, and was suggested to me by Professor Tait as a means of attacking the experimental problems mentioned below.The above sketch which I took of the apparatus in situ may facilitate tha description of the method. The receiver of an air-pump, having a rod capable of being moved air-tight up and down through the neck, was attached to one of the conductors of a Holtz machine in such a manner that the conductor of the machine and the rod formed one conducting system. Projecting from the bottom of the receiver was a short metallic rod, forming one conductor with the metallic parts of the air-pump, and by means of a chain with the uninsulated conductor of the Holtz machine. Brass balls and discs of various sizes were made to order, capable of being screwed on to the ends of the rods. On the table, and at a distance of about six feet from the receiver, was a stand supporting two insulated brass balls, the one fixed, the other having one degree of freedom, viz., of moving in a straight line in the plane of the table. The fixed insulated ball A was made one conductor with the insulated conductor of the Holtz and the rod of the receiver, by means of a copper wire insulated with gutta percha, having one end stuck firmly into a hole in the collar of the receiver, and having the other fitted in between the glass stem and the hollow in the ball, by which it fitted on to the stem tightly. A thin wire similarly fitted in between the ball B and its insulating stem connected the ball with the insulated half ring of a divided ring reflecting electrometer.

scholarly journals The linkage of sugar phosphate polymer to peptidoglycan in walls of Micrococcus sp. 2102

1978 ◽  
Vol 169 (2) ◽  
pp. 329-336 ◽  
Author(s):  
J Heptinstall ◽  
J Coley ◽  
P J Ward ◽  
A R Archibald ◽  
J Baddiley
Keyword(s):  
Staphylococcus Aureus ◽  
Alkaline Hydrolysis ◽  
The Other ◽  
Muramic Acid ◽  
Sugar Phosphate ◽  
Glycerol Phosphate ◽  
Homogeneous Product ◽  
A Chain

1. Protein-free walls of Micrococcus sp. 2102 contain peptidoglycan, poly-(N-acetylglucosamine 1-phosphate) and small amounts of glycerol phosphate. 2. After destruction of the poly-(N-acetylglucosamine 1-phosphate) with periodate, the glycerol phosphate remains attached to the wall, but can be removed by controlled alkaline hydrolysis. The homogeneous product comprises a chain of three glycerol phosphates and an additional phosphate residue. 3. The poly-(N-acetylglucosamine 1-phosphate) is attached through its terminal phosphate to one end of the tri(glycerol phosphate). 4. The other end of the glycerol phosphate trimer is attached through its terminal phosphate to the 3-or 4-position of an N-acetylglucosamine. It is concluded that the sequence of residues in the sugar 1-phosphate polymer-peptidoglycan complex is: (N-acetylglucosamine 1-phosphate)24-(glycerol phosphate)3-N-acetylglucosamine 1-phosphate-muramic acid (in peptidoglycan). Thus in this organism the phosphorylated wall polymer is attached to the peptidoglycan of the wall through a linkage unit comprising a chain of three glycerol phosphate residues and an N-acetylglucosamine 1-phosphate, similar to or identical with the linkage unit in Staphylococcus aureus H.

A Hybrid Highly Parallelizable Algorithm for the Dynamics of Rigid Body Chain Systems

1999 ◽  
Author(s):  
Shanzhong Duan ◽  
Kurt S. Anderson
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Constraint Forces ◽  
Dynamics Of Rigid Body ◽  
A Chain ◽  
Explicit Determination ◽  
Order Algorithm

Abstract The paper presents a new hybrid parallelizable low order algorithm for modeling the dynamic behavior of multi-rigid-body chain systems. The method is based on cutting certain system interbody joints so that largely independent multibody subchain systems are formed. These subchains interact with one another through associated unknown constraint forces f¯c at the cut joints. The increased parallelism is obtainable through cutting the joints and the explicit determination of associated constraint loads combined with a sequential O(n) procedure. In other words, sequential O(n) procedures are performed to form and solve equations of motion within subchains and parallel strategies are used to form and solve constraint equations between subchains in parallel. The algorithm can easily accommodate the available number of processors while maintaining high efficiency. An O[(n+m)Np+m(1+γ)Np+mγlog2Np](0<γ<1) performance will be achieved with Np processors for a chain system with n degrees of freedom and m constraints due to cutting of interbody joints.

Footbridges as an important part of a system: the context as an experience

2021 ◽  
Author(s):  
Toon Maas ◽  
Mohamad Tuffaha ◽  
Laurent Ney
Keyword(s):  
Design Process ◽  
Degrees Of Freedom ◽  
The Other ◽  
Infrastructure Projects ◽  
Good Design ◽  
Cultural Processes ◽  
The Relationship

<p>“A bridge has to be designed”. Every bridge is the exploration of all degrees of a freedom of a project: the context, cultural processes, technology, engineering and industrial skills. A successful bridge aims to dialogue with these degrees of freedom to achieve a delicate equilibrium, one that invites the participation of its users and emotes new perceptions for its viewers. In short, a good design “makes the bridge talk.”</p><p>Too often, the bridge, as an object, is reduced to its functionality. Matters of perceptions and experiences of the users are often not considered in the design process; they are relegated to levels of chance or treated as simple decorative matter. The longevity of infrastructure projects, in general, and bridges, in particular, highlights the deficiencies of such an approach. The framework to design bridges must include historical, cultural, and experiential dimensions. Technology and engineering are of paramount importance but cannot be considered as “an end in themselves but a means to an end”. This paper proposes to discuss three projects by Ney &amp; Partners that illustrate such a comprehensive exploration approach to footbridge design: the Poissy and Albi crossings and the Tintagel footbridge.</p><p>The footbridges of Poissy and Albi dialogue most clearly with their historical contexts, reconfiguring the relationship between old and new in the materiality and typology use. In Tintagel, legend replaces history. Becoming a metaphor for the void it crosses, the Tintagel footbridge illustrates the delicate dialogue of technology and engineering on one side and imagination and experience on the other.</p>

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