Distribution of Wrench-Twist Duality in Over-Constrained Mechanisms

2003 ◽  
Vol 125 (1) ◽  
pp. 81-91 ◽  
Author(s):  
M. Fayet
Keyword(s):  
Degrees Of Freedom ◽  
Contact Forces ◽  
Simple Test ◽  
The Matrix

First, a procedure is presented in order to build the space of statically admissible wrenches. The matrix which generates them is obtained in an intrinsic way. It uses intersection of spaces for the edges (of the associated graph) and the new operation of “triangular projection” for the vertices. From this matrix, the choice of any set of indeterminable contact forces is achieved via a very simple test. This matrix allows to determine also all the possible degrees of freedom to add to the over-constrained mechanism in order to transform it into a non over-constrained one. Wrench-twist duality arises clearly in this last procedure.

Dynamic Analysis and Configuration Design of a Two-Component Wave-Energy Absorber

2012 ◽  
Author(s):  
Christophe Cochet ◽  
Ronald W. Yeung
Keyword(s):  
Wave Energy ◽  
Degrees Of Freedom ◽  
Outer Cylinder ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Energy Extraction ◽  
Energy Absorber ◽  
Compound Cylinder ◽  
Motion Study ◽  
Heave Motion

The wave-energy absorber being developed at UC Berkeley is modeled as a moored compound cylinder, with an outer cylinder sliding along a tension-tethered inner cylinder. With rigid-body dynamics, it is first shown that the surge and pitch degrees of freedom are decoupled from the heave motion. The heaving motion of the outer cylinder is analyzed and its geometric proportions (radii and drafts ratios) are optimized for wave-energy extraction. Earlier works of Yeung [1] and Chau and Yeung [2,3] are used in the present heave-motion study. The coupled surge-pitch motion can be solved and can provide the contact forces between the cylinders. The concept of capture width is used to characterize the energy extraction: its maximization leads to optimal energy extraction. The methodology presented provides the optimal geometry in terms of non-dimensional proportions of the device. It is found that a smaller radius and deeper draft for the outer cylinder will lead to a larger capture width and larger resulting motion.

An Iterative Approach to Dynamic Elastic-Plastic Analysis

1998 ◽  
Vol 65 (4) ◽  
pp. 811-819 ◽  
Author(s):  
F. Giambanco ◽  
L. Palizzolo ◽  
L. Cirone
Keyword(s):  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Degrees Of Freedom ◽  
Linear Complementarity ◽  
Iterative Approach ◽  
Loading History ◽  
Constraint Matrix ◽  
Elastic Plastic ◽  
Recursive Solution ◽  
The Matrix

The step-by-step analysis of structures constituted by elastic-plastic finite elements, subjected to an assigned loading history, is here considered. The structure may possess dynamic and/or not dynamic degrees-of-freedom. As it is well-known, at each step of analysis the solution of a linear complementarity problem is required. An iterative method devoted to solving the relevant linear complementarity problem is presented. It is based on the recursive solution of a linear complementarity, problem in which the constraint matrix is block-diagonal and deduced from the matrix of the original linear complementarity problem. The convergence of the procedure is also proved. Some particular cases are examined. Several numerical applications conclude the paper.

Rolling Condition and Gyroscopic Moments in Curve Negotiations

2012 ◽  
Author(s):  
Ahmed A. Shabana ◽  
Martin B. Hamper ◽  
James J. O’Shea
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
The Body ◽  
Contact Forces ◽  
Body Motion ◽  
Global Coordinate System ◽  
Gyroscopic Moment ◽  
Absolute Angular Velocity ◽  
Pure Rolling ◽  
The Stability

In vehicle system dynamics, the effect of the gyroscopic moments can be significant during curve negotiations. The absolute angular velocity of the body can be expressed as the sum of two vectors; one vector is due to the curvature of the curve, while the second vector is due to the rate of changes of the angles that define the orientation of the body with respect to a coordinate system that follows the body motion. In this paper, the configuration of the body in the global coordinate system is defined using the trajectory coordinates in order to examine the effect of the gyroscopic moments in the case of curve negotiations. These coordinates consist of arc length, two relative translations and three relative angles. The relative translations and relative angles are defined with respect to a trajectory coordinate system that follows the motion of the body on the curve. It is shown that when the yaw and roll angles relative to the trajectory coordinate system are constrained and the motion is predominantly rolling, the effect of the gyroscopic moment on the motion becomes negligible, and in the case of pure rolling and zero yaw and roll angles, the generalized gyroscopic moment associated with the system degrees of freedom becomes identically zero. The analysis presented in this investigation sheds light on the danger of using derailment criteria that are not obtained using laws of motion, and therefore, such criteria should not be used in judging the stability of railroad vehicle systems. Furthermore, The analysis presented in this paper shows that the roll moment which can have a significant effect on the wheel/rail contact forces depends on the forward velocity in the case of curve negotiations. For this reason, roller rigs that do not allow for the wheelset forward velocity cannot capture these moment components, and therefore, cannot be used in the analysis of curve negotiations. A model of a suspended railroad wheelset is used in this investigation to study the gyroscopic effect during curve negotiations.

An Improved Method for Calculating Free Vibrations in Systems of Several Degrees of Freedom

1938 ◽  
Vol 5 (2) ◽  
pp. A61-A66
Author(s):  
Winston M. Dudley
Keyword(s):  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Matrix Theory ◽  
Free Vibrations ◽  
Initial Disturbance ◽  
Improved Method ◽  
Matrix Methods ◽  
Computing Machine ◽  
The Matrix ◽  
Time Required

Abstract In 1934 two English investigators (1) published a method for calculating the various modes and frequencies of vibration of a system having several degrees of freedom. Their method, which is based on matrices, greatly shortens the time spent in obtaining numerical solutions in many important problems, notably those with immovable foundations. In this paper is presented a new theorem which (a) makes possible a further reduction of nearly one half in the time required, so that solutions up to 20 deg or more of freedom are now practical and (b) makes it then possible to determine the motion of the system after any initial disturbance in a few minutes, instead of several hours as required by older methods. It is useful in the latter respect whether the modes have been determined by matrix methods, or not. Although the paper gives simpler proofs than any previously published, knowledge of the matrix theory is not required in using the method. Problems are analyzed by a tabular process, in which an ordinary computing machine helps greatly. Comments based on computing experience are given. A simple numerical example has been given elsewhere (1).

Study of grasp-energy based optimal distribution of contact forces on a humanoid robotic hand during object grasp

Robotica ◽  
2021 ◽  
pp. 1-26
Author(s):  
Sourajit Mukherjee ◽  
Abhijit Mahapatra ◽  
Amit Kumar ◽  
Avik Chatterjee
Keyword(s):  
Optimization Algorithm ◽  
Degrees Of Freedom ◽  
Simulated Data ◽  
Performance Measure ◽  
Contact Forces ◽  
Contact Model ◽  
Robotic Hand ◽  
Net Energy ◽  
Optimal Distribution

Abstract A novel grasp optimization algorithm for minimizing the net energy utilized by a five-fingered humanoid robotic hand with twenty degrees of freedom for securing a precise grasp is presented in this study. The algorithm utilizes a compliant contact model with a nonlinear spring and damper system to compute the performance measure, called ‘Grasp Energy’. The measure, subject to constraints, has been minimized to obtain locally optimal cartesian trajectories for securing a grasp. A case study is taken to compare the analytical (applying the optimization algorithm) and the simulated data in MSC.Adams $^{^{\circledR}}$ , to prove the efficacy of the proposed formulation.

Railway Truck Response to Random Rail Irregularities

1975 ◽  
Vol 97 (3) ◽  
pp. 957-964 ◽  
Author(s):  
Neil K. Cooperrider
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Tangential Force ◽  
Contact Forces ◽  
Guidance Force ◽  
Power Spectral ◽  
Power Spectral Densities ◽  
Rail Irregularities ◽  
Frequency Domain Techniques

This paper discusses the random response of a seven degree of freedom, passenger truck model to lateral rail irregularities. Power spectral densities and root mean square levels of component displacements and contact forces are reported. The truck model used in the study allows lateral and yaw degrees of freedom for each wheelset, and lateral, yaw and roll freedoms for the truck frame. Linear creep relations are utilized for the rail-wheel contact forces. The lateral rail irregularities enter the analysis through the creep expressions. The results described in the paper were obtained using frequency domain techniques to solve the equations of motion. The reported results demonstrate that the guidance force needed when traveling over irregular rail at high speed utilizes a significant portion of the total available tangential force between wheel and rail.

scholarly journals THE HAGEDORN TRANSITION AND THE MATRIX MODEL FOR STRINGS

1998 ◽  
Vol 13 (26) ◽  
pp. 2085-2094 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Matrix Model ◽  
Light Cone ◽  
Degrees Of Freedom ◽  
Low Energy ◽  
Matrix Formalism ◽  
Yang Mills ◽  
Large N ◽  
The Matrix ◽  
The Continuum ◽  
String Worldsheet

We use the matrix formalism to investigate what happens to strings above the Hagedorn temperature. We show that is not a limiting temperature but a temperature at which the continuum string picture breaks down. We study a collection of N D-0-branes arranged to form a string having N units of light-cone momentum. We find that at high temperatures the favored phase is one where the string worldsheet has disappeared and the low-energy degrees of freedom consists of N2 massless particles ("gluons"). The nature of the transition is very similar to the deconfinement transition in large-N Yang–Mills theories.

An Applied Form of Kane’s Equations of Motions

2005 ◽  
Author(s):  
Hossein Nejat Pishkenari ◽  
Amir Lotfi Gaskarimahalle ◽  
Seyed Babak Ghaemi Oskouei ◽  
Ali Meghdari
Keyword(s):  
Degrees Of Freedom ◽  
Control Unit ◽  
Generalized Coordinates ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
The Matrix ◽  
Angular Velocities ◽  
New Form ◽  
Derivatives Of ◽  
Equations Of Motions

In this paper we have presented a new form of Kane’s equations. This new form is expressed in the matrix form with the components of partial derivatives of linear and angular velocities relative to the generalized speeds and generalized coordinates. The number of obtained equations is equal to the number of degrees of freedom represented in a closed form. Also the equations can be rearranged to appear only one of the time derivatives of generalized speeds in each equation. This form is appropriate especially when one intends to derive equations recursively. Hence in addition to the simplicity, the amount of calculations is noticeably reduced and also can be used in a control unit.

Muscle and Contact Contributions to Inverse Dynamic Knee Loads During Gait

2009 ◽  
Author(s):  
Benjamin J. Fregly ◽  
Yi-Chung Lin ◽  
Jonathan P. Walter ◽  
Marcus G. Pandy ◽  
Scott A. Banks ◽  
...  
Keyword(s):  
Articular Cartilage ◽  
Degrees Of Freedom ◽  
Muscle Force ◽  
Human Movement ◽  
Contact Forces ◽  
Cartilage Defects ◽  
Inverse Dynamic ◽  
Joint Replacements ◽  
Joint Contact ◽  
Articular Cartilage Defects

Musculoskeletal computer models capable of predicting muscle and joint contact forces accurately during human movement could facilitate the design of improved joint replacements and new clinical treatments for articular cartilage defects or movement-related disorders [1]. A primary challenge to developing such predictions is the non-uniqueness of the calculated muscle forces, often referred to as the “muscle redundancy problem” [2]. Since more muscles act on the skeleton than the number of degrees of freedom in the skeleton, an infinite number of possible muscle force solutions exist.

Influences of Arm Proprioception and Degrees of Freedom on Postural Control With Light Touch Feedback

2008 ◽  
Vol 99 (2) ◽  
pp. 595-604 ◽  
Author(s):  
Ely Rabin ◽  
Paul DiZio ◽  
Joel Ventura ◽  
James R. Lackner
Keyword(s):  
Postural Control ◽  
Degrees Of Freedom ◽  
Biceps Brachii ◽  
Postural Sway ◽  
Center Of Pressure ◽  
Tactile Feedback ◽  
Contact Forces ◽  
Light Touch ◽  
Postural Stabilization ◽  
And Control

Lightly touching a stable surface with one fingertip strongly stabilizes standing posture. The three main features of this phenomenon are fingertip contact forces maintained at levels too low to provide mechanical support, attenuation of postural sway relative to conditions without fingertip touch, and center of pressure (CP) lags changes in fingertip shear forces by ∼250 ms. In the experiments presented here, we tested whether accurate arm proprioception and also whether the precision fingertip contact afforded by the arm's many degrees of freedom are necessary for postural stabilization by finger contact. In our first experiment, we perturbed arm proprioception and control with biceps brachii vibration (120-Hz, 2-mm amplitude). This degraded postural control, resulting in greater postural sway amplitudes. In a second study, we immobilized the touching arm with a splint. This prevented precision fingertip contact but had no effect on postural sway amplitude. In both experiments, the correlation and latency of fingertip contact forces to postural sway were unaffected. We conclude that postural control is executed based on information about arm orientation as well as tactile feedback from light touch, although precision fingertip contact is not essential. The consistent correlation and timing of CP movement and fingertip forces across conditions in which postural sway amplitude and fingertip contact are differentially disrupted suggests posture and the fingertip are controlled in parallel with feedback from the fingertip in this task.

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