On the Motion of Lineal Bodies Subject to Linear Damping

1997 ◽  
Vol 64 (1) ◽  
pp. 227-229 ◽  
Author(s):  
M. F. Beatty
Keyword(s):  
Differential Equation ◽  
Dynamical Systems ◽  
Rigid Body ◽  
General Class ◽  
Plane Motion ◽  
Rigid Bodies ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Linear Damping

Wilms (1995) has considered the plane motion of three lineal rigid bodies subject to linear damping over their length. He shows that these plane single-degree-of-freedom systems are governed by precisely the same fundamental differential equation. It is not unusual that several dynamical systems may be formally characterized by the same differential equation, but the universal differential equation for these systems is unusual because it is exactly the same equation for the three very different systems. It is shown here that these problems belong to a more general class of problems for which the differential equation is exactly the same for every lineal rigid body regardless of its geometry.

An Optimization Approach to Vibration Isolation of Rigid Bodies

1997 ◽  
Vol 25 (3) ◽  
pp. 165-175
Author(s):  
P. S. Heyns
Keyword(s):  
Design Problem ◽  
Vibration Isolation ◽  
Rigid Bodies ◽  
Degree Of Freedom ◽  
Optimization Approach ◽  
Local Minima ◽  
Single Degree Of Freedom ◽  
Single Degree

The conventional single-degree-of-freedom approach to isolator design dealt with in most undergraduate curricula, is not always adequate for the design of practical isolator systems. In this article, an optimization approach to the design problem is presented and the viability of the approach demonstrated. It is, however, also shown that multiple local minima may exist and that due care should be exercised in the application of the method.

scholarly journals Dynamic Response of Breasting Dolphin Moored with 40,000 DWT Ship due to Parallel Passing Ship Phenomenon

2018 ◽  
Vol 147 ◽  
pp. 05003
Author(s):  
Heri Setiawan ◽  
Muslim Muin
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Dynamic Response ◽  
Computer Program ◽  
Lateral Force ◽  
Degree Of Freedom ◽  
Hydrodynamic Interactions ◽  
Single Degree Of Freedom ◽  
Sdof System ◽  
Single Degree

When a ship is moving through another ship moored nearby, hydrodynamic interactions between these ships result in movements of the moored vessel. The movement may occur as surge, sway, and/or yaw. When a ship is passing a moored vessel parallelly, this effect will give a dominant lateral force on the moored ship and response from this phenomenon will appear in a certain time. Only dynamic response due to sway force is considered in this study, the sway force shall be absorb by the breasting dolphin. 40,000 DWT shall be moored to the breasting dolphin. Three passing ships size are considered, the breasting dolphin shall be modeled as a single degree of freedom model. This model will be subjected to a force caused by parallel passing ship. The model is assumed to be in a state of quiet water, this assumption is taken so that the fluid does not provide additional force on the model. The SDOF system shall be analyzed using a computer program designed to solve an ordinary differential equation.

ON MOTION GENERATION OF WATT I MECHANISMS FOR MECHANICAL FINGER DESIGN

2008 ◽  
Vol 32 (3-4) ◽  
pp. 411-422 ◽  
Author(s):  
QIONG SHEN ◽  
WEN-TZONG LEE ◽  
KEVIN RUSSELL ◽  
RAJ S. SODHI
Keyword(s):  
Rigid Body ◽  
Relative Motion ◽  
Degree Of Freedom ◽  
Planar Motion ◽  
Motion Generation ◽  
Single Degree Of Freedom ◽  
Closed Loops ◽  
Single Degree ◽  
Mechanical Finger

This work formulates and demonstrates a motion generation method for the synthesis of a particular type of planar six-bar mechanism-the Watt I mechanism. The Watt I mechanism is essentially a “stacked” four-bar mechanism (having two closed loops and a single degree of freedom). Extending the planar motion generation method of Suh and Radcliffe [11] to incorporate relative motion between moving pivots, Watt I mechanisms are synthesized to simultaneously approximate two groups of prescribed rigid-body poses for simultaneous dual motion generation capability. The example included demonstrates the synthesis of a finger mechanism to achieve a prescribed grasping pose sequence.

Four-Position Synthesis for Spatial Mechanisms With Two Independent Loops

1992 ◽  
Author(s):  
Chien H. Chiang ◽  
Wei Hua Chieng ◽  
David A. Hoeltzel
Keyword(s):  
Rigid Body ◽  
Mathematical Models ◽  
Analytical Methods ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Practical Applications ◽  
Single Degree ◽  
Spatial Mechanisms ◽  
Position Synthesis ◽  
Independent Loops

Abstract Mathematical models that have been employed to synthesize spatial mechanisms for rigid body guidance have been found to be too complicated to implement in practical applications, especially for four-position guidance synthesis. This paper describes simple analytical methods for synthesizing single degree-of-freedom spatial mechanisms having two independent loops for four precision positions. In addition, prescribed timing has been simultaneously considered for several spatial mechanisms.

A Mechanical Analyzer for the Solution of Vibration Problems of a Single Degree of Freedom

1948 ◽  
Vol 15 (2) ◽  
pp. 146-150
Author(s):  
E. E. Weibel ◽  
N. M. Cokyucel ◽  
R. E. Blau
Keyword(s):  
Generalized Solution ◽  
Nonlinear Damping ◽  
Degree Of Freedom ◽  
Simple Construction ◽  
Dimensionless Form ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Constant Magnitude ◽  
Linear Damping ◽  
Vibration Problems

Abstract A mechanical-analogy-type analyzer is described which is of relatively simple construction being limited to single-degree-of-freedom problems. Whithin this limitation solutions may be obtained for systems which include various types of nonlinear elasticity and of nonlinear damping. Included is a generalized solution obtained on the analyzer giving in dimensionless form the maximum displacements and forces in a system having nonlinear (linear plus cubic) elasticity and linear damping caused by a force pulse of constant magnitude and finite duration. The bearing of the results on the starting torques in nonlinear systems is indicated.

The Study of a Single Degree of Freedom System with Time Dependent Parameters

1967 ◽  
Vol 71 (678) ◽  
pp. 439-440 ◽  
Author(s):  
B. V. Dasarathy ◽  
P. Srinivasan
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Differential Equations ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Time Dependent ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stochastic Nature ◽  
Restoring Forces

The equations of motion of many mechanical systems reduce to ordinary differential equations with time dependent parameters. A single degree of freedom system, with the damping and restoring forces varying with time according to the law … m (t+k)nhas been studied using the WKBJ approximation. The general solution of the differential equation can be used to arrive at the response of such time dependent systems, subjected to excitations which are specified to be of either deterministic or stochastic nature.

Minimum Error Synthesis of Multiloop Plane Mechanisms for Rigid Body Guidance

1974 ◽  
Vol 96 (1) ◽  
pp. 107-116 ◽  
Author(s):  
K. N. Prasad ◽  
C. Bagci
Keyword(s):  
Rigid Body ◽  
Rigid Bodies ◽  
Type I ◽  
Path Generation ◽  
Relaxation Methods ◽  
Single Degree Of Freedom ◽  
Minimum Error ◽  
Numerical Examples ◽  
Single Degree ◽  
Matrix Iteration

A variational method of synthesizing single-degree of freedom, single or multiloop plane mechanisms to guide rigid bodies through specified planar positions is presented. The optimum set of dimensions of a mechanism is determined by minimizing an objective function, which is the sum of the squared errors in the generated coordinates of two body points. The design equations are solved either by matrix iteration or Gaussian relaxation methods. By introducing constraints necessary to coincide the two body points, the problem is reduced to that of optimizing a plane mechanism to generate a planar path. Stephenson six-bar mechanism of Type I and the 4R plane mechanism are synthesized for rigid body guidance and path generation. Numerical examples are given, where all the geometric inversions of a mechanism are synthesized as distinct mechanisms, thereby eliminating the mixing of the geometric inversions at the design positions, thus assuring the mobility of the resulting mechanisms within the design interval.

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