scholarly journals On Nonconservative Stability Problems of Elastic Systems With Slight Damping

1966 ◽  
Vol 33 (1) ◽  
pp. 125-133 ◽  
Author(s):  
G. Herrmann ◽  
I. C. Jong
Keyword(s):  
Degrees Of Freedom ◽  
Compressive Load ◽  
Viscous Damping ◽  
Two Degrees Of Freedom ◽  
Stability Problems ◽  
Damping Coefficients ◽  
Stability And Instability ◽  
Elastic Systems ◽  
Nonconservative Loading ◽  
Two Degree Of Freedom

A linear two-degree-of-freedom system with slight viscous damping and subjected to nonconservative loading is analyzed with the aim of studying the effects of damping on stability of equilibrium. It is found that, in such systems, multiple ranges of stability and instability may exist in a richer variety than in corresponding systems without damping. Further, for certain systems, instability either by divergence (static buckling) or by flutter may occur first as the compressive load increases, depending upon the ratio of the damping coefficients in the two degrees of freedom. It is shown finally that systems exist for which the destabilizing effect of slight viscous damping cannot be removed completely whatever the ratio of the (positive) damping coefficients.

Harmonic Oscillations of Nonlinear Two-Degree-of-Freedom Systems

1955 ◽  
Vol 22 (1) ◽  
pp. 107-110
Author(s):  
T. C. Huang
Keyword(s):  
Nonlinear System ◽  
Degrees Of Freedom ◽  
Forced Oscillations ◽  
Viscous Damping ◽  
Free Oscillations ◽  
Response Curves ◽  
Harmonic Oscillations ◽  
Restoring Force ◽  
Nonlinear Restoring Force ◽  
Two Degree Of Freedom

Abstract In this paper an investigation is made of equations governing the oscillations of a nonlinear system in two degrees of freedom. Analyses of harmonic oscillations are illustrated for the cases of (1) the forced oscillations with nonlinear restoring force, damping neglected; (2) the free oscillations with nonlinear restoring force, damping neglected; and (3) the forced oscillations with nonlinear restoring force, small viscous damping considered. Amplitudes of oscillations and frequency equations are derived based on the mathematically justified perturbation method. Response curves are then plotted.

On the Stability of Elastic Systems Subjected to Nonconservative Forces

1964 ◽  
Vol 31 (3) ◽  
pp. 435-440 ◽  
Author(s):  
G. Herrmann ◽  
R. W. Bungay
Keyword(s):  
Critical Loads ◽  
Kinetic Method ◽  
Euler Method ◽  
Parameter Instability ◽  
Linear Elastic ◽  
Elastic Systems ◽  
Nonconservative Loading ◽  
The Stability ◽  
Two Degree Of Freedom ◽  
Increasing Load

Free motions of a linear elastic, nondissipative, two-degree-of-freedom system, subjected to a static nonconservative loading, are analyzed with the aim of studying the connection between the two instability mechanisms (termed divergence and flutter by analogy to aeroelastic phenomena) known to be possible for such systems. An independent parameter is introduced to reflect the ratio of the conservative and nonconservative components of the loading. Depending on the value of this parameter, instability is found to occur for compressive loadings by divergence (static buckling), flutter, or by both (at different loads) with multiple stable and unstable ranges of the load. In the latter case either type of instability may be the first to occur with increasing load. For a range of the parameter, divergence (only) is found to occur for tensile loads. Regardless of the non-conservativeness of the system, the critical loads for divergence can always be determined by the (static) Euler method. The critical loads for flutter (occurring only in nonconservative systems) can be determined, of course, by the kinetic method alone.

scholarly journals Turning characteristics of biomimetic robotic fish driven by two degrees of freedom of pectoral fins and flexible body/caudal fin

2018 ◽  
Vol 15 (1) ◽  
pp. 172988141774995 ◽  
Author(s):  
Zonggang Li ◽  
Liming Ge ◽  
Weiqiang Xu ◽  
Yajiang Du
Keyword(s):  
Numerical Simulations ◽  
Degrees Of Freedom ◽  
Robotic Fish ◽  
Flexible Body ◽  
Caudal Fin ◽  
Two Degrees Of Freedom ◽  
Pectoral Fins ◽  
Turn On ◽  
Biomimetic Robotic Fish ◽  
Two Degree Of Freedom

This article considers the turning characteristics of robotic fish with two-degree-of-freedom pectoral fins and flexible body/caudal fin. The hydrodynamics are first established for three cases propelled by both sides of pectoral fins, flexible body/caudal fin, and composite of them. Then, the turning characteristics of such three cases are analyzed by numerical simulations and experiments. The results show that if robotic fish is cooperatively propelled by pectoral fins and flexible body, it can obtain the fast turning speed and the average turning speed is up to 0.6 rad s−1. The smallest turning speed is achieved as robotic fish is only propelled by pectoral fins; however, it can turn on the spot in this case. The presented results provide the more abundant ways of turning, the better maneuverability, and the higher turning speed for the proposed robotic fish.

Stability of Dynamic Systems

1983 ◽  
Vol 50 (4b) ◽  
pp. 1086-1096 ◽  
Author(s):  
H. H. E. Leipholz
Keyword(s):  
Finite Number ◽  
Infinite Number ◽  
Dynamic Systems ◽  
Stability Theory ◽  
Degrees Of Freedom ◽  
Continuous Systems ◽  
Specific Nature ◽  
Stability Problems ◽  
Comprehensive Theory ◽  
Elastic Systems

It is shown how stability theory of dynamic systems, emerging from various beginnings strewn over the realm of mechanics, developed into a unified, comprehensive theory for dynamic systems with a finite number of degrees of freedom. It is then demonstrated, how such theory could be adapted over the last five decades to the specific nature of stability problems involving continuous elastic systems. The need for such adaption is stressed by pointing to systems with follower forces. The difficulties arising from the fact that continuous systems are systems with an infinite number of degrees of freedom are emphasized, and an adequate approach to a unified stability theory including also continuous systems is outlined.

The Design of Three Jointed Two-Degree-of-Freedom Robot Fingers

1987 ◽  
Author(s):  
S. O. Leaver ◽  
J. M. McCarthy
Keyword(s):  
Mechanical Model ◽  
Degrees Of Freedom ◽  
Two Degrees Of Freedom ◽  
Mechanical Hand ◽  
Planar Manipulators ◽  
Payload Capacity ◽  
Human Finger ◽  
Finger Tip ◽  
Fully Coupled ◽  
Two Degree Of Freedom

Abstract The design of modern mechanical hands requires a choice for the kinematic structure of the finger. The typical finger is a planar manipulator with one, two, or three independently controllable joints. Each controllable joint requires a motor and sensor system which increases the weight of the hand. There is a desire to minimize the number of degrees of freedom in a mechanical hand because the payload capacity of a manipulator is limited. Two degrees of freedom provides the required positioning capability of a finger tip (though not the ability to control contact angle). Three joints are required to provide the ability to enclose grasped objects. This paper considers the design of fingers which are planar manipulators with three joints but only two degrees of freedom. In addition to the fully coupled design, twelve classes of finger designs with varying degrees of de-coupling are presented. It happens that one of these classes includes the human finger, a mechanical model of which is presented in detail.

A 7R-Based, Two Degrees of Freedom Robomech

2000 ◽  
Author(s):  
Ahmad A. Smaili
Keyword(s):  
Degrees Of Freedom ◽  
Parallel Architecture ◽  
Degree Of Freedom ◽  
Robot Arm ◽  
End Effector ◽  
Kinematic Constraints ◽  
Two Degrees Of Freedom ◽  
Synthesis Procedure ◽  
Two Degree Of Freedom

Abstract A robomech is a crossbreed of a mechanism and a robot arm. It has a parallel architecture equipped with more than one end effector to accomplish tasks that require the coordination of many functions. Robomechs with multi degrees of freedom that are based on the 4R and 5R chains have found their way into the literature. This article presents a new, two-degree of freedom robomech whose architecture is based on the 7R chain. The robomech is capable of performing two-function tasks. The features, kinematic constraints, and synthesis procedure of the robomech are outlined and an application example is given.

Two-Degree-of-Freedom Decoupled Nonredundant Cable-Loop-Driven Parallel Mechanism

2013 ◽  
Vol 6 (1) ◽  
Author(s):  
Hanwei Liu ◽  
Clément Gosselin ◽  
Thierry Laliberté
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
The Other ◽  
End Effector ◽  
Two Degrees Of Freedom ◽  
Actuation Redundancy ◽  
Rigid Link ◽  
Force Closure ◽  
Two Degree Of Freedom

A novel two-degree-of-freedom (DOF) cable-loop slider-driven parallel mechanism is introduced in this paper. The novelty of the mechanism lies in the fact that no passive rigid-link mechanism or springs are needed to support the end-effector (only cables are connected to the end-effector) while at the same time there is no actuation redundancy in the mechanism. Sliders located on the edges of the workspace are used and actuation redundancy is eliminated while providing force closure everywhere in the workspace. It is shown that 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. The proposed mechanism's workspace is essentially equal to its footprint and there are no singularities.

Period-1 Motions in a Two-Degree-of-Freedom Nonlinear Oscillator With Periodic Excitation

2015 ◽  
Author(s):  
Albert C. J. Luo ◽  
Bo Yu
Keyword(s):  
Analytical Solutions ◽  
Nonlinear Oscillator ◽  
Degrees Of Freedom ◽  
Harmonic Amplitude ◽  
Periodic Excitation ◽  
Periodic Motions ◽  
Two Degrees Of Freedom ◽  
Approximate Analytical Solutions ◽  
The Stability ◽  
Two Degree Of Freedom

In this paper, analytical solutions for period-1 motions in a periodically forced, two-degrees-of-freedom system with a nonlinear spring are developed. The stability and bifurcation of the periodic motions are completed by the eigenvalue analysis. Both symmetric and asymmetric periodic motions are found in the system. Analytical solutions of both stable and unstable period-1 are presented. Finally, numerical simulations of stable and unstable motions in the two degrees of freedom systems are presented. The harmonic amplitude spectrums show the harmonic effects on periodic motions, and the corresponding accuracy of approximate analytical solutions can be observed.

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