Parameter–Excited Instabilities of a 2UPU-RUR-RPS Spherical Parallel Manipulator With a Driven Universal Joint

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
Guanglei Wu
Keyword(s):  
Parallel Manipulator ◽  
Floquet Theory ◽  
Monodromy Matrix ◽  
Critical Parameters ◽  
Parametric Stability ◽  
Parametrically Excited ◽  
Lateral Vibrations ◽  
Stability Chart ◽  
The Stability ◽  
Spherical Parallel Manipulator

This paper presents the parametrically excited lateral instabilities of an asymmetrical spherical parallel manipulator (SPM) by means of monodromy matrix method. The linearized equation of motion for the lateral vibrations is developed to analyze the stability problem, resorting to the Floquet theory, which is numerically illustrated. To this end, the parametrically excited unstable regions of the manipulator are visualized to reveal the effect of the system parameters on the stability. Critical parameters, such as rotating speeds of the driving shaft, are identified from the constructed parametric stability chart for the manipulator.

scholarly journals Calculating periodic vibrations of nonlinear autonomous multi-degree-of-freedom systems by the incremental harmonic balance method

2004 ◽  
Vol 26 (3) ◽  
pp. 157-166
Author(s):  
Nguyen Van Khang ◽  
Thai Manh Cau
Keyword(s):  
Harmonic Balance ◽  
Floquet Theory ◽  
Monodromy Matrix ◽  
Harmonic Balance Method ◽  
Degree Of Freedom ◽  
Balance Method ◽  
Incremental Harmonic Balance Method ◽  
Van Der Pol ◽  
Incremental Harmonic Balance ◽  
The Stability

In this paper the incremental harmonic balance method is used to calculate periodic vibrations of nonlinear autonomous multip-degree-of-freedom systems. According to Floquet theory, the stability of a periodic solution is checked by evaluating the eigenvalues of the monodromy matrix. Using the programme MAPLE, the authors have studied the periodic vibrations of the system multi-degree van der Pol form.

A Study of the Parametrically Excited Behavior of Passenger and Freight Railway Vehicles Using Linear Models

1991 ◽  
Vol 113 (2) ◽  
pp. 336-338 ◽  
Author(s):  
J. Lieh ◽  
I. Haque
Keyword(s):  
Parametric Resonance ◽  
Parametric Excitation ◽  
Floquet Theory ◽  
Linear Models ◽  
Stability Boundaries ◽  
Parametrically Excited ◽  
Critical Speeds ◽  
Railway Vehicles ◽  
Principal Parametric Resonance ◽  
The Stability

This paper presents a study of the parametrically excited behavior of passenger and freight vehicles on tangent track due to harmonic variations in conicity using linear models. The effect of primary and secondary stiffnesses on parametric excitation is also studied. Floquet theory is used to find the stability boundaries. The results show that wavelengths associated with conicity variation that are in the vicinity of half the kinematic wavelengths of the vehicles can lead to significant reductions in critical speeds. Results also show that the primary and warp stiffnesses can affect the severity of principal parametric resonance depending on the vehicle models and magnitude of stiffnesses chosen.

Parametrically Excited Behavior of a Railway Wheelset

1988 ◽  
Vol 110 (1) ◽  
pp. 8-17 ◽  
Author(s):  
J. Lieh ◽  
I. Haque
Keyword(s):  
Floquet Theory ◽  
Initial Conditions ◽  
Excitation Frequency ◽  
Time History ◽  
Parametrically Excited ◽  
Load Variations ◽  
Rail Vehicles ◽  
Stability And Instability ◽  
Instability Regions ◽  
The Stability

The dynamic response of rail vehicles is affected by parameters such as wheel-rail geometry, track gage, and axle load. Variations in these parameters, as a rail vehicle moves down the track, can cause instabilities that are related to parametrically excited behavior. This paper reports on the use of Floquet Theory to predict the stability and instability regions for a single wheelset subjected to harmonic variations in wheel-rail geometry, track gage and axle load. Time studies showing the response of a wheelset to various initial conditions are also included. The results show that harmonic variations in the wheel-rail geometry can influence the behavior of a wheelset significantly. The system is especially susceptible to variations in conicity. Time history studies show that the response is dependent on initial conditions, the amount of variations and the magnitude of the excitation frequency.

Investigation of Parametric Vibration Stability in Slider-Crank Mechanisms With Elastic Coupler

1991 ◽  
Author(s):  
K. Farhang ◽  
A. Midha
Keyword(s):  
Differential Equations ◽  
Floquet Theory ◽  
Continuous Model ◽  
Parametric Vibration ◽  
Connecting Rod ◽  
Parametric Stability ◽  
Vibration Stability ◽  
Geometric Stiffening ◽  
Instability Regions ◽  
The Stability

Abstract An analytical model for investigating parametric vibration stability of slider-crank mechanisms with flexible coupler is presented. The continuous model is formulated to account for initial curvature as well as internal material damping in the coupler. The governing partial differential equations are reduced to a system of ordinary differential equations in terms of the time-dependent modal coefficients. Floquet theory is employed to determine the effects of geometric stiffening as well as relative component mass on parametric stability of mechanism response. Results indicate the existence of instability regions due to combination resonances of various modes. In addition, the stability characteristics of the mechanism is found to improve when slider forces are directed away from the crank-ground pin (i.e. the connecting rod is in tension), and when a relatively smaller slider mass is used.

On the Stability of a Differential Equation With Application to Parametrically Excited Systems

1970 ◽  
Vol 37 (1) ◽  
pp. 218-220
Author(s):  
R. H. Rand ◽  
H. Simon
Keyword(s):  
Differential Equation ◽  
Positive Integer ◽  
Computer Program ◽  
Parametric Excitation ◽  
Digital Computer ◽  
Floquet Theory ◽  
Parametrically Excited ◽  
The Stability

The stability of the equation z¨ + (Δ + ε cos t)−mz = 0, where m is a positive integer, is studied by using Floquet theory and perturbations. The results are confirmed by a digital computer program based on Floquet theory. Physical examples involving parametric excitation for m = 1, 3 are cited from the literature.

Influence of viscosity temperature dependence on the spectral characteristics of the thermoviscous liquids flow stability equation

2019 ◽  
Vol 14 (1) ◽  
pp. 52-58 ◽  
Author(s):  
A.D. Nizamova ◽  
V.N. Kireev ◽  
S.F. Urmancheev
Keyword(s):  
Reynolds Number ◽  
Spectral Characteristics ◽  
Wave Number ◽  
Critical Parameters ◽  
Fluid Viscosity ◽  
Flat Channel ◽  
Stability Equation ◽  
The Stability ◽  
Thermoviscous Fluid ◽  
Sommerfeld Equation

The flow of a viscous model fluid in a flat channel with a non-uniform temperature field is considered. The problem of the stability of a thermoviscous fluid is solved on the basis of the derived generalized Orr-Sommerfeld equation by the spectral decomposition method in Chebyshev polynomials. The effect of taking into account the linear and exponential dependences of the fluid viscosity on temperature on the spectral characteristics of the hydrodynamic stability equation for an incompressible fluid in a flat channel with given different wall temperatures is investigated. Analytically obtained profiles of the flow rate of a thermovisible fluid. The spectral pictures of the eigenvalues of the generalized Orr-Sommerfeld equation are constructed. It is shown that the structure of the spectra largely depends on the properties of the liquid, which are determined by the viscosity functional dependence index. It has been established that for small values of the thermoviscosity parameter the spectrum compares the spectrum for isothermal fluid flow, however, as it increases, the number of eigenvalues and their density increase, that is, there are more points at which the problem has a nontrivial solution. The stability of the flow of a thermoviscous fluid depends on the presence of an eigenvalue with a positive imaginary part among the entire set of eigenvalues found with fixed Reynolds number and wavenumber parameters. It is shown that with a fixed Reynolds number and a wave number with an increase in the thermoviscosity parameter, the flow becomes unstable. The spectral characteristics determine the structure of the eigenfunctions and the critical parameters of the flow of a thermally viscous fluid. The eigenfunctions constructed in the subsequent works show the behavior of transverse-velocity perturbations, their possible growth or decay over time.

Systems with Condensates and Pairing

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Critical Parameters ◽  
Einstein Condensation ◽  
Cooper Pairs ◽  
Pair Breaking ◽  
Systematic Theory ◽  
Bose Einstein Condensation ◽  
T Matrix ◽  
The Stability ◽  
Bose Einstein

The Bose–Einstein condensation and appearance of superfluidity and superconductivity are introduced from basic phenomena. A systematic theory based on the asymmetric expansion of chapter 11 is shown to correct the T-matrix from unphysical multiple-scattering events. The resulting generalised Soven scheme provides the Beliaev equations for Boson’s and the Nambu–Gorkov equations for fermions without the usage of anomalous and non-conserving propagators. This systematic theory allows calculating the fluctuations above and below the critical parameters. Gap equations and Bogoliubov–DeGennes equations are derived from this theory. Interacting Bose systems with finite temperatures are discussed with successively better approximations ranging from Bogoliubov and Popov up to corrected T-matrices. For superconductivity, the asymmetric theory leading to the corrected T-matrix allows for establishing the stability of the condensate and decides correctly about the pair-breaking mechanisms in contrast to conventional approaches. The relation between the correlated density from nonlocal kinetic theory and the density of Cooper pairs is shown.

Task-based torque minimization of a 3-PṞR spherical parallel manipulator

Robotica ◽  
2021 ◽  
pp. 1-30
Author(s):  
Soheil Zarkandi
Keyword(s):  
Closed Form ◽  
Dynamic Modeling ◽  
Dynamic Equation ◽  
Parallel Manipulator ◽  
Optimization Problem ◽  
Dynamic Constraints ◽  
Part C ◽  
Euler Approach ◽  
Three Degree Of Freedom ◽  
Spherical Parallel Manipulator

Abstract A comprehensive dynamic modeling and actuator torque minimization of a new symmetrical three-degree-of-freedom (3-DOF) 3-PṞR spherical parallel manipulator (SPM) is presented. Three actuating systems, each of which composed of an electromotor, a gearbox and a double Rzeppa-type driveshaft, produce input torques of the manipulator. Kinematics of the 3-PṞR SPM was recently studied by the author (Zarkandi, Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 2020, https://doi.org/10.1177%2F0954406220938806). In this paper, a closed-form dynamic equation of the manipulator is derived with the Newton–Euler approach. Then, an optimization problem with kinematic and dynamic constraints is presented to minimize torques of the actuators for implementing a given task. The results are also verified by the SimMechanics model of the manipulator.

Optimal design of a redundant spherical parallel manipulator

Robotica ◽  
1997 ◽  
Vol 15 (4) ◽  
pp. 399-405 ◽  
Author(s):  
Sylvie Leguay-Durand ◽  
Claude Reboulet
Keyword(s):  
Optimal Design ◽  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Structure Optimization ◽  
Kinematic Design ◽  
Spherical Wrist ◽  
Redundant Structure ◽  
Spherical Parallel Manipulator

A new kinematic design of a parallel spherical wrist with actuator redundancy is presented. A special feature of this parallel manipulator is the arrangement of co-axial actuators which allows unlimited rotation about any axis inside a cone-shaped workspace. A detailed kinematic analysis has shown that actuator redundancy not only removes singularities but also increases workspace while improving dexterity. The structure optimization has been performed with a global dexterity criterion. Using a conditioning measure, a comparison with a non-redundant structure of the same type was performed and shows that a significant improvement in dexterity has been obtained.

Sign in / Sign up

Export Citation Format

Share Document