Non-periodic motion reduction in globoidal cam with roller follower mechanism

2021 ◽  
pp. 095440622110336
Author(s):  
Louay S Yousuf
Keyword(s):  
Numerical Simulation ◽  
Periodic Motion ◽  
Nonlinear Dynamic ◽  
Degrees Of Freedom ◽  
Nonlinear Response ◽  
Phase Plane ◽  
Infrared Camera ◽  
Power Spectrum Analysis ◽  
Dynamic Movement ◽  
Acquisition Technique

Non periodic motion has been investigated using power spectrum analysis of Fast Fourier Transform (FFT), Lyapunov exponent parameter using Wolf algorithm, and Phase-plane mapping. A multi degrees of freedom (spring-damper system) are added at the end of the follower stem to reduce the nonlinear dynamic behavior of the follower. In the experiment setup, data acquisition technique with signal processing approach is used through an infrared camera device to capture the nonlinear dynamic movement of the follower. A numerical simulation is done using SolidWorks software. An OPTOTRAK/3020 with an infrared camera device is used to track the follower position experimentally. The peak of nonlinear response of the roller follower is reduced by (20.89%, 47.76%, 58.2%, and 67.16%) after using multi degrees of freedom systems.

Insight Into the Non Periodic Motion of the Knife Follower With a Polydyne Cam Mechanism

2020 ◽  
Author(s):  
Louay S. Yousuf ◽  
Yaakob K. H. Dabool
Keyword(s):  
Numerical Simulation ◽  
Fourier Transform ◽  
Lyapunov Exponent ◽  
Angular Velocity ◽  
Power Spectrum ◽  
Periodic Motion ◽  
Phase Plane ◽  
Power Spectrum Analysis ◽  
Cam Follower ◽  
The Impact

Abstract A polydyne cam and knife follower system are studied. The effect of cam angular velocity and follower guides internal dimensions on Lyapunov parameter is considered. Wolf algorithm is used to quantify largest Lyapunov exponent parameter. The impact between the cam, follower and the two guides is occurred due to the impulse and momentum phenomenon. Positive value of Lyapunov exponent parameter indicates to non-periodic motion and chaos for the follower. Non-periodic motion is examined using power spectrum analysis of Fast Fourier Transform (FFT) and phase plane diagram. The numerical simulation has been done using SolidWorks software. Follower movement is processed experimentally through an infrared 3-D camera device with a high precision optical sensor. A polydyne cam and knife follower system are studied. The effect of cam angular velocity and follower guides internal dimensions on Lyapunov parameter is considered. Wolf algorithm is used to quantify largest Lya-punov exponent parameter. The impact between the cam, follower and the two guides is occurred due to the impulse and momentum phenomenon. Positive value of Lyapunov exponent parameter indicates to non-periodic motion and chaos for the follower. Non-periodic motion is examined using power spectrum analysis of Fast Fourier Transform (FFT) and phase plane diagram. The numerical simulation has been done using Solid-Works software. Follower movement is processed experimentally through an infrared 3-D camera device with a high precision optical sensor. The simulation and experimental results are compared and verified for non-periodic motion of the follower. The follower motion is non-periodic when the orbit of phase-plane diagram diverges with no limit of spiral cycles.

Lyapunov Exponent for a Globoidal Cam With a Roller Follower Mechanism Using Wolf Algorithm

2020 ◽  
Author(s):  
Louay S. Yousuf ◽  
Dan B. Marghitu
Keyword(s):  
Numerical Simulation ◽  
Fourier Transform ◽  
Lyapunov Exponent ◽  
Angular Velocity ◽  
Fast Fourier Transform ◽  
Periodic Motion ◽  
Phase Plane ◽  
Largest Lyapunov Exponent ◽  
Cam Follower ◽  
The Impact

Abstract A globoidal cam and roller follower system is analyzed and discussed for non-periodic motion of the follower. Wolf algorithm is used to calculate the largest Lyapunov exponent. The impact between the cam, follower and the two guides is occurred due to the impulse and momentum phenomenon. The effect of the internal dimension of the follower guide on the non-periodic motion of the follower is considered at distinct angular velocity of the cam. The numerical simulation has been done using SolidWorks software. Follower movement is processed experimentally through an infrared 3-D camera device. Phase plane diagram is used to explain the variation in follower motion. Phase-plane diagram and Fast Fourier Transform (FFT) are used to investigate follower non-periodicity. The follower motion is non-periodic when the orbit of phase-plane diagram diverges with no limit of spiral cycles.

Robustness Analysis of a Simple and Augmented Proportional Plus Derivative Controller in Trajectory Following Robots Using the Floquet Theory

2018 ◽  
Vol 13 (7) ◽  
Author(s):  
B. Sandeep Reddy ◽  
Ashitava Ghosal
Keyword(s):  
Numerical Simulation ◽  
Degrees Of Freedom ◽  
Floquet Theory ◽  
Robustness Analysis ◽  
Periodic Trajectory ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Pd Controller ◽  
Simulation Results ◽  
Trajectory Following

This paper deals with the issue of robustness in control of robots using the proportional plus derivative (PD) controller and the augmented PD controller. In the literature, a variety of PD and model-based controllers for multilink serial manipulator have been claimed to be asymptotically stable for trajectory tracking, in the sense of Lyapunov, as long as the controller gains are positive. In this paper, we first establish that for simple PD controllers, the criteria of positive controller gains are insufficient to establish asymptotic stability, and second that for the augmented PD controller the criteria of positive controller gains are valid only when there is no uncertainty in the model parameters. We show both these results for a simple planar two-degrees-of-freedom (2DOFs) robot with two rotary (R) joints, following a desired periodic trajectory, using the Floquet theory. We provide numerical simulation results which conclusively demonstrate the same.

scholarly journals 3DOF Ultrasonic Motor with Two Piezoelectric Rings

Sensors ◽  
2020 ◽  
Vol 20 (3) ◽  
pp. 834 ◽  
Author(s):  
Vytautas Jūrėnas ◽  
Gražvydas Kazokaitis ◽  
Dalius Mažeika
Keyword(s):  
Numerical Simulation ◽  
Magnetic Dipole ◽  
Attitude Control ◽  
Degrees Of Freedom ◽  
High Reliability ◽  
Experimental Studies ◽  
Main Idea ◽  
Ultrasonic Motor ◽  
Response Analysis ◽  
Magnetic Sphere

A novel design of a multiple degrees of freedom (multi-DOF) piezoelectric ultrasonic motor (USM) is presented in the paper. The main idea of the motor design is to combine the magnetic sphere type rotor and two oppositely placed ring-shaped piezoelectric actuators into one mechanism. Such a structure increases impact force and allows rotation of the sphere with higher torque. The main purpose of USM development was to design a motor for attitude control systems used in small satellites. A permanent magnetic sphere with a magnetic dipole is used for orientation and positioning when the sphere is rotated to the desired position and the magnetic field synchronizes with the Earth’s magnetic dipole. Also, the proposed motor can be installed and used for robotic systems, laser beam manipulation, etc. The system has a minimal number of components, small weight, and high reliability. Numerical simulation and experimental studies were used to verify the operating principles of the USM. Numerical simulation of a piezoelectric actuator was used to perform modal frequency and harmonic response analysis. Experimental studies were performed to measure both mechanical and electrical characteristics of the piezoelectric motor.

Numerical simulation of incompressible flows within simple boundaries: accuracy

1971 ◽  
Vol 49 (1) ◽  
pp. 75-112 ◽  
Author(s):  
Steven A. Orszag
Keyword(s):  
Numerical Simulation ◽  
Finite Difference ◽  
Spectral Methods ◽  
Degrees Of Freedom ◽  
Incompressible Flows ◽  
Finite Difference Methods ◽  
Fourier Method ◽  
Passive Scalar ◽  
Mathematical Basis ◽  
Improved Accuracy

Galerkin (spectral) methods for numerical simulation of incompressible flows within simple boundaries are shown to possess many advantages over existing finite-difference methods. In this paper, the accuracy of Galerkin approximations obtained from truncated Fourier expansions is explored. Accuracy of simulation is tested empirically using a simple scalar-convection test problem and the Taylor–Green vortex-decay problem. It is demonstrated empirically that the Galerkin (Fourier) equations involving Np degrees of freedom, where p is the number of space dimensions, give simulations at least as accurate as finite-difference simulations involving (2N)p degrees of freedom. The theoretical basis for the improved accuracy of the Galerkin (Fourier) method is explained. In particular, the nature of aliasing errors is examined in detail. It is shown that ‘aliasing’ errors need not be errors at all, but that aliasing should be avoided in flow simulations. An eigenvalue analysis of schemes for simulation of passive scalar convection supplies the mathematical basis for the improved accuracy of the Galerkin (Fourier) method. A comparison is made of the computational efficiency of Galerkin and finite-difference simulations, and a survey is given of those problems where Galerkin methods are likely to be applied most usefully. We conclude that numerical simulation of many of the flows of current interest is done most efficiently and accurately using the spectral methods advocated here.

Effects of Flexibility and Damping on Momentum Transfer During Locking of Two Moving Links, Part I: Numerical Simulation

1998 ◽  
Vol 65 (2) ◽  
pp. 479-484 ◽  
Author(s):  
W. Szyszkowski ◽  
K. Fielden
Keyword(s):  
Numerical Simulation ◽  
Momentum Transfer ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Slow Motion ◽  
Critical Values ◽  
Governing Equations ◽  
Two Degrees Of Freedom

The system consisting of two links and two joints is examined. The joints are idealy frictionless when unlocked. Due to flexibility of the links, the locking generates some damped vibrations. It is demonstrated that the presence of these vibrations, even of very small and seemingly neglegible amplitudes, have dramatic effects on the after-locking motion of the links. Depending on the level of flexibility and damping involved, the locking triggers a large-scale “slow” motion that may have either oscillatory or circular (clockwise or counterclockwise) characters. The links will stop at some resting configuration only at certain “critical” values of damping. The set of “critical dampings” seems to be infinite, though only two degrees-of-freedom are used to model the system. Governing equations for these phenomena are derived and discussed in Part II of this paper.

Optimizing Fourier Series Based Gaits for Modular Robots Using an Evolutionary Algorithm

2013 ◽  
Author(s):  
David Ko ◽  
Harry H. Cheng
Keyword(s):  
Genetic Algorithm ◽  
Fourier Series ◽  
Evolutionary Algorithm ◽  
Periodic Motion ◽  
Degrees Of Freedom ◽  
Series Representation ◽  
Robotic System ◽  
Experimental Results ◽  
New Method ◽  
Modular Robots

A new method of controlling and optimizing robotic gaits for a modular robotic system is presented in this paper. A robotic gait is implemented on a robotic system consisting of three Mobot modules for a total of twelve degrees of freedom using a Fourier series representation for the periodic motion of each joint. The gait implementation allows robotic modules to perform synchronized gaits with little or no communication with each other making it scalable to increasing numbers of modules. The coefficients of the Fourier series are optimized by a genetic algorithm to find gaits which move the robot cluster quickly and efficiently across flat terrain. Simulated and experimental results show that the optimized gaits can have over twice as much speed as randomly generated gaits.

Nonlinear Dynamic Analysis of a Polydyne Cam With Translated Roller Follower Mechanism With Clearance

2018 ◽  
Author(s):  
Louay S. Yousuf ◽  
Anis Drira
Keyword(s):  
Fourier Transform ◽  
Lyapunov Exponent ◽  
Power Spectrum ◽  
Phase Plane ◽  
Nonlinear Dynamic Analysis ◽  
Power Spectrum Analysis ◽  
Largest Lyapunov Exponent ◽  
Experimental Setup ◽  
Angular Velocities ◽  
The Impact

In this paper, a polydyne cam with translated roller follower over a range of speeds are analyzed. There is a clearance between the follower and the guide. The dynamic simulation is investigated taking into account the impact and the friction. The simulation has been done by using Solidworks program. The effect of follower guides’ clearances on roller follower non-periodicity is considered based on Lyapunov exponent technique. Rosenstein method is used to calculate largest Lyapunov exponent for different angular velocities of the cam. The experimental setup has been implemented by using OPTOTRAK/3020 through a 3-D infrared markers to track follower motion. The power spectrum analysis of Fast Fourier Transform and phase plane contour are examined roller follower non-periodicity.

Elastically Mounted Double Aerodynamic Pendulum

2019 ◽  
Vol 19 (05) ◽  
pp. 1941007 ◽  
Author(s):  
Yury D. Selyutskiy ◽  
Andrei P. Holub ◽  
Marat Z. Dosaev
Keyword(s):  
Experimental Data ◽  
Numerical Simulation ◽  
Degrees Of Freedom ◽  
State University ◽  
Periodic Motions ◽  
Aeroelastic System ◽  
Subsonic Wind Tunnel ◽  
Trivial Equilibrium ◽  
Rotational Degrees Of Freedom ◽  
Moscow State University

Elastically mounted double aerodynamic pendulum is an aeroelastic system with two rotational degrees of freedom. A wing is attached to the second link of the pendulum. It is shown that it is possible to select values of parameters in such a way as to make the trivial equilibrium (where both links of the pendulum are stretched along the flow) unstable. Numerical simulation of behavior of the system in such situations is performed, and arising limit cycles are studied. Experimental investigation of such aerodynamic pendulum is performed in the subsonic wind tunnel of the Institute of Mechanics of Lomonosov Moscow State University. Characteristics of periodic motions are registered for different values of parameters of the system. It is shown that experimental data are in qualitative agreement with results of numerical simulation.

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