Lateral Dynamics and Stability of the Skateboard

1979 ◽  
Vol 46 (4) ◽  
pp. 931-936 ◽  
Author(s):  
M. Hubbard
Keyword(s):  
Critical Speed ◽  
Experimental Validation ◽  
Degree Of Freedom ◽  
Forward Speed ◽  
Stability Criteria ◽  
Vehicle Model ◽  
Inertia Effects ◽  
Lateral Dynamics ◽  
Parameter Values ◽  
Two Degree Of Freedom

The natural lateral dynamic behavior of a skateboard is described in the absence of rider control. The effects of vehicle and rider parameters are investigated and stability criteria are derived in terms of these parameters. It is shown that for certain parameter values a simple one-degree-of-freedom vehicle model predicts a critical speed above which inertia effects can stabilize the roll motion, and that the frequency of roll oscillations is a function of forward speed. A more complicated two-degree-of-freedom vehicle model, including independent roll of both the board and of the rider, is also derived and is shown to have the possibility of speed stabilization as well. Experimental validation of the first theory is included.

Non-linear torsional oscillation of a two-degree-of-freedom system incorporating a Hooke joint

1964 ◽  
Vol 277 (1368) ◽  
pp. 92-106 ◽  
Keyword(s):  
Large Amplitude ◽  
Critical Speed ◽  
Torsional Oscillation ◽  
Degree Of Freedom ◽  
Non Linear ◽  
Two Degree Of Freedom

The non-linear torsional oscillation of the system is analyzed by means of a variant of Kryloff and Bogoliuboff’s method. It is shown that each mode of the system can perform oscillations of large amplitude in a number of critical speed ranges, and that hysteresis effects and discontinuous jumps in amplitude are to be expected in these speed ranges if the damping is light.

The Galloping Response of a Two-Degree-of-Freedom System

1974 ◽  
Vol 41 (4) ◽  
pp. 1113-1118 ◽  
Author(s):  
R. D. Blevins ◽  
W. D. Iwan
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Natural Frequencies ◽  
Analytic Solutions ◽  
Degree Of Freedom ◽  
Approximate Analysis ◽  
Stability Criteria ◽  
Integer Multiple ◽  
Two Degree Of Freedom ◽  
Steady State Solutions

The galloping response of a two-degree-of-freedom system is investigated using asymptotic techniques to generate approximate steady-state solutions. Simple closed-form analytic solutions and stability criteria are presented for the case where the two structural natural frequencies are harmonically separated. Examples of the nature of the galloping response of a particular section are presented for the case where the frequencies are harmonically separated as well as for the case where the two natural frequencies are near an integer multiple of each other. The results of the approximate analysis are compared with experimental and numerical results.

Decentralized Control of Active Vehicle Suspensions With Preview

1995 ◽  
Vol 117 (4) ◽  
pp. 478-483 ◽  
Author(s):  
Aleksander Hac´
Keyword(s):  
Decentralized Control ◽  
The Body ◽  
Degree Of Freedom ◽  
Vehicle Model ◽  
Fast Subsystem ◽  
Interconnected System ◽  
Single Degree Of Freedom ◽  
Vehicle Suspensions ◽  
Slow Subsystem ◽  
Two Degree Of Freedom

In this paper, decentralized control of active vehicle suspensions with preview of road irregularities is considered using a two-degree-of-freedom vehicle model. It is shown that by taking advantage of the separation between the eigenvalues of the slow subsystem representing the body mode, and the fast subsystem corresponding to the wheel mode, the design of the preview controller can be decoupled. Since decentralized preview controllers are synthesized independently for two single-degree-of-freedom systems, analytical solutions are obtained. The results of the analysis and simulations demonstrate that the performance of the system with the proposed controller is comparable to that of the optimal preview controller based on a fully interconnected system.

On the Response of a Two-Degree-of-Freedom Rigid Disk With a Moving Massive Load

1973 ◽  
Vol 40 (1) ◽  
pp. 114-120 ◽  
Author(s):  
K. J. Stahl ◽  
W. D. Iwan
Keyword(s):  
Critical Speed ◽  
Equations Of Motion ◽  
Circular Disk ◽  
Instability Region ◽  
Degree Of Freedom ◽  
Viscous Damping ◽  
Elastically Supported ◽  
Two Degree Of Freedom ◽  
Limiting Value ◽  
Mathieu Equations

An analysis of the dynamic response of an elastically supported two-degree-of-freedom rigid circular disk excited by a moving massive load is presented. The equations of motion of the system are solved by transforming a set of coupled Hill-Mathieu equations into an ordinary eigenvalue problem. Two types of system instability are observed. A stiffness instability region exists above the critical speed of the disk and a terminal instability region exists for all load speeds exceeding a certain limiting value. The introduction of viscous damping may destabilize the system.

Design and Experimental Validation of a Two-Degree-of-Freedom Force Illusion Device

2014 ◽  
Author(s):  
Nicolò Pedemonte ◽  
Frédérik Berthiaume ◽  
Thierry Laliberté ◽  
Clément Gosselin
Keyword(s):  
External Force ◽  
Parallel Mechanism ◽  
Visually Impaired ◽  
Experimental Validation ◽  
Degree Of Freedom ◽  
Haptic Device ◽  
Visually Impaired People ◽  
Impaired People ◽  
Two Degree Of Freedom

In this paper, a new hand-held haptic device that aims at producing the illusion of an external force is presented. This device is based on a planar two-degree-of-freedom parallel mechanism that can be programmed to produce the force illusion in any direction of the plane. Two tests are proposed to a group of people, in order to evaluate the device’s capabilities. The results obtained from the tests are analyzed and shown to be promising. Finally, modifications to the device are proposed in order to further improve the effectiveness of the system. The device proposed in this work is envisioned as a guidance tool for visually impaired people.

Non-Linear Torsional Vibration of a Two-Degree-of-Freedom System Having Variable Inertia

1965 ◽  
Vol 7 (1) ◽  
pp. 101-113 ◽  
Author(s):  
B. Porter
Keyword(s):  
Normal Mode ◽  
Torsional Vibration ◽  
Large Amplitude ◽  
Critical Speed ◽  
Degree Of Freedom ◽  
Reciprocating Engine ◽  
Non Linear ◽  
Two Degree Of Freedom

A variant of Kryloff and Bogoliuboff's method is used to analyse the periodic vibrations of a non-linear two-degree-of-freedom system which is an idealization of the crankshaft of a two-cylinder in-line reciprocating engine. It is shown that there are two critical speed ranges associated with each normal mode of the system within which periodic harmonic or subharmonic vibrations of large amplitude can occur as a result of variable-inertia excitation. Extensions of the results to homogeneous in-line engines having any number of cylinders are indicated.

Asymptotic Analysis of the Torsional Vibrations in Reciprocating Machinery

1996 ◽  
Vol 118 (3) ◽  
pp. 485-490 ◽  
Author(s):  
H. Ashrafiuon ◽  
A. M. Whitman
Keyword(s):  
Numerical Modeling ◽  
Steady State ◽  
Asymptotic Analysis ◽  
Degree Of Freedom ◽  
Torsional Vibrations ◽  
Transient Vibration ◽  
Asymptotic Expressions ◽  
Parameter Values ◽  
Two Degree Of Freedom ◽  
Good Agreement

A class of two degree of freedom reciprocating machines is analyzed and simple asymptotic expressions for both the steady state and transient vibration levels are obtained. The results are compared with those of a standard numerical modeling package, and are found to be in good agreement for parameter values typical of real machines. This happens because real machines are designed so that the vibration levels are small, thereby satisfying the conditions for the validity of the approximation.

Asymptotic Analysis of the Torsional Vibrations in Reciprocating Machinery

1995 ◽  
Author(s):  
Hashem Ashrafiuon ◽  
Alan M. Whitman
Keyword(s):  
Numerical Modeling ◽  
Steady State ◽  
Asymptotic Analysis ◽  
Degree Of Freedom ◽  
Torsional Vibrations ◽  
Transient Vibration ◽  
Asymptotic Expressions ◽  
Parameter Values ◽  
Two Degree Of Freedom ◽  
Good Agreement

Abstract A class of two degree of freedom reciprocating machines is analysed and simple asymptotic expressions for both the steady state and transient vibration levels are obtained. The results are compared with those of a standard numerical modeling package, and are found to be in good agreement for parameter values typical of real machines. This happens because real machines are designed so that the vibration levels are small, thereby satisfying the conditions for the validity of the approximation.

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