Vibration of Cams Having Two Degrees of Freedom

1964 ◽  
Vol 86 (4) ◽  
pp. 343-349 ◽  
Author(s):  
N. S. Eiss
Keyword(s):  
Analytical Solutions ◽  
Vibration Analysis ◽  
Vibration Amplitude ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
The Other ◽  
Tabular Form ◽  
Two Degrees Of Freedom ◽  
Cam Follower ◽  
Two Degree Of Freedom

The vibration analysis of cam-follower systems is extended to models having two degrees of freedom. Two models are considered, one in which the cam support is rigid and the follower has two degrees of freedom, and the other, in which the cam support and follower each have one degree of freedom. Analytical solutions to six acceleration pulses are listed in tabular form. An example shows how tabulated solutions are added to give the displacement of a follower to a modified trapezoidal acceleration function. In another example, it is demonstrated how the parameters of a two-degree-of-freedom model are selected to give the minimum vibration amplitude.

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.

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.

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.

A meshing principle for generating a cylindrical gear using an Archimedes hob with two degrees of freedom

2009 ◽  
Vol 224 (1) ◽  
pp. 169-181 ◽  
Author(s):  
Y Zhao ◽  
D Su ◽  
W Wei ◽  
X Dong
Keyword(s):  
Numerical Simulations ◽  
Industrial Application ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Verification And Validation ◽  
Cylindrical Gear ◽  
Two Degrees Of Freedom ◽  
Numerical Examples ◽  
Two Degree Of Freedom

Thorough and systematic investigations are performed into the meshing principium of generating a cylindrical gear by an Archimedes hob based on the two-degree-of-freedom theory of gearing geometry. The numerical examples show the verification and validation of the formulated principium and the developed model. Conclusions suitable for industrial application are reached by means of numerical simulations.

Period-3 Motions in a Two Degree-of-Freedom Nonlinear Oscillator

2016 ◽  
Author(s):  
Albert C. J. Luo ◽  
Bo Yu
Keyword(s):  
Analytical Solutions ◽  
Nonlinear Oscillator ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Harmonic Amplitude ◽  
Periodic Motions ◽  
Approximate Analytical Solutions ◽  
Amplitude Spectra ◽  
Stability And Bifurcations ◽  
Two Degree Of Freedom

In this paper, periodic motions of a two-degree-of-freedom nonlinear oscillator are studied by using general harmonic balanced method. Stable and unstable period-3 motions are obtained. The corresponding stability and bifurcations of the period-3 motions are determined through the eigenvalue analysis. Both symmetric and asymmetric period-3 motions are found in the system with a certain set of parameter. Numerical simulations of both stable and unstable period-3 motions in the two degrees of freedom systems are illustrated. The harmonic amplitude spectra show the harmonic effects on periodic motions, and the corresponding accuracy of approximate analytical solutions can be observed.

Two-Degree-of-Freedom Decoupled Non-Redundant Cable-Loop-Driven Parallel Mechanism

2012 ◽  
Author(s):  
Hanwei Liu ◽  
Clément Gosselin ◽  
Thierry Laliberté
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
The Other ◽  
Dynamic Equations ◽  
End Effector ◽  
Actuation Redundancy ◽  
Rigid Link ◽  
Force Closure ◽  
Two Degree Of Freedom

A novel two-degree-of-freedom cable-loop slider-driven parallel mechanism is introduced in this paper. 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. Finally, the dynamic equations of the mechanism, including the compliance and the damping of the cables are obtained. The proposed mechanism’s workspace is essentially equal to its footprint and there are no singularities. The mechanism does not require the use of a rigid-link passive bridge and trolley (only cables are connected to the end-effector). Sliders located on the edges of the workspace are used and actuation redundancy is eliminated while providing force closure everywhere in the workspace.

Strouhal Number for VIV Excitation of Long Slender Structures

2018 ◽  
Author(s):  
Andrew E. Potts ◽  
Douglas A. Potts ◽  
Hayden Marcollo ◽  
Kanishka Jayasinghe
Keyword(s):  
Reynolds Number ◽  
Strouhal Number ◽  
Degrees Of Freedom ◽  
Measurement Techniques ◽  
Cross Flow ◽  
Degree Of Freedom ◽  
Circular Cylinders ◽  
Two Degrees Of Freedom ◽  
Shedding Frequency ◽  
Eddy Shedding

The prediction of Vortex-Induced Vibration (VIV) of cylinders under fluid flow conditions depends upon the eddy shedding frequency, conventionally described by the Strouhal Number. The most commonly cited relationship between Strouhal Number and Reynolds Number for circular cylinders was developed by Lienhard [1], whereby the Strouhal Number exhibits a consistent narrow band of about 0.2 (conventional across the sub-critical Re range), with a pronounced hump peaking at about 0.5 within the critical flow regime. The source data underlying this relationship is re-examined, wherein it was found to be predominantly associated with eddy shedding frequency about fixed or stationary cylinders. The pronounced hump appears to be an artefact of the measurement techniques employed by various investigators to detect eddy-shedding frequency in the wake of the cylinder. A variety of contemporary test data for elastically mounted cylinders, with freedom to oscillate under one degree of freedom (i.e. cross flow) and two degrees of freedom (i.e. cross flow and in-line) were evaluated and compared against the conventional Strouhal Number relationship. It is well established for VIV that the eddy shedding frequency will synchronise with the near resonant motions of a dynamically oscillating cylinder, such that the resultant bandwidth of lock-in exhibits a wider range of effective Strouhal Numbers than that reflected in the narrow-banded relationship about a mean of 0.2. However, whilst cylinders oscillating under one degree of freedom exhibit a mean Strouhal Number of 0.2 consistent with fixed/stationary cylinders, cylinders with two degrees of freedom exhibit a much lower mean Strouhal Number of around 0.14–0.15. Data supports the relationship that Strouhal Number does slightly diminish with increasing Reynolds Number. For oscillating cylinders, the bandwidth about the mean Strouhal Number value appears to remain largely consistent. For many practical structures in the marine environment subject to VIV excitation, such as long span, slender risers, mooring lines, pipeline spans, towed array sonar strings, and alike, the long flexible cylinders will respond in two degrees of freedom, where the identified difference in Strouhal Number is a significant aspect to be accounted for in the modelling of its dynamic behaviour.

Galloping Vibration of Nonlinear Cables Through a Two Degree-of-Freedom Oscillator

2016 ◽  
Author(s):  
Albert C. J. Luo ◽  
Bo Yu
Keyword(s):  
Transmission Line ◽  
Analytical Solutions ◽  
Transmission Lines ◽  
Nonlinear Oscillator ◽  
Numerical Solutions ◽  
Degree Of Freedom ◽  
Periodic Motions ◽  
Stability And Bifurcation ◽  
Two Degree Of Freedom

In this paper, galloping vibrations of a lightly iced transmission line are investigated through a two-degree-of-freedom (2-DOF) nonlinear oscillator. The 2-DOF nonlinear oscillator is used to describe the transverse and torsional motions of the galloping cables. The analytical solutions of periodic motions of galloping cables are presented through generalized harmonic balanced method. The analytical solutions of periodic motions for the galloping cable are compared with the numerical solutions, and the corresponding stability and bifurcation of periodic motions are analyzed by the eigenvalues analysis. To demonstrate the accuracy of the analytical solutions of periodic motions, the harmonic amplitudes are presented. This investigation will help one better understand galloping mechanism of iced transmission lines.

Design and Evaluation of a Multi-Degree-of-Freedom Foot/Pedal Interface for Cycling

1992 ◽  
Vol 8 (2) ◽  
pp. 152-164 ◽  
Author(s):  
Dennis Wootten ◽  
Maury L. Hull
Keyword(s):  
Knee Joint ◽  
Significant Interaction ◽  
Degrees Of Freedom ◽  
Knee Injuries ◽  
Degree Of Freedom ◽  
Two Degrees Of Freedom ◽  
Factors Affecting ◽  
Freedom Of Movement ◽  
Sample Data ◽  
Comprehensive Study

Described is the design of a foot/pedal interface intended as a research tool in the study of overuse knee injuries in cycling. The interface enables the systematic variation of factors that may affect loads transmitted by the knee joint. It permits two degrees of freedom of movement, inversion/eversion and abduction/adduction rotations, either separately or in combination. The movement permitted by each degree of freedom can be either free or resisted by spring assemblies. Sample data were collected to demonstrate the function of the foot/pedal interface. With no spring resistance, the interface functioned as intended by allowing free movement of the foot. Significant interaction was seen between the two degrees of freedom, with more motion and a larger absolute mean occurring when both degrees of freedom were allowed simultaneously. This emphasizes the need for a multi-degree-of-freedom interface when undertaking a comprehensive study of the factors affecting loads transmitted by the knee.

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