Preface to Dynamics: Theory and Applications

Kane, T. R.; Levinson, David A.

doi:10.1017/cbo9781139047524.002

Cited by 84 publications

(157 citation statements)

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“…With regards to efficiency, Kane has revealed the notion of generalized speeds to increase the efficiency of expressions [19]. The generalized speeds are functions of generalized coordinates (scalar joint values) and their speeds.…”

Section: Kane's Methodsmentioning

confidence: 99%

“…where the dynamic coordinates are calculated from Kane's method [19]. Dynamic coordinates are obtained as follows: (i) Projecting the resultant forces of each of the kinematic elements through the kinematic coordinates onto the axes of the chosen motion basis of the mechanism; (ii) Then, summing separately all the projected contributions on each of the axes of the motion basis gives the dynamic coordinates of the mechanism.…”

Section: Kinematic and Dynamic Model Of A Parallel Robotmentioning

confidence: 99%

“…. ,q nq } of a robot, was proposed for the first time by Kane [19]. He called this motion basis as generalized speeds.…”

Section: Motion Basismentioning

confidence: 99%

“…Such restrictions are expressed through the implicit kinematic model (ImplKM) of the robot or so-called the holonomic constraint equation [19]:…”

Section: Kinematic Constraints Of a Parallel Robot 531 Configuratimentioning

confidence: 99%

“…Kane [19] expresses the linear and rotational velocities of kinematic elements with the independent generalized scalar coordinates (i.e., state variables), the generalized speeds (i.e., a motion basis) defined in (25) and the partial velocities (i.e., kinematic coordinates). Then, Kane writes the linear velocity for the mass center and the rotational velocity of a kinematic element as follows:…”

Section: Kinematic Coordinates Of a Parallel Robotmentioning

confidence: 99%

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Linear dynamic modeling of parallel kinematic manipulators from observable kinematic elements

Özgür

Andreff

Martinet

2013

Mechanism and Machine Theory

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This paper presents a linear method for kinematic and dynamic modeling of parallel kinematic manipulators. This method is simple, compact and clear. One can write all the equations from the beginning till the end with pen and paper. It is thus well suited to mechanical understanding and computer implementation. We can apply it to many parallel robots. This method relies on a body-oriented representation of observable rectilinear kinematic structures (kinematic elements) which form the robot legs.

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Section: Kane's Methodsmentioning

confidence: 99%

Section: Kinematic and Dynamic Model Of A Parallel Robotmentioning

confidence: 99%

“…. ,q nq } of a robot, was proposed for the first time by Kane [19]. He called this motion basis as generalized speeds.…”

Section: Motion Basismentioning

confidence: 99%

“…Such restrictions are expressed through the implicit kinematic model (ImplKM) of the robot or so-called the holonomic constraint equation [19]:…”

Section: Kinematic Constraints Of a Parallel Robot 531 Configuratimentioning

confidence: 99%

Section: Kinematic Coordinates Of a Parallel Robotmentioning

confidence: 99%

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Linear dynamic modeling of parallel kinematic manipulators from observable kinematic elements

Özgür

Andreff

Martinet

2013

Mechanism and Machine Theory

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Flapwise bending vibration of rotating plates

Yoo

Kim

2002

Numerical Meth Engineering

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SUMMARYLinear equations of motion for the apwise bending vibration analysis of rotating plates are derived in the present work. The equations of motion are transformed into dimensionless forms in which three dimensionless parameters are identiÿed. The e ects of the dimensionless parameters on the characteristics of the apwise bending vibration of rotating plates are investigated. The accuracy of the present modelling method is veriÿed through comparing its numerical results to those obtained by an existing method in the related literature. Eigenvalue loci crossing and eigenvalue loci veering phenomena are observed and discussed. The variations of mode shapes associated with the phenomena are also exhibited.

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Coupling dynamic behaviors of spatial flexible beam with weak damping

Liu

Jiang

et al. 2017

Numerical Meth Engineering

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Summary As a typical high‐dimensional nonlinear dynamic problem, the difficulties of the dynamic analysis on the spatial flexible damping beam mostly result from the coupling between the spatial motion and the transverse vibration. Considering the coupling effect and the weak structure damping, the dynamic behaviors of the spatial flexible beam are investigated by a complex structure‐preserving method in this paper. Based on the variational principle, the dynamic model of the spatial flexible damping beam is established, which can be decoupled into two parts approximately, one controls the spatial motion and another mainly controls the transverse vibration. For the first part, the classic fourth‐order Runge–Kutta method can be used to discrete it expediently. For the latter part, based on the generalized multi‐symplectic idea, the approximate symmetric form as well as the generalized multi‐symplectic conservation law is formulated, and a 15‐point scheme equivalent to the Preissmann scheme is constructed. Numerical iterations are performed for six typical initial cases between the two parts to study the dynamic behaviors of the spatial flexible beam. In the numerical experiments, the effects of the damping factor and the initial conditions (including the initial radial velocity and the initial attitude angle) on the dynamic behaviors of the spatial flexible beam are investigated in detail. From the numerical results, it can be concluded that the damping effect on the long‐time dynamic behaviors of the spatial flexible beam could not be neglected even if it is weak; the numerical method proposed in this paper owns the tiny numerical dissipation as well as the excellent long‐time numerical stability. Copyright © 2016 John Wiley & Sons, Ltd.

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Preface to Dynamics: Theory and Applications

Cited by 84 publications

References 0 publications

Linear dynamic modeling of parallel kinematic manipulators from observable kinematic elements

Linear dynamic modeling of parallel kinematic manipulators from observable kinematic elements

Flapwise bending vibration of rotating plates

Coupling dynamic behaviors of spatial flexible beam with weak damping

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