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Piedbœuf, Jean-Claude; Carufel, J. de; Hurteau, R.

doi:10.1023/a:1009888213333

Cited by 34 publications

(6 citation statements)

References 9 publications

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“…While the drag force is proportional and opposite in direction to the velocity, the solid friction force is just a constant and points in the opposite direction of the velocity. The problem of solid friction is a very old problem, arises in many contexts, ranging from geology and engineering to physics and biology and to study the dynamics of a mesoscopic system [5,6,7,8]. Solid friction is necessary in the study of stick-slip motion [9,10,11,12], dynamics of dense granular fluids [13,14,15], vibrated granular media [16,17], pouring of granular particles on an inclined plane and through a chute [18,19,20] as well as ratchet motion of a solid object on a vibrated surface [21,22].…”

Section: Introductionmentioning

confidence: 99%

Single particle Brownian motion with solid friction

2017

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We study the Brownian dynamics of a solid particle on a vibrating solid surface. Phenomenologically, the interaction between the two solid surfaces is modeled by solid friction, and the Gaussian white noise models the vibration of the solid surface. The solid friction force is proportional to the sign of relative velocity. We derive the Fokker-Planck (FP) equation for the time-dependent probability distribution to find the particle at a given location. We calculate analytically the steady state velocity distribution function, mean-square velocity and diffusion coefficient in d-dimensions. We present a generic method of calculating the autocorrelations in d-dimensions. This results in one dimension in an exact evaluation of the steady state velocity autocorrelation. In higher dimensions our exact general expression enables the analytic evaluation of the autocorrelation to any required approximation. We present approximate analytic expressions in two and three dimensions. Next, we numerically calculate the mean-square velocity and steady state velocity autocorrelation function up to d = 3 . Our numerical results are in good agreement with the analytically obtained results.

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Section: Introductionmentioning

confidence: 99%

Single particle Brownian motion with solid friction

2017

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“…An object of mass m initially at rest, v(0) = 0, will therefore remain at rest unless an external force F greater in magnitude than the threshold or contact force ∆ F is applied. This simple description of dry friction is commonly used in engineering and physics to study macroscopic systems in which solid-solid friction plays a significant role [4][5][6][7]. It is used, for example, to study stick-slip motion [8][9][10][11], vibrated granular media [12,13], as well as the ratchet motion of solid objects moving on a surface which is vibrated horizontally by a time-dependent force [14] (see also [15]).…”

Section: Introductionmentioning

confidence: 99%

“…This expression determines a nonnegative bounded real function 6. ∂ Λ D Λ (δ) stands for the derivative of the parabolic cylinder function with respect to its index.…”

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confidence: 99%

Brownian motion with dry friction: Fokker–Planck approach

Touchette¹,

Straeten²,

Just³

2010

J. Phys. A: Math. Theor.

136

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We solve a Langevin equation, first studied by de Gennes, in which there is a solid-solid or dry friction force acting on a Brownian particle in addition to the viscous friction usually considered in the study of Brownian motion. We obtain both the time-dependent propagator of this equation and the velocity correlation function by solving the associated time-dependent Fokker-Planck equation. Exact results are found for the case where only dry friction acts on the particle. For the case where both dry and viscous friction forces are present, series representations of the propagator and correlation function are obtained in terms of parabolic cylinder functions. Similar series representations are also obtained for the case where an external constant force is added to the Langevin equation.

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“…In this concept, the dynamics of a spacecraft including the microgravity condition is predicted by computer simulation [2]. SPDM is a two-arm space robot developed by CSA for the assembly and maintenance of the International Space Station.…”

Section: Introductionmentioning

confidence: 99%

“…The manipulator used in this new system is a cable-driven parallel robot. Unlike the Stewart platform such as the one used in [1] and other rigid-link serial robots such as the one used in [2,3], the cable robot has a much simpler dynamics model because: (1) its cable "links" have negligible inertia compared to its endeffector and thus, the inertia forces and moments of all the links can be ignored; (2) the force in each cable is 1-dimensional only while a rigid link must have a 3-D force plus a 3-D moment instead. As a result, the robot's own dynamics can be accurately predicted and then compensated, which is the most critical requirement for such an HIL simulator.…”

Section: Introductionmentioning

confidence: 99%

Workspace Analysis of a 6-DOF Cable Robot for Hardware-in-the-Loop Dynamic Simulation

Diao

2006

2006 IEEE/RSJ International Conference on Intelligent Robots and Systems

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This paper describes the study of the force-closure workspace of a 6-DOF, cable-driven, parallel robot for the application in a hardware-in-the-loop dynamic simulator, which is used for simulating microgravity contact dynamics of spacecraft or robotic systems. The workspace under study is defined as the set of all end-effector poses satisfying force-closure condition. Force-closure also means that the inverse dynamics problem of the manipulator has a feasible solution. Since there is no limitation on the external wrench and the dynamic motion of the end-effector, such a workspace is the most desirable (or nonrestricted) workspace for the intended application -simulating low-speed impact-contact dynamics. A systematic method of determining whether or not a given end-effector's pose is inside the workspace is proposed with mathematical proof. Based on this method, the shape, boundary, dimensions, and volume of the workspace of a 6-DOF cable robot are displayed and discussed.

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Cited by 34 publications

References 9 publications

Single particle Brownian motion with solid friction

Single particle Brownian motion with solid friction

Brownian motion with dry friction: Fokker–Planck approach

Workspace Analysis of a 6-DOF Cable Robot for Hardware-in-the-Loop Dynamic Simulation

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