The painleve paradoxes and the law of motion of mechanical systems with Coulomb friction

1990 ◽  
Vol 54 (4) ◽  
pp. 430-438 ◽  
Author(s):  
Le Suan An
Keyword(s):  
Coulomb Friction ◽  
Mechanical Systems ◽  
The Law ◽  
Painlevé Paradoxes

The simulation of Coulomb friction in mechanical systems

SIMULATION ◽  
1980 ◽  
Vol 34 (1) ◽  
pp. 11-16 ◽  
Author(s):  
James E. Bernard
Keyword(s):  
Coulomb Friction ◽  
Mechanical Systems

Geometrical conditions for wedging in mechanical systems with Coulomb friction

2009 ◽  
Vol 223 (5) ◽  
pp. 1171-1179 ◽  
Author(s):  
M M Zhechev ◽  
M V Khramova
Keyword(s):  
Mechanical System ◽  
Coulomb Friction ◽  
Theoretical Study ◽  
Mechanical Systems ◽  
Process Automation ◽  
Frictional Contacts ◽  
Rigorous Definition ◽  
Automation Systems ◽  
The Cost

It is known that a phenomenon referred to as wedging can occur in mechanical systems with friction. This phenomenon occurs in certain system positions, and an actual mechanical system can be started from a wedged position only at the cost of irreversible deformations. Although the results of the theoretical study of wedging are of great importance in the development and operation of process automation systems, the theory of this phenomenon is still in the making. In this work, the notion of a wedgeable system is introduced and its rigorous definition is given. Within the framework of the traditional formulation, this definition reflects the properties of wedging in actual mechanical systems in the most adequate manner. Based on this notion, a number of statements on wedging conditions in mechanical systems with two and three frictional contacts are proved. Simple, convenient in use rules are given for identifying the possibility of wedging in peg-in-hole systems with two and three frictional contacts.

Simulation of Friction in Multi-Degree-of-Freedom Vibration Systems

1998 ◽  
Vol 120 (1) ◽  
pp. 144-146 ◽  
Author(s):  
Xi Tan ◽  
R. J. Rogers
Keyword(s):  
Analytical Solutions ◽  
Coulomb Friction ◽  
Mechanical Systems ◽  
Friction Model ◽  
Degree Of Freedom ◽  
Force Balance ◽  
Dynamic Mechanical ◽  
Slipping Friction ◽  
Piecewise Continuous ◽  
Coulomb Friction Model

A force-balance friction model for the simulation of dynamic mechanical systems is presented. An extension of Karnopp’s model (1985), it can be applied to multi-degree-of-freedom vibration systems with sticking/slipping friction acting on a surface. The model is compared with piecewise continuous analytical solutions which use the classical Coulomb friction model. During sticking periods, the results from the present friction model change smoothly, whereas chattering appears when using the classical Coulomb friction model.

scholarly journals On the regularization of impact without collision: the Painlevé paradox and compliance

2017 ◽  
Vol 473 (2202) ◽  
pp. 20160773 ◽  
Author(s):  
S. J. Hogan ◽  
K. Uldall Kristiansen
Keyword(s):  
Coulomb Friction ◽  
Exact Formula ◽  
Rigid Bodies ◽  
Painlevé Paradox ◽  
Asymptotic Expressions ◽  
Reaction Forces ◽  
Lift Off ◽  
Stiffness And Damping ◽  
Impact Without Collision ◽  
Painlevé Paradoxes

We consider the problem of a rigid body, subject to a unilateral constraint, in the presence of Coulomb friction. We regularize the problem by assuming compliance (with both stiffness and damping) at the point of contact, for a general class of normal reaction forces. Using a rigorous mathematical approach, we recover impact without collision (IWC) in both the inconsistent and the indeterminate Painlevé paradoxes, in the latter case giving an exact formula for conditions that separate IWC and lift-off. We solve the problem for arbitrary values of the compliance damping and give explicit asymptotic expressions in the limiting cases of small and large damping, all for a large class of rigid bodies.

Three Dimensional Digital Simulation of Legged Robots

1996 ◽  
Vol 8 (3) ◽  
pp. 266-271 ◽  
Author(s):  
Yasutaka Fujimoto ◽  
◽  
Atsuo Kawamura
Keyword(s):  
Coulomb Friction ◽  
Digital Simulation ◽  
Three Dimensional ◽  
Mechanical Systems ◽  
Biped Robot ◽  
Simulation Method ◽  
Legged Robots ◽  
Control Algorithms ◽  
Robot System ◽  
Rigid Body Mechanics

This paper describes a new simulation method of multidegree-of-motion-freedom mechanical systems with the time-dependent contact and the Coulomb friction, such as a legged robot interacting with the ground and a satellite-mounted manipulator catching an object. The proposed approach is the extension of the open link manipulator simulation method and the contact simulation method of rigid body mechanics. The proposed simulation model can be said to be mathematically exact, thus this approach enables the essential investigation for control algorithms of the mechanical systems. The method is tested on a biped robot system and some results are shown.

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