scholarly journals The dynamics of rigid body whose sharp edge is in contact with a inclined surface with dry friction

2013 ◽  
pp. 567-594
Author(s):  
I. S. Mamaev ◽  
◽  
T. B. Ivanova ◽  
Keyword(s):  
Rigid Body ◽  
Dry Friction ◽  
Sharp Edge ◽  
Dynamics Of Rigid Body ◽  
Inclined Surface

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

A Hybrid Highly Parallelizable Algorithm for the Dynamics of Rigid Body Chain Systems

1999 ◽  
Author(s):  
Shanzhong Duan ◽  
Kurt S. Anderson
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Constraint Forces ◽  
Dynamics Of Rigid Body ◽  
A Chain ◽  
Explicit Determination ◽  
Order Algorithm

Abstract The paper presents a new hybrid parallelizable low order algorithm for modeling the dynamic behavior of multi-rigid-body chain systems. The method is based on cutting certain system interbody joints so that largely independent multibody subchain systems are formed. These subchains interact with one another through associated unknown constraint forces f¯c at the cut joints. The increased parallelism is obtainable through cutting the joints and the explicit determination of associated constraint loads combined with a sequential O(n) procedure. In other words, sequential O(n) procedures are performed to form and solve equations of motion within subchains and parallel strategies are used to form and solve constraint equations between subchains in parallel. The algorithm can easily accommodate the available number of processors while maintaining high efficiency. An O[(n+m)Np+m(1+γ)Np+mγlog2Np](0<γ<1) performance will be achieved with Np processors for a chain system with n degrees of freedom and m constraints due to cutting of interbody joints.

The Motion of a Rolling Polygon

2003 ◽  
Vol 70 (2) ◽  
pp. 275-280 ◽  
Author(s):  
E. M. Beunder ◽  
P. C. Rem
Keyword(s):  
Angular Velocity ◽  
Dry Friction ◽  
Coulomb’S Law ◽  
Inclined Surface ◽  
Coulomb's Law

Galileo was the first to analyze the motion of spheres rolling down an inclined surface. Since then, Coulomb’s law of dry friction has covered the case of sliding particles. However, a particle that is not round can still roll, although in a way that is essentially different from the motion studied by Galileo. Instead of keeping contact with the surface, such particles will start bouncing after reaching a certain angular velocity. This motion is a combination of flying and colliding. It is shown that the acceleration of a bouncing particle is always bounded by the accelerations for perfect rolling and sliding. In order to describe the motion of a not perfectly round particle, the polygon is used as a model. The aim of the model is to predict the trajectories of particles that cannot be covered by the models for perfect rolling and sliding.

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