Kinematical Analysis of Overconstrained Mechanism Using Computational Geometric Algebra

2008 ◽  
Author(s):  
Samuli Piipponen ◽  
Jukka Tuomela ◽  
Teijo Arponen
Keyword(s):  
Configuration Space ◽  
Wide Class ◽  
Geometric Algebra ◽  
Multibody Systems ◽  
Closed Curve ◽  
Point Of View ◽  
Rigid Multibody Systems ◽  
New Formulation ◽  
Rigid Multibody ◽  
Better Than

In this paper we will show how the methods of computational and geometric algebra can be used to analyze the kinematics of multibody systems. As an example we treat thoroughly the well known Bricard’s mechanism which is a classic example of so called overconstrained mechanism, but the same methods can be applied to wide class of rigid multibody systems. It turns out that the configuration space of Bricard’s system is a smooth closed curve which can be explicitly parametrized. Our computations also yield a new formulation of constraints which is better than the original one from the point of view of numerical simulations.

On the Stability of Rigid Multibody Systems With Applications to Robotic Grasping and Locomotion

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Péter L. Várkonyi
Keyword(s):  
Potential Energy ◽  
Wide Class ◽  
Multibody Systems ◽  
Local Minima ◽  
Small Perturbations ◽  
Rigid Multibody Systems ◽  
The Stability ◽  
External Forces ◽  
Rigid Multibody ◽  
Accelerating Motion

This paper shows that the equilibria of a wide class of multibody systems with quasi-rigid, frictional, or frictionless supports correspond to local minima of their potential energy; hence they are stable against small perturbations of external forces. This is a generalization of a theorem by Howard and Kumar on the stability of a single rigid body held by a gripper. It is also demonstrated that ambiguous equilibria (those, which coexist with the possibility of accelerating motion) may be stable. These results help finding safe grasps on nonrigid objects and assessing the stability of quasi-static robots moving over complex terrains.

Rigid Multibody Systems: The Plastic Hinge Approach

2001 ◽  
pp. 205-237 ◽  
Author(s):  
J. A. C. Ambrósio ◽  
M. Seabra Pereira ◽  
J. F. A. Milho
Keyword(s):  
Multibody Systems ◽  
Plastic Hinge ◽  
Rigid Multibody Systems ◽  
Rigid Multibody

SYMBOLIC TREATMENT FOR THE EQUATIONS OF MOTION FOR RIGID MULTIBODY SYSTEMS

2010 ◽  
Vol 34 (1) ◽  
pp. 37-55 ◽  
Author(s):  
Bukoko C. Ikoki ◽  
Marc J. Richard ◽  
Mohamed Bouazara ◽  
Sélim Datoussaïd
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Dynamic Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
The World ◽  
Rigid Multibody Systems ◽  
Symbolic Approach ◽  
Rigid Multibody

The library of symbolic C++ routines is broadly used throughout the world. In this article, we consider its application in the symbolic treatment of rigid multibody systems through a new software KINDA (KINematic & Dynamic Analysis). Besides the attraction which represents the symbolic approach and the effectiveness of this algorithm, the capacities of algebraical manipulations of symbolic routines are exploited to produce concise and legible differential equations of motion for reduced size mechanisms. These equations also constitute a powerful tool for the validation of symbolic generation algorithms other than by comparing results provided by numerical methods. The appeal in the software KINDA resides in the capability to generate the differential equations of motion from the choice of the multibody formalism adopted by the analyst.

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