Self-Adaptation of Natural-Coordinate System

2013 ◽  
Vol 367 ◽  
pp. 286-291
Author(s):  
Ke Wei Zhang ◽  
Yun Qing Zhang
Keyword(s):  
Coordinate System ◽  
Equal Weight ◽  
Natural Coordinates ◽  
Model Quality ◽  
Step Method ◽  
Natural Coordinate System ◽  
Self Adaptation ◽  
Natural Coordinate ◽  
Analysis Platform ◽  
Adaptation Method

A self-adaptation method for natural-coordinate systems is proposed, in order to automate the selection of natural coordinates for each rigid element of a multibody system. The four-step method includes: First, find out all empty positions, which come from the feature points or vectors of the joints attached to the element, and give equal weight to them; second, delete redundant empty positions and add their weight to the unique one; third, select at most four empty positions which have a maximum total weight and can be occupied by a natural-coordinate system at the same time; fourth, the standard natural-coordinate system on the element can adapt itself to the selected empty positions, leading to an actual natural-coordinate system, which contains twelve rational natural coordinates for the element. The implementation of the method has been achieved on a multibody dynamics and motion analysis platform, InteDyna, with the result that modeling efficiency is enhanced and model quality improved.

Modeling and Simulation of Big Pendulum Hammer with Natural Coordinates

2013 ◽  
Vol 753-755 ◽  
pp. 1016-1019
Author(s):  
Ke Wei Zhang ◽  
Zhi Gang Hu ◽  
Peng Wei Guo
Keyword(s):  
Selection Method ◽  
Natural Coordinates ◽  
Step Method ◽  
Natural Coordinate System ◽  
Self Adaptation ◽  
Natural Coordinate ◽  
Step Selection ◽  
Adaptation Method ◽  
Rigid Element ◽  
Selection Of

The dynamic of a type of play equipment, Big Pendulum Hammer, was modeled and simulated in computer and the approach of natural coordinates was adopted to build its equation of motion. In order to obtain appropriate natural coordinates, a two-step selection method was chosen, which based on concept of natural coordinate system (NCS). The two-step method treats selecting natural coordinates for a rigid element as building an actual NCS which should be adapted from a standard NCS. In order to automate the process of adaptation for 18 rigid elements in the model of Big Pendulum Hammer, a four-step self-adaptation method was also adopted, which can help automate the selection of natural coordinates for multi-rigidbody systems.

scholarly journals Symmetry types of the piezoelectric tensor and their identification

2013 ◽  
Vol 469 (2155) ◽  
pp. 20120755 ◽  
Author(s):  
W.-N. Zou ◽  
C.-X. Tang ◽  
E. Pan
Keyword(s):  
Coordinate System ◽  
Mirror Symmetry ◽  
Symmetry Type ◽  
Third Order ◽  
Order Linear ◽  
The Third ◽  
Natural Coordinate System ◽  
Linear Piezoelectricity ◽  
Rotation Transformation ◽  
Natural Coordinate

The third-order linear piezoelectricity tensor seems to be simpler than the fourth-order linear elasticity one, yet its total number of symmetry types is larger than the latter and the exact number is still inconclusive. In this paper, by means of the irreducible decomposition of the linear piezoelectricity tensor and the multipole representation of the corresponding four deviators, we conclude that there are 15 irreducible piezoelectric symmetry types, and thus further establish their characteristic web tree. By virtue of the notion of mirror symmetry and antisymmetry, we define three indicators with respect to two Euler angles and plot them on a unit disk in order to identify the symmetry type of a linear piezoelectricity tensor measured in an arbitrarily oriented coordinate system. Furthermore, an analytic procedure based on the solved axis-direction sets is also proposed to precisely determine the symmetry type of a linear piezoelectricity tensor and to trace the rotation transformation back to its natural coordinate system.

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