On the equilibrium of a rigid body suspended by a set of linear springs
Yükleniyor...
Dosyalar
Tarih
2000-08
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
John Wiley & Sons
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In this paper an approach is described for determining equilibrium states of a rigid body suspended elastically in space by a set of linear springs. This system is considered as a two-terminal generalized spring with terminal across (translational and rotational velocities, V-G, omega(G)) and terminal through (terminal force and moment, f(G), m(G)) variables. The algorithmic approach used for the solution of six nonlinear and coupled equilibrium equations consists of two major steps. The first step is to assign an initial orientation to the rigid body which is represented by the transformation (rotation) matrix T(theta,n) and reduce the problem to the solution of force equations only through a computer program. This yields the position vector xi of a preselected point G on the rigid body. Although the terminal force f(G) becomes zero at this position, the calculated terminal moment m(G), in general, is not equal to zero. The second step is to try to determine the correct orientation of the rigid body based on an argument that the terminal moment should vanish. The same argument is also used for the solution of force equilibrium equations. These two steps are repeated several times until both f(G) and m(G) vanish simultaneously yielding an equilibrium state (xi,T(theta, n)). Application of the approach is illustrated through various examples. It is observed that, if there are nonstable equilibrium states of the system, then sometimes all possible physical equilibrium states may not be obtained with this approach.
Açıklama
Anahtar Kelimeler
Stiffness, Algorithms, Computer software, Matrix algebra, Nonlinear equations, Springs (components), Vectors, Equilibrium states, Linear springs, Manipulators
Kaynak
Journal of Robotic Systems
WoS Q Değeri
Q1
Scopus Q Değeri
N/A
Cilt
17
Sayı
8
Künye
Tokad, Y. (2000). On the equilibrium of a rigid body suspended by a set of linear springs. Journal of Robotic Systems, 17(8), 417-427. doi:10.1002/1097-4563(200008)17:8<417::AID-ROB2>3.0.CO;2-3
