Title :
A screw theory of static beams
Author :
Selig, J.M. ; Ding, X.
Author_Institution :
Sch. of Comput., Inf. Syst. & Math., South Bank Univ., London, UK
Abstract :
We derive the deflection equation of a simple beam using the screw theory. The effects of tension, torsion and bending of the beam can be unified into a single equation. We begin by looking at the compliance matrix for small elements of the beam. This is loosely based on the work by von Mises (1924). We reproduce von Mises´ results for the compliance matrix of the entire beam by integrating along the beam. This allows us to make some general comments concerning the use of beams as compliant design element. Then we derive the equation for the deflection of the beam considering the deflection as a rigid body motion
Keywords :
Lie algebras; bending; flexible structures; Lie algebra; beam deflection; bending; compliance matrix; screw theory; tension; torsion; Aerodynamics; Algebra; Bars; Deformable models; Equations; Fasteners; Manipulators; Robot kinematics; Shape; Stress;
Conference_Titel :
Intelligent Robots and Systems, 2001. Proceedings. 2001 IEEE/RSJ International Conference on
Conference_Location :
Maui, HI
Print_ISBN :
0-7803-6612-3
DOI :
10.1109/IROS.2001.973376
