A screw theory of static beams

In this article we derive the deflection equation of a simple beam using 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 work by von Mises in the 1920s. 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. “© 2001 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.