Expansion of the Euler Bernoulli equation [articol]

Abstract

A new notion of joint is defined. The article is concerned with the relationship between the Euler- Bernoulli equation and equation of equilibrium at the point of elastic line tip. The Euler-Bernoulli equations should be expanded according to the requirements of the motion complexity of elastic robotic systems. This yields the difference in the structure of Euler-Bernoulli equations for each mode. Mathematical model of the actuators also comprises coupling between elasticity forces. General form of the elastic line is a direct outcome of the system motion dynamics, and must be described by six equations for position and orientation of every point on that elastic line.