Abstract
This paper discusses a force control problem for a flexible Timoshenko arm. The effect of shear deformation and the effect of rotary inertia are considered in Timoshenko beam theory. Most of the research about force control of the flexible arm is based on Euler Bernoulli beam theory. There are a few researches about force control of the flexible arm using Timoshenko beam theory. The aim of the force control is to control the contact force at the contact point. To solve this problem, we propose a simple controller using Timoshenko beam theory. Finally, we describe simulation results using a numerical inversion of Laplace transform carried out to investigate the validity of the proposed controller for the force control problem. The results of the time response show the transverse displacement, the angle of deflection, the slider position, the rotational angle and the contact force toward the desired their values.
Highlights
In recent years, there has been a great deal of interest in the modeling and control of flexible arms [1]-[11]
Under author’s knowledge, there has not yet been a study of force control of a flexible Timoshenko arm based on the infinite dimensional model
The effect of shear deformation and the effect of rotary inertia are considered in Timoshenko beam theory and the Timoshenko beam theory is modified for a non-slender beam and high-frequency response
Summary
There has been a great deal of interest in the modeling and control of flexible arms [1]-[11] This interest has been motivated by the prospect of fast, light, robot whose links, due to material characteristics, will bend under heavy loads. As a first step towards designing controllers for such robots, researchers have begun studying controllers for simple flexible links. These links, in most cases modeled as Euler-Bernoulli beams because of the small deflections involved, are often analyzed through an eigen-function series expansion of the solution to beam equation. We discuss the force control problem for the flexible Timoshenko arm
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