 The Use of a Robotic Arm for Displacement Measurements in a Cantilever Beam

George Lucas Dias (Federal University of Lavras, Brazil), Ricardo Rodrigues Magalhães (Federal University of Lavras, Brazil), Danton Diego Ferreira (Federal University of Lavras, Brazil) and Felipe Augusto Vitoriano (University of Minas Gerais, Brazil)
DOI: 10.4018/978-1-7998-1754-3.ch036
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Abstract

This paper is aimed to present a displacement measurements technique which was performed automatically in a cantilever beam using a robotic arm manipulator. This technique is based on the difference of measured coordinates of the robotic arm manipulator in order to provide displacement results. The robotic arm was supported by a micro-switch sensor which in contact with a sample, measured 21x3 points distributed along the sample. Measurements were performed before and after adding the loads on the free end of the cantilever beam, manufactured in ASTM A36 steel. Experiments were performed through loads of 1.96 N, 4.9 N, 9.8 N and 19.6 N using the robotic manipulator controller. Ten sets of measurement were performed for each load. The average and standard deviation for each set of points were also performed. Results were compared to Finite Element Method (FEM) simulations in order to verify the accuracy of the proposed compared to FEM results. Sum of squared errors presented values lower than 3% demonstrating the potentiality of the proposed technique for industries application.
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2. Theory/Calculation

A bar with constant cross section clamped at one end and an extremity in balance is called cantilever beam (Timoshenko and Goodier, 1970) which is illustrated by Figure 1.

Figure 1.

Bending of a mono-cantilever, in which the variables P, L, v, x and M represent the load, distance between the applied load and clamping, vertical displacement, distance between load and point of analysis and bending moment, respectively

When a cantilever beam is subjected by a static load on the free end, the load tends to cause deflection along the beam. The bending moment (M) equations are represented by:M(x) = ‑Px(1)M(x) = EI(d2v) / (dx2)(2) where v is the vertical displacement, I is the moment of inertia, E is the elastic modulus of the material, P is the applied load and x is the distance between load and point of analysis.

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