In this work, the problem of shape optimization of flexible robotic manipulators of circular cross sections is studied. Two different manipulators are considered—a manipulator with revolute joint and a roller supported Cartesian manipulator. The finite element method is used to find the natural frequency and dynamic response of a flexible manipulator by treating it as an Euler-Bernoulli beam. The cross-sectional diameter is varied along the length keeping the constraint on the mass of the manipulator and static tip deflection in order to maximize the fundamental frequency of the beam. This optimization problem is compared with other optimization problems (with different objective functions and constraints). It is observed that the proposed optimization problem is superior to other optimization problems.
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Dixit et al. (2005) studied this question.
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