# An investigation of axial shortening effects on the vibration frequencies of a rotating constrained flexible robotic arm carrying an end mass

 Author: Yau, Tai-wai David Title: An investigation of axial shortening effects on the vibration frequencies of a rotating constrained flexible robotic arm carrying an end mass Degree: M.Sc. Year: 1999 Subject: Robots, IndustrialRobot handsRoboticsFrequencies of oscillating systemsHong Kong Polytechnic University -- Dissertations Department: Multi-disciplinary StudiesDept. of Mechanical Engineering Pages: x, 83 leaves : ill. ; 30 cm Language: English InnoPac Record: http://library.polyu.edu.hk/record=b1479174 URI: http://theses.lib.polyu.edu.hk/handle/200/1327 Abstract: A clamped-free rotating flexible robotic arm is modelled by the Euler-Bernoulli beam theory. The arm is rotating horizontally about the clamped axis while the other end is constrained to move against a curve. The arm has an end mass attached at its tip. An axial compressive force which is derived from the contact force between the tip of the arm and the constrained curve is applied at the free end. When the flexible robotic arm is rotated, a centrifugal force is produced on the arm by the centrifugal stiffening effect. The work done by this centrifugal force will produce an axial shortening effect on the arm. Hamilton's principle is used to derive the equation of motion of the arm together with the associated boundary conditions. The non-homogeneous boundary condition is transformed into a homogeneous one by defining a new variable. The equation of motion and the boundary conditions are then expressed in non-dimensional form. Power series method is used to solve the equation of motion. A frequency equation is derived giving the relationship between the non-dimensional modal frequencies and the four non-dimensional parameters, i.e., the axially compressed force, the end mass, the angular velocity of the arm and the total moment of inertia about the hub. Numerical bisection method is used to solve for the natural frequencies under different values of axial force, end mass, angular velocity of the arm and total moment of inertia about the hub. Results are presented for the first three modes of vibration. These results are useful in the understanding of the dynamic behavior of the rotating constrained flexible beam with an end mass.

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