Author:  Yau, Taiwai 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, Industrial Robot hands Robotics Frequencies of oscillating systems Hong Kong Polytechnic University  Dissertations 
Department:  Multidisciplinary Studies Dept. 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 clampedfree rotating flexible robotic arm is modelled by the EulerBernoulli 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 nonhomogeneous 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 nondimensional form. Power series method is used to solve the equation of motion. A frequency equation is derived giving the relationship between the nondimensional modal frequencies and the four nondimensional 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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