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A One Degree of Freedom Mechanical Positioning device with
2 Mathematical Modeling Stability Analysis
3 Numerical Simulation
8 other sections not shown
algorithm attractor chaos chaotic behavior chaotic boundaries chaotic motion chaotic oscillations chaotic region chaotic response chaotic solutions combination resonances control the motion coriolis damping defined degree of freedom delay map diagram dots dynamics Effect of velocity equations of motion experiment and numerical experimental and numerical experimental measurements Fast Fourier Transform flexible arm robotic forcing amplitude fractal dimension frequency power spectra frequency spectrum function Hence implies increase internal resonance jump phenomenon kinematic nonlinearities linear feedback control Lyapunov dimension Lyapunov exponent Lyapunov exponent method mathematical model mechanical positioning device natural frequencies nondimensional nonlinear systems numerical model numerical simulation obtained periodic motion perturbation solutions phase plane Phase plot x,y physical system plane Poincare map position feedback gain primary resonance quasi-periodic motion rad/s robotic mechanism root locus rotational servo shown in Figure signal spectrum of displacement stability subharmonic system response translational unstable velocity feedback gain velocity gain xr(t