| A two-degree-of-freedom robot manipulator with flexible joints has been modeled and fabricated based on system parameters which are scaled from a PUMA 560 industrial robot. The complete dynamic equations of motion were derived and linearized to determine the stability of zero solutions of the homogeneous equations. The complete equations of motion are nonlinear ordinary differential equations with time varying coefficients. By choosing compliance motions as the generalized coordinates, these complete equations of motion are linearized.; System component properties, such as center of gravity locations, component mass, and moment of inertia, are experimentally evaluated and compared against analytical calculations of these parameters. System damping ratio and natural frequencies are also determined experimentally. Then the complete equations of motion was verified by comparing the numerical solutions against these obtained experimentally.; The stability of the zero solution of the linear homogeneous equation system has been numerically investigated using Floquet. Transition points where stability boundaries originate are evaluated and corresponding stability types are identified. Various resonance conditions are also specified along with stability types.; The excitation amplitude and frequency are chosen to be the primary system parameters and system response of the complete nonlinear equations of motion with all higher order nonlinearities have been investigated for a wide system parameter range. A complete nonlinear system response map has been developed and various nonlinear responses are identified. In order to verify nonlinear responses, diagnostic tools, such as period doubling sequence, Fourier transform power spectrum, Lyapunov exponents, and Fractal dimensions, are introduced and applied. The dynamic response of the two-degree-of-freedom robot manipulator has been mapped for input amplitude-frequency pairs of the first manipulator joint. Amplitude and frequency ranges used for this mapping were 0.0 to 0.5 radians and 0 to 55 rad/sec, respectively. Common routes to chaos include partial period doubling sequence, quasi-periodic response, and sudden appearance of chaos.; Finally, nonlinear response ranges are compared with location of parametric excitation stability boundaries of the linear system. Quasi-periodic, transient chaotic and chaotic regions are observed only in the neighborhood of the parametric instability region which originate from the {dollar}omegasb1 = {lcub}1over2{rcub}omegasb2=omegasb2-Omega,{dollar} where {dollar}omegasb{lcub}rm i{rcub}{dollar} are natural frequencies and {dollar}Omega{dollar} is excitation frequency, transition point. |
