The harmonics structure of robots and mechanisms with rigid links

In this dissertation, the result of research are reported in a number of areas related to the harmonic structure of the output motion of rigid linkage mechanisms with closed-loop chains and the trajectory of robot manipulators. It is shown that the closed-loop structure of the kinematics of such linkage mechanisms imposes a specific relationship between the amplitudes of the output motion. The basis and the process of obtaining the relationship between the high harmonic amplitudes of the output motion are described. Since the kinematic parameters of any mechanical system are finite, the values of amplitudes of different harmonics of the system's output motion are not all independent. A systematic method is developed to: (1) identify the values of all the kinematic parameters of the nonlinear mechanical system; and (2) explore all the possible combinations of the harmonics' amplitudes of the output motion.; For an open-loop chain robot manipulator, point-to-point motions are usually synthesized to satisfy the requirements of different boundary conditions with lowest harmonic structure. It is shown that the minimal harmonic structure of the trajectory always happens when the fundamental frequency of the trajectory is π/t where t is the required traveling time. It is also shown that the minimal harmonic structure derived in this work is always consistent with the one derived by TPM method. A method to determine the inherent characteristics and the effects of payload of the nonlinear dynamics of open-loop chain robot manipulators with rigid links is also developed using the trajectory pattern method. The harmonic content and the relative contribution of each harmonic are shown to be functions of the length of the path of motion in the joint coordinate space, path positioning, and the fundamental frequency of the trajectory, but independent of the number of degrees-of-freedom of the manipulator.; A systematic method of model parameter identification for non-linear dynamic systems is further investigated and the mathematical models are built to explore the conditions of the convergence and applicability. It is shown that when the initial estimated values of the parameters are close to the actual values or they are in the same decreasing (or increasing) region, the upgrading methodology is always convergent. If they are not in the same decreasing (or increasing) region, however, the updating procedure may or may not reach a convergent result.