System parameter analysis for robot manipulators with position-invariant natural frequencies

Abstract

The flexible PFBL (parallel-four-bar-linkage) link mechanism is designed to increase rigidity and to reduce the position variation of natural frequencies. The position variation of natural frequencies is the change of natural frequencies with the configuration of the robot manipulator. The configuration of the robot manipulator is described by relative (rigid) positions. Compared to the conventional flexible link mechanism design, the PFBL flexible robot manipulator provides the potential of decoupled and linear structural dynamic behavior so that position-invariant natural frequencies can be obtained. The objective of this research is to conduct a theoretical analysis and numerical simulations of the system parameters on the position-invariant natural frequencies of a two-link manipulator which has one PFBL flexible link and one rigid outer link. The equations of the flexural motion of the PFBL flexible manipulator are derived by the Lagrangian-Euler method in symbolic form in order to clarify the structure of the vibrational motion of the model. The eigenvalues of the system are derived in nondimensionalized form for the analysis of the natural frequencies of the flexible manipulator. The nondimensionalization is applied to reduce the number of system parameters and to provide a wider range of applications of the system parameters to the numerical simulations. The influence of the system parameters on the natural frequencies is determined by sampling from a set of ranges of the system parameters. The study consists of three major tasks: (1) the influence of the system parameters on the natural frequencies, (2) the influence of the system parameters on the position variation of the first natural frequency, and (3) the sensitivity of the position variation with respect to the system parameters. A design criterion of the aspect ratio is proposed to increase the structural stiffness so that the position-invariant natural frequency is obtained and the natural frequencies higher than the first natural frequency can be ignored. A similar analysis is applied to the conventional model under the same conditions to compare the merits of the structural dynamic behavior of the two models. The influence of the non-parallelism of the PFBL link and the buckling are also discussed.