Influences of generic payload and constraint force on modal analysis and dynamic responses of flexible manipulator

Elastodynamic analysis of multibody systems and parametric mass matrix derivation

Abstract: One important aspect of the dynamic performance evaluation of a parallel manipulator is the elastodynamic analysis which calls for the calculation of the stiffness and mass matrices. In the elastod...

Blind-Kriging based natural frequency modeling of industrial Robot

Abstract: High-precision assembly conditions tend to necessitate consideration of the vibration modes of industrial robots. The modal characteristics of complex systems such as industrial robots are highly nonlinear. It means that mechanics experiments and finite element methods (FEM) to evaluate such features are usually expensive. Surrogate models combined with simulation-based design are widely used in engineering issues. However, few investigations apply surrogate models to industrial robots' modal analysis. We propose a practical scheme, i.e., the Blind-Kriging (KRG-B) based natural frequency prediction of the industrial robot, utilizing the Latin Hypercube Sampling (LHS) technique. A reliable dataset with 120 samples is generated for surrogate models based on the FEM. Then, the fourteen surrogate models with different optimization algorithms are evaluated to identify the optimal model for the natural frequency. In addition, the accuracy and robustness of the optimal surrogate model are investigated under different training samples. KRG-B model has better robustness (good fitting accuracy for both higher and lower order modes) and higher computational efficiency (1.133 s, the shortest time among all models). The proposed scheme mapping robot's joint angle and the natural frequency offers a valuable basis for further studying dynamic characteristics in industrial robotics.

Inverse Dynamics and Kinematics of Multi- Link Elastic Robots: An Iterative Frequency Domain Approach

Abstract: A technique is presented and experimentally validated for solving the inverse dynamics and kinematics of multi-link flexible robots. The proposed method finds the joint torques necessary to produce a specified end-effector motion. Since the inverse dynamic problem in elastic manipulators is closely coupled to the inverse kinematic problem, the solution of the first also renders the displacements and rotations at any point of the manipulator, including the joints. Further more the formulation is complete in the sense that it includes all the nonlinear terms due to the large rotation of the links. The Timoshenko beam theory is used to model the elastic characteristics, and the resulting equations of motion are discretized using the finite element method. An iterative solu tion scheme is proposed that relies on local linearization of the problem. The solution of each linearization is carried out in the frequency domain.The performance and capabilities of this technique are tested, first through simulation an...

Functionally graded microbeams: Simultaneous presence of imperfection and viscoelasticity

Abstract: As the first endeavour, the coupled nonlinear mechanical behaviour of extensible functionally graded microbeams, when both viscoelasticity and imperfection are present, is investigated. The imperfect viscoelastic microbeam is subject to a transverse harmonic excitation load of a constant amplitude. The Kelvin–Voigt viscoelastic model and Mori–Tanaka homogenisation method are used together in order to describe the internal energy loss and the variation of the material properties of the microsystem along the transverse direction, respectively. The geometric imperfection is modelled by imposing an initial curvature in the transverse deformation of the viscoelastic microscale beam. Using the Euler–Bernoulli strain–displacement relations, the geometric nonlinearity is taken into account. The non-classical nonlinear equations of motion are derived on the basis of Hamilton's principle and the modified couple stress theory. The resulting equations are found to be coupled between transverse and longitudinal oscillations. Galerkin's technique and the method of pseudo-arclength continuation as well as direct time-integration approach are finally employed to solve the governing differential equations for oscillation frequencies and nonlinear dynamic response. It is found that the nonlinear forced oscillations of extensible functionally graded microbeams are greatly affected by the internal energy loss together with geometric imperfection. It is shown that the simultaneous presence of viscoelasticity and geometric imperfections governs both the amplitude and softness/hardness of the dynamical behaviour.

A Lagrangian Formulation of the Dynamic Model for Flexible Manipulator Systems

Abstract: This paper presents a procedure for deriving dynamic equations for manipulators containing both rigid and flexible links. The equations are derived using Hamilton's principle, and are nonlinear integro-differential equations. The formulation is based on expressing the kinetic and potential energies of the manipulator system in terms of generalized coordinates. In the case of flexible links, the mass distribution and flexibility are taken into account. The approach is a natural extension of the well-known Lagrangian method for rigid manipulators. Properties of the dynamic matrices, which lead to a less computation, are shown. Boundary-value problems of continuous systems are briefly described. A two-link manipulator with one rigid link and one flexible link is analyzed to illustrate the procedure.

Non-linear parametric vibration and stability of axially moving visco-elastic Rayleigh beams

Abstract: An axially moving visco-elastic Rayleigh beam with cubic non-linearity is considered, and the governing partial-differential equation of motion for large amplitude vibration is derived through geometrical, constitutive, and dynamical relations. By directly applying the method of multiple scales to the governing equations of motion, and considering the solvability condition, the linear and non-linear frequencies and mode shapes of the system are analytically formulated. In the presence of damping terms, it can be seen that the amplitude is exponentially time-dependent, and as a result, the non-linear natural frequencies of the system will be time-dependent. For the resonance case, through considering the solvability condition and Routh–Hurwitz criterion, the stability conditions are developed analytically. Eventually, the effects of system parameters on the vibrational behavior, stability and bifurcation points of the system are investigated through parametric studies.

Parametric vibrations and stability of an axially accelerating string guided by a non-linear elastic foundation

Abstract: Parametric vibrations and stability of an axially accelerating string guided by a non-linear elastic foundation are studied analytically. The axial speed, as the source of parametric vibrations, is assumed to involve a mean speed, along with small harmonic variations. The method of multiple scales is applied to the governing non-linear equation of motion and then the natural frequencies and mode shape equations of the system are derived using the equation of order one, and satisfying the compatibility conditions. Using the equation of order epsilon, the solvability conditions are obtained for three distinct cases of axial acceleration frequency. For all cases, the stability areas of system are constructed analytically. Finally, some numerical simulations are presented to highlight the effects of system parameters on vibration, natural frequencies, frequency–response curves, stability, and bifurcation points of the system.