Fundamentals of Vibrations

There is a high demand for developing effective controllers to perform fast and accurate operations for either flexible link manipulators (FLMs) or rigid link manipulators (RLMs). Thus, this paper is beneficial for such vast field, and it is also advantageous and indispensable for researchers who are interested in robotics to have sufficient knowledge about various controllers of FLMs and RLMs as the controllers’ concepts are elaborated in detail. The paper concentrates in critically reviewing classical controllers, intelligent controllers, robust controllers, and hybrid controllers for both FLMs and RLMs. The advantages and disadvantages of the aforementioned control methods are summarized in this paper; it also has a detailed comparison for the controllers in terms of the design difficulty, performance, and the suitability for controlling FLMs or RLMs.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/77234C86571FA246BCFD0B8331BE37DC/S0263574720000223a.pdf/div-class-title-a-critical-review-of-control-techniques-for-flexible-and-rigid-link-manipulators-div.pdf

A Critical Review of Control Techniques for Flexible and Rigid Link Manipulators

Mathematical modelling plays an important role for robotic manipulators in order to design their particular controllers. Also, it is hard challenge to obtain an accurate mathematical model or obtain a suitable modelling method in such vast field. Thus, this critical review is advantageous and indispensable for researchers who are interested in the area to gain fruitful knowledge on the mathematical modelling methods. This paper is classified based on the type of robotic manipulators such as flexible link manipulators (FLMs), rigid link manipulators (RLMs) and hybrid manipulators which involves rigid links and flexible links. The used modelling methods for FLMs are the assumed mode method, the finite element method, and the lumped parameter method as approximation techniques which are well explained and reviewed. The Lagrangian method has inclusive explanation and review which is widely participated for obtaining the dynamic equations of FLMs, and it is appropriate and commonly employed for modelling RLMs. The Newtonian method, the forward kinematic, and the inverse kinematic are also well discussed and reviewed which are suitable and commonly employed for modelling RLMs. The critical discussion of 170 articles reported in this paper guides researchers to select the suitable method for modelling. This paper reviews the published articles in the period of 2010–2020 except for few older articles for the need of providing essential theoretical knowledge. The advantages and disadvantages of each method are well summarized at the end of the paper. The intelligent identification methods are briefly discussed due to the lack of publications especially on the period of 2010–2020.

A critical review of modelling methods for flexible and rigid link manipulators

In this paper, the three-dimensional nonlinear dynamics and force transmissibility characteristics of a flexible shaft-disk rotor system are investigated numerically. The rotor system is comprised of a flexible shaft supporting a rigid disk, and the shaft ends are mounted on viscoelastic elements (bearing/support). The dynamic model of the system is developed considering the coupled axial and bending–bending elastic motions of the shaft while the disk is modeled as a rigid body. The equations of motion (EOM) obtained using Lagrange’s equation are discretized using the assumed mode method utilizing large number of modes to examine the system dynamics accurately for multiple resonance regions. The EOM are then linearized to obtain the natural frequencies to construct the Campbell diagrams and investigate the influence of the bearing stiffness and disk location on critical speeds and whirling modes. The harmonic balance method combined with the pseudo-arclength continuation method is used to construct the nonlinear frequency response and force transmissibility curves due to disk unbalance force. The effects of the bearing stiffness and damping, unbalance force magnitude and disk location on the nonlinear multi-mode primary frequency response and force transmissibility are then thoroughly investigated.

Nonlinear dynamic response and transmissibility of a flexible rotor system mounted on viscoelastic elements

Rotor vibration control is crucial for the reliability of rotating machines. This article applies active vibration control to reduce the vibration of a rotor bearing system using flexible piezoelec...

Active vibration control of a rotor bearing system using flexible piezoelectric patch actuators

http://www.scielo.org.mx/pdf/jart/v13n1/v13n1a6.pdf

Trajectory Tracking Control in a Single Flexible-Link Robot using Finite Differences and Sliding Modes

http://www.scielo.org.mx/pdf/jart/v12n5/v12n5a8.pdf

G. Silva-Navarro

Papers

Trajectory Tracking Control in a Single Flexible-Link Robot using Finite Differences and Sliding Modes

Active Vibration Control in a Rotor System by an Active Suspension with Linear Actuators