Analytical methodology for the analysis of vibration for unconstrained discrete systems and applications to impedance control of redundant robots

This paper presents a general methodology for the analysis and synthesis of a positive semi-definite system described by mass, damping and stiffness matrices that is often encountered in impedance control in robotics research. This general methodology utilizes the fundamental kinematic concept of rigid-body and non-rigid-body motions of which all motions consist. The rigid-body mode results in no net change in the potential energy from the stiffness matrix of the multiple degree-of-freedom (DoF) discrete mechanical system. Example of an unconstrained discrete mechanical system is presented to illustrate the theoretical principle as applied in obtaining the free and forced vibration responses, as well as the dynamic characteristics of the system in natural frequency, $$\omega_n$$ ω n and damping ratio, $$\zeta$$ ζ . In addition, the methodology is applied to the impedance control of redundant robots. The rigid-body mode is equivalent to the motions of a redundant robot which result in no net change in potential energy, also called the zero-potential or ZP mode, of impedance control. Example of a redundant robot is used to demonstrate the application of the methodology in robotics. The dynamic characteristics of $$\omega _n$$ ω n and $$\zeta$$ ζ in the modal space are analyzed, which can be synthesized to modulate the damping of the system analytically.

BAYESIAN DESIGN OF EXPERIMENT FOR THE ESTIMATION OF VISCOELASTIC PARAMETERS

The present work has as its main objective the formulation and solution of inverse problems aiming at the estimation of viscoelastic parameters of a discrete mechanical system. Its application potential covers several areas in the most varied segments of engineering and industry. For the formulation and solution of the direct problem, a discrete mechanical system with viscoelastic damping is considered. The parameter estimation problem is then formulated as an inverse problem, whose objective is to estimate the viscoelastic properties of a discrete system using a Bayesian approach. First, a Bayesian design of experiment its carried out in order to identify optimal experimental conditions for solving the inverse problem, taking into account the positioning of the sensors and actuators. To solve the parameter estimation inverse problem, an Adaptive Monte Carlo Markov Chain Method is employed.

Dynamic fracture effects observed in a one-dimensional discrete mechanical system

Dynamic fracture of a one-dimensional chain of identical linear oscillators (masses connected by springs) is considered in the work. The system is supposed to consist of arbitrary but finite number of links and the first mass is supposed to be fixed. Two loading conditions are discussed: free oscillations of an initially statically prestressed chain and loading the chain with a short deformation pulse. Both problems are solved analytically for an arbitrary number of links. The obtained solutions are investigated and a dynamic fracture effect related to an explicitly discrete structure of the system is revealed: a deformation wave travelling through the chain is distorted and some links may be subjected to critical deformation. The obtained solutions for the chain are compared to the solutions of analogous problems stated for an elastic rod – a continuum counterpart of the considered discrete system. It is shown that the discussed fracture effect cannot be found in a continuous system.

Competing Responses in a Discrete Mechanical System

This short paper takes a close look at a relatively simple harmonically-excited mechanical oscillator. Throughout the range of forcing frequencies the basins of attraction are investigated by applying strong perturbations to steady-state behavior. In this way, a more general solution space is mapped out. Numerical simulation of the equation of motion agrees very closely with data generated from a laboratory experiment.

Sensitivity of Mechanical Systems with One Viscous Damper: Application to a Uniform n-Mass Oscillator

The structural design sensitivity problem of a discrete mechanical system with a single viscous damper is considered. The sensitivity of the eigenvalues and the eigenvectors with respect to the damping parameter is evaluated. Exact analytical expressions for the eigenvalues and the eigenvectors of the modified system are obtained in addition to approximate expressions. A uniform n-mass oscillator viscously damped by a single damper is taken as an application example. Good agreement between the exact and approximate formulae is observed.