Stability analysis of mechanisms having unpowered degrees of freedom

Robotica ◽  
1989 ◽  
Vol 7 (4) ◽  
pp. 349-357 ◽  
Author(s):  
B. Borovac ◽  
M. Vukobratović ◽  
D. Stokić

SUMMARYThe stability analysis of active spatial mechanisms comprising both powered and unpowered joints is carried out for the first time using aggregation-decomposition method via Lyapunov vector functions. This method has already been used for analysis of mechanisms with all powered joints. To extend the application of the method to the stability analysis of mechanisms containing unpowered joints we developed modelling of special subsystem consisting of one powered and one unpowered joint. Then, we consider the stability of the complete system without neglecting any dynamic effect. The stability analysis is demonstrated by a numerical example of a particular biped system.

Author(s):  
Roberto Ricci ◽  
Paolo Pennacchi

It is a common notion in literature that cracks in horizontal rotating shafts can cause instability of the system. Actually the stiffness variation due to the breathing mechanism may cause parametric excitation to the rotor system. This phenomenon has been investigated by means of both analytical models and simulation, but the studies are related to simple Jeffcott’s rotors. In this paper the method normally used to investigate the stability of cracked rotors, i.e. Floquet’s theory, is applied for the first time to a model of a real rotor with several degrees of freedom, considering also the bearings and the foundation. Huge calculation resources have been necessary and this may explain why this analysis was not performed before. The results are very different from those obtained by means of simple Jeffcott’s rotor.


2010 ◽  
Vol 133-134 ◽  
pp. 403-410
Author(s):  
Adil Ahmad ◽  
Khalid Moin

Present study deals with the stability analysis of an existing historical monument “Safdarjung Tomb” under Seismic Load. The tomb is situated at New Delhi, India. The building is classified as protected monument by the Archaeological Survey of India (ASI). This is a ground plus two storey masonry structure with a central dome. The basic seismic parameters have been evaluated using Bureau of Indian Standards (BIS) Codal method. Distribution of lateral forces is carried out to individual piers and walls using Rigidity Approach. The seismic performance of the building is studied under the gravity and earthquake loads. The building is modeled as a two-degree-of-freedom shear-beam system. The piers, which are located parallel to the direction of earthquake shaking are assumed to provide spring action. The mass of the walls and slabs are lumped at the storey levels. The lumped masses are assumed to be connected to each other through massless springs. The degree of each mass in horizontal direction is considered, neglecting the vertical translational and rotational degrees of freedom. Stiffness of the walls parallel to longitudinal and transverse directions of the building has been computed separately which was used for computation of lateral forces in each direction. The forces so evaluated are used in pier analysis to evaluate stress induced in various elements. The majority of the structural elements were found safe and the overall structure is stable. The stresses due to shear and bending are within permissible limit


1979 ◽  
Vol 16 (2) ◽  
pp. 126-143 ◽  
Author(s):  
Gregory Stephanopoulos ◽  
L.M. Schuelke ◽  
George Stephanopoulos

Robotica ◽  
2014 ◽  
Vol 33 (9) ◽  
pp. 1926-1947 ◽  
Author(s):  
Jorge Orrante-Sakanassi ◽  
Víctor Santibánez ◽  
Víctor M. Hernández-Guzmán

SUMMARYIn this paper we propose new tuning conditions for three saturated nonlinear proportional-integral-derivative (PID) global regulators with bounded torques for robot manipulators, which have been presented previously in the literature. The motivation of this work relies on the fact that the tuning conditions presented previously in the literature for assuring global asymptotic stability are so restrictive that it had been impossible, until now, to carry out experimental tests. New tuning criteria of unsaturated PID controllers for robot manipulators with stability conditions more relaxed than those presented previously in the literature have been proposed recently in some works by the authors. This was achieved by setting the stability conditions as expressions that have to be satisfied at each joint instead of general conditions for the whole robot. Based on this idea, we now obtain stability conditions for saturated global PID controllers which are so relaxed that they have allowed to perform, by the first time, experimental tests using controller gains which completely satisfy the proposed stability conditions. The results of such experiments are presented in this paper, where we have used a two-degrees-of-freedom robot manipulator.


Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Yang Peng ◽  
Jiang Wu ◽  
Limin Zou ◽  
Yuming Feng ◽  
Zhengwen Tu

In this paper, we first present a generalization of the Cauchy-Schwarz inequality. As an application of our result, we obtain a new sufficient condition for the stability of a class of nonlinear impulsive control systems. We end up this note with a numerical example which shows the effectiveness of our method.


1997 ◽  
Vol 3 (4) ◽  
pp. 329-371
Author(s):  
Henryk Flashner ◽  
Ramesh S. Guttalu

Apoint mappinganalysis is employed to investigate the stability of periodic systems. The method is applied to simplified rotorcraft models. The proposed approach is based on a procedure to obtain an analytical expression for the period-to-period mapping description of system's dynamics, and its dependence on system's parameters. Analytical stability and bifurcation conditions are then determined and expressed as functional relations between important system parameters. The method is applied to investigate the parametric stability of flapping motion of a rotor and the ground resonance problem encountered in rotorcraft dynamics. It is shown that the proposed approach provides very accurate results when compared with direct numerical results which are assumed to be an “exact solution” for the purpose of this study. It is also demonstrated that the point mapping method yields more accurate results than the widely used classical perturbation analysis. The ability to perform analytical stability studies of systems with multiple degrees-of-freedom is an important feature of the proposed approach since most existing analysis methods are applicable to single degree-of-freedom systems. Stability analysis of higher dimensional systems, such as the ground resonance problems, by perturbation methods is not straightforward, and is usually very cumbersome.


2019 ◽  
Vol 24 (2) ◽  
pp. 224-240 ◽  
Author(s):  
Mehmet Emir Koksal

In this paper, the stability of fractional differential equations (FDEs) with unknown parameters is studied. Using the graphical based D-decomposition method, the parametric stability analysis of FDEs is investigated without complicated mathematical analysis. To achieve this, stability boundaries are obtained firstly by a conformal mapping from s-plane to parameter space composed by unknown parameters of FDEs, and then the stability region set depending on the unknown parameters is found. The applicability of the presented method is shown considering some benchmark equations, which are often used to verify the results of a new method. Simulation examples show that the method is simple and give reliable stability results.


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