One-degree Of Freedom Research Articles

Kinematic Analysis and Synthesis of the Knotting Mechanisms Can be Used in the Production of Handmade Carpet: A Case Study

The weaving process in a handmade carpet contains independent knots, which have a complex structure. A new production method, mechanism, or machine for producing knots in handmade carpets has not been developed since thousands of years. They are still woven by human hand. Two different types of knots are used to form handmade carpets, which are called as the Turkish (Gördes knot) and the Persian (Sehna knot) knots. In this article, the conceptual design and dimensional synthesis for mechanisms used to produce these knots are studied. To generate all-acceptable one-degree of freedom (DOF) and two-DOF planar knotting mechanism, a systematic methodology is presented. First, the functional requirements of the knotting mechanism are established according to the problem statement. Some of the functional requirements of the knotting mechanism are then translated into the structural characteristics of mechanism. On the basis of the requirements and the structural considerations, the unwanted mechanism is screened out. Finally, two different mechanisms are developed for the knotting mechanism and their dimensions are determined by dimensional synthesis method.

A comprehensive study of the non-linear euler-bernoulli rotating beam

The main goal of this work is to analyze the behavior of Euler-Bernoulli rotating beam with constant angular velocity around Z-axis. Our dynamic model is analyzed considering only the in-plane transverse deformation. Thus the model is defined by an ordinary differential equation with one degree of freedom (O.D.F) and the governing differential equation is Duffing's equation with a variable coefficient for the linear term. When the damping coefficient and the amplitude of the excitation force are zeros, the system is autonomous with an explicitly known homoclinic orbit. The homoclinic orbits is calculated. Melnikov function due to the homoclinic orbit is calculated to detect the transverse homoclinic orbit. Also a dynamic numerical simulation methods are used to obtain the time history, phase portrait, Laypunov exponent, power spectrum, Poincare’ maps and their fractal dimensions. A comparison has been done between this O.D.F. model and the 2nd D.F. model that we have analyzed in [23]. The numerical results showed the occurrence of regular motion and chaotic motion in both models. Thus, by reducing the order of the two-coupled Duffing's equations into an ordinary differential equation with O.D.F. a more simplified model for the flexible rotating beam is achieved.

ANALYSIS OF WAVELETS IN CHAOTIC STATES FOR A ONE-DEGREE-OF-FREEDOM SYSTEM WITH VISCOELASTIC RESTRAINTS

A qualitative numerical technique is presented for identifying chaotic states of a non-linear one-sided constrained one-degree of freedom (1-d.o.f.) deterministic system under a dynamic non-conservative load. Discrete wavelet analysis in its classic and packet versions was used to search for the boundaries of chaotic and non-chaotic solutions. The results obtained were verified by an analysis of the Lyapunov exponents of the investigated system. On the basis of numerical tests, one can state that wavelet analysis may be a fast and reliable tool suitable for searching for the boundaries of chaotic and non-chaotic solutions.

Assembly as a noncooperative game of its pieces: analysis of 1D sphere assemblies

We propose an event-driven algorithm for the control of simple robot assembly problems based on noncooperative game theory. We examine rigorously the simplest setting – three bodies with one degree of freedom and offer extensive simulations for the 2 DOF extension. The initial analysis and the accompanying simulations suggest that this approach may indeed, offer an attractive means of building robust event driven assembly systems.

Approximate first integrals of nonlinear oscillators with one-degree of freedom

Exact symmetries of the unperturbed (linear) part of the dynamical systems are determined. Resonance conditions which lead to the symmetry-breaking of the symmetries of the unperturbed part are obtained. The second-order approximate symmetries of the one degree of freedom, damped-driven oscillators are found. By employing an approximate version of Noether’s theorem, second-order approximate first integrals are obtained for undamped oscillators. The results are discussed on the contour plots of the first integrals.

Direct adaptive impedance control

This note presents a new direct adaptive impedance controller for force /position task. We assume that the environment stiffness is unknown and we consider the one-degree of freedom (dof) case. One of the major consequence of this study is that a generalization of the time-varying impedance leads to integral force feedback. Experimental results on a 2-dof planar manipulator are reported.

Complex modal analysis of the flexural vibration of a three-layered beam.

This paper deals with the flexural vibration of the three-layered beam, the boundary condition of which is free-free. Three kinds of three-layered beams, core materials of which are all different and a normal steel beam, for reference, are tested. It was clarified that if the correct core material is chosen for the temperature, the vibration mode becomes a complex function and a high modal loss factor is achieved. Further, this paper presents the analysis method used to determine the damped normal mode (it is a complex function) described by Mead. The calculated modal loss factors have the same physical meaning as that in the one-degree of freedom. The accelerance at the driving point is calculated by the superposition of the obtained modes and values of the resonant frequency nearly equal to the result of the experiments are predicted.

Two-degree-of-freedom dead-beat control system with robustness: multivariable case

Abstract A design procedure for two-degree-of-freedom (TDF) dead-beat controllers for multivariable systems is presented. Based on the parametrization of all stabilizing TDF controllers, a minimal-time dead-beat control system with optimal robustness is constructed for an arbitrary reference input. The optimal robustness is achieved under the constraint of robust tracking. A comparison of a TDF system with a one-degree-of-freedom (ODF) system reveals that, under the same robustness criterion, the optimal robustness of the TDF system is always superior to that of the ODF system irrespective of its settling time. It is also shown that the optimal robustness of the ODF system becomes identical to that of the TDF only when the settling time of the ODF system goes to infinity. Some numerical examples are given to illustrate the theoretical results.

Two-degree-of-freedom dead-beat control system with robustness: multivariable case

Abstract A design procedure for two-degree-of-freedom (TDF) dead-beat controllers for multivariable systems is presented. Based on the parametrization of all stabilizing TDF controllers, a minimal-time dead-beat control system with optimal robustness is constructed for an arbitrary reference input. The optimal robustness is achieved under the constraint of robust tracking. A comparison of a TDF system with a one-degree-of-freedom (ODF) system reveals that, under the same robustness criterion, the optimal robustness of the TDF system is always superior to that of the ODF system irrespective of its settling time. It is also shown that the optimal robustness of the ODF system becomes identical to that of the TDF only when the settling time of the ODF system goes to infinity. Some numerical examples are given to illustrate the theoretical results.

Two-degrees-of-freedom dead-beat control system with robustness

This paper deals with the design of a two-degrees-of-freedom (TDF) dead-beat controller with both optimal robustness and minimum settling time. Based on the parametrization of all stabilizing TDF controllers, optimal robustness and minimum-time control are achieved simultaneously. The minimum-time dead-beat control is constructed for arbitrary real-rational reference input. At the same time, optimal robustness is achieved under the constraint that the error between reference input and output asymptotically vanishes for any plant perturbation that does not violate the internal stability. It is proved that under the same robustness criterion, irrespective of its length of settling time, the optimal robustness of the TDF system is always superior to that of the one-degree-of-freedom (ODF) system as long as its settling time is finite, and they become identical only when the settling time of the ODF system goes to infinity. A numerical example is given to illustrate the theoretical results.

Methods for Determining the Second Accelerations in a Plane Linkage Mechanism with One-Degree of Freedom

W.J.Carter reported the method by which the second accelerations or the change of accelerations in a lever crank mechanism could be solved. His method necessitates the construction of a drawing by means of relative velocity method and the calculation of the third time derivatives of angular motions of crank, and different formulas must be applied considering whether the rotopole for crank and lever is outside the fixed centers or between them. His method, moreover, has defects, namely, errors are likely to occur, and some of the lines in the drawing frequently come outside the paper. Authors derive the general formula of the second acceleration of the driven lever of the plane four-bar linkage mechanism, and propose the graphical method by which the second accelerations in the plane four-bar linkage mechanism can be solved rapidly, simply and accurately. Also it is found that their method can be applied to solve the velocity, acceleration, and second acceleration of any link when those terms of one of the links of multi-bar linkage, especially, sixbar linkage mechanism are given.

Graphical Method for Determining Accelerations in a Plane Linkage Mechanism with One-Degree of Freedom

Of the graphical methods for determining accelerations in a plane linkage mechanism with one-degree of freedom, the method of projection and the method of closed circuit of vectors are already known. But these methods have the fault that one may mistake in solving a problem because of their complicated procedures and lack of the clear arrangement of their constructions. In this paper, a new graphical method is proposed in order to obtain readily accelerations in the mechanism by applying the method which was already shown by the authors in the paper of The Analysis of Complex Motion in Cam Mechanism. This method is also convenient to solve rapidly and mechanically the actual accelerations in any type of four-bar linkage mechanisms and multi-bar linkage mechanisms, for instance, six-bar linkage mechanisms.