TSAI–TOKAD (T–T) Graph: The Combination of Non-oriented and Oriented Graphs for the Kinematics of Articulated Gear Mechanisms

The non-oriented and oriented linear graph techniques are used for the kinematic analysis of bevel-gear trains. In this paper, these two techniques are compared and the weaknesses of each technique are shown. In order to overcome the weaknesses of these techniques a new graphical technique called Tsai–Tokad (T–T) graph is introduced incorporating the important feature of the non-oriented graph which helps to determine the transfer vertex and the oriented graph technique. The theory is demonstrated by the kinematic analysis of articulated robotic mechanism used by Cincinnati Milacron T³     

Chaotic Phenomena and Fractional-Order Dynamics in the Trajectory Control of Redundant Manipulators

Redundant manipulators have some advantages when compared with classicalarms because they allow the trajectory optimization, both on the freespace and on the presence of obstacles, and the resolution ofsingularities. For this type of arms the proposed kinematic controlalgorithms adopt generalized inverse matrices but, in general, thecorresponding trajectory planning schemes show important limitations.Motivated by these problems this paper studies the chaos revealed by thepseudoinverse-based trajectory planning algorithms, using the theory offractional calculus.     

刚弹耦合的机器人机构动力学方程及其解

本文给出了一般开链弹性机器人机构动力学方程。该方程是由关节广义坐标和杆件模态坐标联立的非线性微分方程组。对方程的刚性性质作了讨论,根据Rosenbrock的二级二阶半隐式Runge—Kutta公械,导出了一种求解弹性机器人机构动力学方程的算法。对一平面二杆操作手机构作了计算。对该例同时也用Gill方法作了计算,验证了上述算法的精度和效率。     

Dynamic instability of axially loaded shafts in the Mathieu map

It is shown that the Mathieu eigenvalues can be straightforwardly utilized to study the instability regions of an axially loaded simply supported shaft, the shaft being modeled as a continuous rotating beam. When a harmonic axial load is taken into account, the equation of motion of the system, here written according to the Lagrangian formulation of continuous systems, proves to be the Mathieu equation. It follows that the conditions for the stable or unstable motion of the shaft can be graphically investigated once the operation line corresponding to an actual rotating shaft is drawn in the Mathieu map.     

Use of genetic algorithms for the design of rotors

The problem of finding an optimum shape for rotating discs is a classical one and has received considerable attention; in the present paper an attempt to use genetic algorithms is described.The problem of finding the constant stress profile by using genetic algorithms is tackled, firstly using the well known results of conventional methods. The problem of optimizing the shape of pierced discs is then attempted with results which are affected by strong stress concentrations, owing to simplifying assumptions in the stress analysis implicit in the so-called disc theory. This drawback is exactly the same which limits the usefulness of conventional solutions. In order to overcome this problem, particular formulations of the fitness function aimed to discourage shapes leading to strong stress concentrations are introduced, showing that profiles which lead to very favourable stress patterns when analysed using tri-dimensional methods can be obtained even with an optimization procedure essentially based on the disc theory. A profile of a disc flywheel with the rim and hub obtained using the genetic approach shows the results which can be obtained using this optimization technique.

---

Sommario Il problema di ricavare il profilo ottimale per un disco rotante ha ricevuto in passato considerevole attenzione e soluzioni analitiche sono conosciute da circa un secolo. Scopo del presente lavoro è quello di illustrare un tentativo di soluzione basato sugli algoritmi genetici.Per prima cosa è affrontato il problema della definizione del disco di uniforme resistenza, ottenendo un profilo che coincide con la ben nota soluzione descritta in letteratura. Viene poi affrontata l'ottimizzazione di dischi forati, ottenendo profili che portano a forti concentrazioni di tensione, dovute alle ipotesi semplificative usate per il calcolo dello stato di tensione, generalmente note come teoria dei dischi. Per superare questo problema, che limita peraltro l'utilità delle soluzioni classiche, sono state introdotte formulazioni delle funzioni obiettive che scoraggiano profili che portano a forti concentrazioni di tensione. Si mostra cosi come sia possibile ottenere profili che, analizzati con procedure di calcolo tridimensionale, portano a distribuzioni di tensione molto favorevoli, anche operando con procedure di ottimizzazione basate essenzialmente sulla teoria dei dischi. Un volano a disco con mozzo e corona ottenuto mediante l'approccio genetico mostra i risultati che possono essere ottenuti attraverso questa tecnica di ottimizzazione.

---

Symbols e kinetic energy - h thickness at radiusr - m mass - r radial coordinate - r _o outer radius - B parameter for constant stress profile - I _p performance index - difference between the maximum and minimum values of - density - stress - _c circumferential stress - _e equivalent stress - _r radial stress - nondimensional radial coordinate (=r/r _o ) - angular velocity     

Jounce and Impact in Cam-Tappet Conjunction Induced by the Elastodynamics of Valve train System

The paper highlights the importance of a multi-physics integrated approach in the design evaluation of complex valve trains. The multi-disciplinarity of the problems requires simultaneous solution to inertial dynamics, structural compliance of system elements and tribological conditions in load bearing conjunctions, all of which are critical to thermodynamic functional assurance of the system as the primary objective, and system efficiency in terms of reduced mechanical and frictional losses. This paper is an extended version of: ‘PREDICTION OF CAM-TO-TAPPET CONTACT LOSS WITH VALVE TRAIN ELASTODYNAMIC ANALYSIS’, 2004 AIMETA International Tribology Conference, September 14–17, 2004, Rome, Italy.     

Characterization of the Dynamic Response of Structures to Damaging Pulse-type Near-fault Ground Motions

The presence of long-period pulses in near-fault records can be considered as an important factor in causing damage due to the transmission of large amounts of energy to the structures in a very short time. Under such circumstances high-energy dissipation demands usually occur, which are likely to concentrate in the weakest parts of the structure. The maximum nonlinear response or collapse often happens at the onset of directivity pulse and fling, and this time is not predicted by the natural structural vibration periods. Nonlinear response leading to collapse may in most cases occur only during one large amplitude pulse of displacement. From the study of the response of both linear and nonlinear SDOF systems, the effects of these distinctive long-period pulses have been assessed by means of : (i) synthetic parameters directly derived from the strong ground motion records, and (ii) elastic and inelastic spectra of both conventional and energy-based seismic demand parameters. SDOF systems have first been subjected to records obtained during recent earthquakes in near-fault areas in forward directivity conditions. The results indicate that long duration pulses strongly affect the inelastic response, with very high energy and displacement demands which may be several times larger than the limit values specified by the majority of codes. In addition, from the recognition of the fundamental importance of velocity and energy-based parameters in the characterization of near-fault signals, idealized pulses equivalent to near-fault signals have been defined on account of such parameters. Equivalent pulses are capable of representing the salient observed features of the response to near-fault recorded ground motions.     

Kinematic analysis of a novel pin-wheel joint

In this paper an innovative joint for the transmission of motion between parallel and incident axes is presented. It is made up of two frontal pin-wheels with cylindrical pins. The kinematics in case of parallel axes is discussed in detail. It is shown that, quite surprisingly, it may behave in many different ways, depending on the value of the center distance between the two axes. A systematic way to analyze the joint kinematics is provided.     

柔性机械臂的两种逆动力学方法

本文提出了柔性机械臂运动控制和振动抑制的两种有效的开环控制方法——两点边值逆动力学方法和轨迹规划逆动力学方法。两种逆动力学方法所设计的开环输入不仅可以实现柔性机械臂的点位运动或跟踪优化轨迹，而且同时显著降低或消除了结构柔性对其精确定位的影响。数值模拟和实验证实了理论分析结果     

Kinematics of single-loop mechanisms and serial robot arms: A systematic approach

This paper presents a systematic approach, based on displacement group properties, to the kinematic analysis of spatial linkages with one closed loop and to the solution of the inverse kinematic problem for robot manipulators. By using the proposed approach, a set of kinematic chains can be determined such that a first closure equation with one unknown can be derived directly and explicitly. Then the remaining closure equations are obtained: it is proved that they can be expressed in triangular form. The basic algorithms used to solve these equations in closed form are also presented. For each algorithm, the conditions of applicability, the initial information required, the results, the type and form of equations, and the maximum number of solutions are given. The proposed approach is well suited to the symbolic explicit solution of the inverse kinematic problem of a wide range of robut mechanisms. An example of its application is given.

---

Sommario Il lavoro presenta un appreceio sistematico, basato sulle proprietà dei gruppi di spostamento, all'analisi cinematica di posizione di meccanismi spaziali ad una maglia e alla cinematica inversa di robot manipolatori seriali. L'approccio consente di determinare un insieme di catene cinematiche per le quali può essere scritta e risolta direttamente una prima equazione di chiusura in una sola incognita. Viene successivamente dimostrato esaustivamente che, per tali catene, le successive equazioni di chiusura possono essere espresse e risolte in forma triangolare. Inoltre sono presentati gli algoritmi di base utilizzabili per la soluzione del problema posto. Per ciascuno di essi sono dati: le condizioni di applicabilità, l'informazione iniziale richiesta, i risultati ottenuti, il tipo e la forma delle equazioni e il massimo numero di soluzioni possibili. L'approccio presentato è utilizzabile per la soluzione simbolica esplicita, manuale o automatica, di un esteso insieme di meccanismi per robot. Viene dato un esempio di uso del metodo.

     

Optimum synthesis of spatial function generator mechanisms

In this study a numerical method for optimum synthesis of spatial function generator four-bar linkages is presented. The key features of the method are: the embedding of the assembly criterion and of the transmission ratio in the penalty function; the non-derivative minimization procedure; the parametric variation of the first-guess mechanism. The effectiveness of the method is illustrated by means of examples of optimum design. In some examples articulated mechanisms, which can replace cam systems in automatic machinery, are synthesized.

---

Sommario In questo studio si presenta un metodo per la sintesi ottimale di quadrilateri articolati spaziali generatori di funzione. Le principali caratteristiche del metodo proposto sono: l'inclusione del criterio di assemblabilità e dell'angolo di pressione nella funzione penalità; l'utilizzazione di un algoritmo di minimizzazione non derivativo; la variazione parametrica del meccanismo di primo tentativo. L'efficacia del metodo è messa in luce tramite una serie di esempi di progetto ottimale; in alcuni di essi sono stati sintetizzati dei quadrilateri spaziali in grado di sostituire i sistemi a camma spaziale nelle macchine automatiche.

     

Vibration reduction in a flexible-link mechanism through synthesis of an optimal controller

In this paper, reduction of vibration of a flexible planar mechanism is achieved through synthesis of an optimal controller. A finite element model, based on the equivalent rigid-link system theory, is used to accurately describe the dynamic behavior of the system. The model, which accounts for geometric and inertial nonlinearities of the mechanism, has been fully validated through experimental tests. In order to be able to employ the classical optimal control theory, a suitable linear model has been derived from the original one by means of a suitable linearization procedure. Vibration reduction can then be obtained by first defining an adequate performance index, which accounts for vibration amplitude, then by solving Riccati’s equation in order to find the controller that minimizes the performance index, i.e. the optimal controller. The results of several tests that have been carried out are also reported, to show the effectiveness of the synthesized control system.     

Simulation of centrifugal inertia forces on a test bed of blow-molding machines

This paper deals with the simulation of the centrifugal inertia forces on a fixed test bed that reproduces only the opening and closing motions of the half-molds of blow-molding machines. The suggested solution is realized by the addition of springs, which allows the reproduction of the moment of the inertia forces about the vertical axis of the mold. By using the approximation method based on the mean-square-value minimization, satisfactory results are obtained. The efficiency of such a solution is illustrated by numerical example.     

Vibrations of a continuous web on elastic supports

We consider an infinite, homogenous linearly elastic beam resting on a system of linearly elastic supports, as an idealized model for a paper web in the middle of a cylinder-based dryer section. We obtain closed-form analytical expressions for the eigenfrequencies and the eigenmodes. The frequencies increase as the support rigidity is increased. Each frequency is bounded from above by the solution with absolutely rigid supports, and from below by the solution in the limit of vanishing support rigidity. Thus in a real system, the natural frequencies will be lower than predicted by commonly used models with rigid supports.     

Detection of rolling bearing defects using discrete wavelet analysis

In the detection of bearing faults the so much desired objective remains the extraction of the defect vibratory signature from the measured signal in which immerses the random noise and other components of the machine. In this article a denoising method of the measured signals is presented. Based on the optimization of wavelet multiresolution analysis, it uses the kurtosis as an optimization and evaluation criterion, several parameters were then selected. The experimental results show the validity of this method within the detection of several defects simulated on ball bearings. The various configurations, in which the signals were measured, allow leading to optimum conditions of its application. The application of WMRA on filtered signals allows better results than its application on wide bands signals or a simple band pass filtering.     

On the Role of Vibrational Excitation in Hypersonic Flow Computations

Abstract. The paper investigates the influence of the thermochemical modeling on the flow-field properties for both compressing and expanding flows. For the nitrogen hypersonic flow over a cylinder a comparison between a model neglecting vibrational energy and two-temperature Park's nonequilibrium model has been performed in a wide variety of experimental and free flight conditions. It is shown that the differences are confined in a thin layer behind the bow shock while the overall flow properties are slightly affected. For the expanding air flows inside hypersonic facilities, besides the two models mentioned above, vibrational equilibrium and CVDV model have been compared. It was found that vibrational nonequilibrium can not be disregarded but no discernible differences have been observed between Park's and CVDV model results, unless the enthalpy is very large.Sommario. L'articolo analizza l'influenza della modellizzazione termochimica sul campo fluidodinamico nel caso di flussi ipersonici sia in compressione che in espansione. Per il flusso di azoto attorno ad un cilindro è stato effettuato un confronto fra un modello che trascura l'energia vibrazionale ed il modello di non-equilibrio a due temperature di Park. L'analisi è stata condotta per un ampio intervallo di variazione dei parametri caratteristici comprendente condizioni sia di volo che di prove in laboratorio. Il confronto ha mostrato che l'effetto del non-equilibrio vibrazionale è sempre limitato ad una regione molto sottile dietro l'onda d'urto e che l'influenza sulle proprietà generali del flusso è in ogni caso modesta. Per il caso dei flussi in espansione in gallerie ipersoniche si è invece assunto come gas l'aria ed oltre ai due modelli già menzionati sono stati utilizzati anche il modello di equilibrio vibrazionale ed il modello CVDV. Si è osservato che per i flussi in espansione il non-equilibrio vibrazionale non può essere trascurato ma che comunque i modelli di Park e CVDV sono sostanzialmente equivalenti tranne nei casi di valori molto elevati dell'entalpia totale.     

On the Logical Status of the Virtual Work Law

The law of virtual work (VWL) is probably the first law in the history of mechanics; it is previous to the one on the lever, though not completely distinct from it. Here I will discuss the logical status of VWL, that is whether it is an autonomous principle or a theorem of some sort of mechanics. The problem is complicated by the fact that up to now no universally recognised expression has been accepted for it. From this article the problematical nature of VWL demonstrability is quite clear when the mechanics does not characterise completely the constraints. Italian schools in the XVIII century, even if we do not take Lagrange into consideration, had an important role, both in the development of VWL and in the discussion of its role.     

Cycle-to-cycle oscillations of heat release in a spark ignition engine

Fluctuations of combustion were studied using experimental time series of internal pressure in one of four cylinders in a spark ignition engine. Employing standard statistical methods like histograms and return maps, cycle-to-cycle variations of heat release were analyzed. A substantial difference in system behavior corresponding to quality of combustion was observed with a changing spark advance angle. Examining recurrence plots for a higher spark advance angle formation of specific patterns of vertical lines characteristic to intermittent behavior was found.