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.

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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.

     

Spatial-based iterative learning control for motion control applications

For many motion control applications spatial constraints are often more important than temporal constraints. In recent work, we have developed a spatial control strategy called the ε-controller for mobile robot applications. The control strategy is based solely on static path geometry with position (in space) feedback. Motivated by this idea, in this paper, we consider the notion of spatial-based iterative learning control (ILC). Specifically, we consider repetitive operation problems where corrections are made to the control signal from trial to trial. Unlike traditional ILC, however, which updates control signals based on the time elapsed along a trajectory, we instead make updates based on path errors and progress along the path. The idea is demonstrated via simulation for a system with bang–bang velocity control. Experimental results using a high-precision, two-axis gimbal mechanism are presented to show the effectiveness of the strategy.     

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.     

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.     

On the Characterization of the Dynamic Performances of Planar Manipulators

The characterization of the dynamic performances of a manipulator is important both to compare different manipulators and to improve the dynamic performances of a manipulator during the design stage. In a previous paper the concepts of swiftness and of dynamic isotropy were used to characterize some dynamic performances of 3-dof manipulators. This paper analyzes the usefulness of these concepts for three-dof planar manipulators and shows that the concept of swiftness is still significant, whereas the concept of dynamic isotropy has no practical interest. Moreover, it introduces three new dynamic properties that are useful in the design of a 3-dof planar manipulator. Finally, it proposes some indices that measure both the swiftness and the three new dynamic properties and shows how to use them, both for evaluating the dynamic performances of a given 3-dof planar manipulator and for improving the dynamic performances during its design.     

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.

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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.

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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     

The variational structure of a nonlinear theory for spatial lattices

A theory for spatial lattices is presented in a variational setting and conditions restricting stable deformations are discussed. In particular, new results on the second variation of the energy are established and used to generate pointwise necessary conditions for locally energy-minimizing configurations.

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Sommario Viene presentata una teoria per i reticoli spaziali in un ambito variazionale e sono inoltre discusse condizioni che limitano deformazioni stabili. In particolare vengono stabiliti nuovi risultati sulla variazione seconda dell'energia. Tali risultati vengono usati per stabilire condizioni necessarie puntuali per configurazioni che minimizzano l'energia localmente.

     

Theoretical analysis of the spatial variability in tillage forces for fatigue analysis of tillage machines

This paper presents a new theoretical model to describe the spatial variability in tillage forces for the purpose of fatigue analysis of tillage machines. The proposed model took into account both the variability in tillage system parameters (soil engineering properties, tool design parameters and operational conditions) and the cyclic effects of mechanical behavior of the soil during failure ahead of tillage tools on the spatial variability in tillage forces. The stress-based fatigue life approach was used to determine the life time of tillage machines, based on the fact that the applied stress on tillage machines is primarily within the elastic range of the material. Stress cycles with their mean values and amplitudes were determined by the rainflow algorithm. The damage friction caused by each cycle of stress was computed according to the Soderberg criterion and the total damage was calculated by the Miner’s law. The proposed model was applied to determine the spatial variability in tillage forces on the shank of a chisel plough. The equivalent stress history resulted from these forces were calculated by means of a finite element model and the Von misses criterion. The histograms of mean stress and stress amplitude obtained by the rainflow algorithm showed significant dispersions. Although the equivalent stress is smaller than the yield stress of the material, the failure by fatigue will occur after a certain travel distance. The expected distance to failure was found to be d_f = 0.825 × 10⁶ km. It is concluded that the spatial variability in tillage forces has significant effect on the life time of tillage machines and should be considered in the design analysis of tillage machines to predict the life time. Further investigations are required to correlate the results achieved by the proposed model with field tests and to validate the proposed assumptions to model the spatial variability in tillage forces.     

Some explicit relations in kinematics of mechanisms

Using Lie group theory, we propose to give some explicit relations in kinematics of mechanisms without introducing coordinates. After a presentation of the mathematical tools, the kinematics of closed mechanisms is presented using Lie group language. We give first a family of relations between dependent and independent variables and their derivatives which may be useful for linearisation or for numerical integration. Two examples are then proposed to illustrate these relations.     

A multi level approach to synthesis of planar mechanisms

A multi level approach to synthesis of planar mechanisms is presented. The approach covers both structural and dimensional synthesis of planar rigid body mechanisms containing revolute and translational joints. The synthesis is based on four different criteria. Firstly the type of mechanism is chosen with a view to get the simplest mechanism that satisfactorily fulfills the remaining three criteria. Two of these criteria are formulated as constraints on the kinematic behavior and the total area occupied by the mechanism, respectively. The fourth criteria is simply the desired minimization of the reactive forces/moments that appear in the mechanism. The desired kinematic behavior is based on a finite number, typically 1, ..., 6, of points in time (positions of the mechanism) where the position and orientation of up to two output bodies may be prescribed. The constraints on occupied areas are labelled territory constraints and formulated as a number of restricted areas (boxes). A synthesis is automatically performed at five levels. At the first level the structure of the mechanism is decided. At the second level initial dimensions for the given type of mechanism are found by random checking. At the third level the constraints on the kinematic behavior is fulfilled. At the fourth level the territory constraints are taken into account and, finally, at the fifth level the minimization of reactions is carried out. The entire approach has been implemented in a software package SYNMEC that runs on PCs and constitutes a way of performing the synthesis of a mechanism that is general and flexible with respect to both the type of mechanism that may be synthesized as well as the desired behavior upon which the synthesis is based.     

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.     

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.     

Design and experimental validation of piecewise-linear state observers for flexible link mechanisms

The design of an observer estimating the state variables of a plant is an essential step towards the synthesis of high-performance model-based control schemes. In this paper, the problem of designing accurate state observers for flexible link mechanisms is tackled. The complexity of such a problem is considerable due to the nonlinear characteristics of flexible link mechanism dynamic models. Since nonlinear state observers have limited practical utility, in this work an investigation is made on the possibility of employing the Kalman filter theory together with suitable piecewise-linear truncated dynamic models. A general approach is developed and experimental results are given for the case of a four bar linkage with flexible links. Not only do these results confirm the theoretical and numerical results, but they also prove the practical effectiveness and efficiency of the proposed approach.     

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.     

Design and development of planar reconfigurable motion generators

This article presents the concept of a new class of mechanical devices for multi-phase motion generation tasks. Reconfigurable Motion Generators are a new class of mechanical devices that are designed for a specific part family and their associated motion generation tasks. The research endeavors to realize a novel concept for Reconfigurable Motion Generators (RMGs) for multi-phase planar motion generation. Reconfigurable Motion Generators are capable of configuration changes according to variations in the motion generation requirements. Thus, Reconfigurable Motion Generators bridge the gap between the relative high flexibility and high cost of totally flexible devices (e.g., industrial robots) and the low flexibility and low cost of fully dedicated devices (e.g., cams and linkages). This paper introduces the concept of Reconfigurable Motion Generators that may be deployed in various automated manufacturing environments involving multi-phase motion generation tasks. The development, manufacturing, and testing of a prototype and the control system for a planar Reconfigurable Motion Generator based on a five-bar mechanism are discussed.     

评定磨合表面的最佳形貌参数

磨合是新机器设备投入使用之前的必经过程，而且对摩件的表面形貌都要发生明显的变化，因此，如何评定磨合表面形貌值得深入研究，实际上，磨合是对摩件的表面形貌由初始状态逐渐趋于相互吻合的过程，因而磨合之后配对表面的形貌具有相关性，在此基础上上，研究提出了利用互相关结构函数评定磨合，这种评定方法具有能够同时反映两个表面形貌和对表面形貌变化反映敏感，以及能够将表面轮廓的峰和谷分开考虑等优点，理论分析和应用实例     

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.