Nonlinear dynamics and control of multibody systems

The dynamics of flexible systems, such as robot manipulators , mechanical chains or multibody systems in general, is becoming increasingly important in engineering. This article deals with some nonlinearities that arise in the study of dynamics and control of multibody systems in connection to large rotations. Specifically, a numerical scheme that adresses the conservation of fundamental constants is presented in order to analyse the control-structure interaction problems.

On the numerical integration of rigid body nonlinear dynamics in presence of parameters singularities

One of the main complexities in the simulation of the nonlinear dynamics of rigid bodies consists in describing properly the finite rotations that they may undergo. It is well known that, to avoid singularities in the representation of the SO(3) rotation group, at least four parameters must be used. However, it is computationally expensive to use a four-parameters representation since, as only three of the parameters are independent, one needs to introduce constraint equations in the model, leading to differential-algebraic equations instead of ordinary differential ones. Three-parameter representations are numerically more efficient. Therefore, the objective of this paper is to evaluate numerically the influence of the parametrization and its singularities on the simulation of the dynamics of a rigid body. This is done through the analysis of a heavy top with a fixed point, using two three-parameter systems, Euler's angles and rotation vector. Theoretical results were used to guide the numerical simulation and to assure that all possible cases were analyzed. The two parametrizations were compared using several integrators. The results show that Euler's angles lead to faster integration compared to the rotation vector. An Euler's angles singular case, where representation approaches a theoretical singular point, was analyzed in detail. It is shown that on the contrary of what may be expected, 1) the numerical integration is very efficient, even more than for any other case, and 2) in spite of the uncertainty on the Euler's angles themselves, the body motion is well represented.

Analysis of Regular and Irregular Dynamics of a Non Ideal Gear Rattling Problem

This paper presents a study on the dynamics of the rattling problem in gearboxes under non-ideal excitation. The subject has being analyzed by a number of authors such as Karagiannis and Pfeiffer (1991), for the ideal excitation case. An interesting model of the same problem by Moon (1992) has been recently used by Souza and Caldas (1999) to detect chaotic behavior. We consider two spur gears with different diameters and gaps between the teeth. Suppose the motion of one gear to be given while the motion of the other is governed by its dynamics. In the ideal case, the driving wheel is supposed to undergo a sinusoidal motion with given constant amplitude and frequency. In this paper, we consider the motion to be a function of the system response and a limited energy source is adopted. Thus an extra degree of freedom is introduced in the problem. The equations of motion are obtained via a Lagrangian approach with some assumed characteristic torque curves. Next, extensive numerical integration is used to detect some interesting geometrical aspects of regular and irregular motions of the system response.

On non-ideal and non-linear portal frame dynamics analysis using bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.

Market integration, return and volatility dynamics; empirical evidence from African stock markets

Frontier and Emerging economies have implemented policies with the objective of liberalizing their equity markets. Equity market liberalization opens the domestic equity market to foreign investors and as well paves the way for domestic investors to invest in foreign equity securities. Among other things, equity market liberalization results in diversification benefits. Moreover, equity market liberalization leads to low cost of equity capital resulting from the lower rate of return by investors. Additionally, foreign and local investors share any potential risks. Liberalized equity markets also become liquid considering that there are more investors to trade. Equity market liberalization results in financial integration which explains the movement of two markets. In crisis period, increased volatility and co-movement between two markets may result in what is termed contagion effects. In Africa, major moves toward financial liberalization generally started in the late 1980s with South Africa as the pioneer. Over the years, researchers have studied the impact of financial liberalization on Africa’s economic development with diverse results; some being positive, others negative and still others being mixed. The objective of this study is to establish whether African stock-markets are integrated into the United States (US) and World market. Furthermore, the study helps to see if there are international linkages between the Africa, US and the world markets. A Bivariate- VAR- GARCH- BEKK model is employed in the study. In the study, the effect of thin trading is removed through series of econometric data purification. This is because thin trading, also known as non-trading or inconsistency of trading, is a main feature of African markets and may trigger inconsistency and biased results. The study confirmed the widely established results that the South Africa and Egypt stock markets are highly integrated with the US and World market. Interestingly, the study adds to knowledge in this research area by establishing the fact that Kenya is very integrated with the US and World markets and that it receives and exports past innovations as well as shocks to and from the US and World market.

Mathematics inspired by Darwin. Adaptive dynamics of dispersal and cooperation

In 1859, Charles Darwin published his theory of evolution by natural selection, the process occurring based on fitness benefits and fitness costs at the individual level. Traditionally, evolution has been investigated by biologists, but it has induced mathematical approaches, too. For example, adaptive dynamics has proven to be a very applicable framework to the purpose. Its core concept is the invasion fitness, the sign of which tells whether a mutant phenotype can invade the prevalent phenotype. In this thesis, four real-world applications on evolutionary questions are provided. Inspiration for the first two studies arose from a cold-adapted species, American pika. First, it is studied how the global climate change may affect the evolution of dispersal and viability of pika metapopulations. Based on the results gained here, it is shown that the evolution of dispersal can result in extinction and indeed, evolution of dispersalshould be incorporated into the viability analysis of species living in fragmented habitats. The second study is focused on the evolution of densitydependent dispersal in metapopulations with small habitat patches. It resulted a very surprising unintuitive evolutionary phenomenon, how a non-monotone density-dependent dispersal may evolve. Cooperation is surprisingly common in many levels of life, despite of its obvious vulnerability to selfish cheating. This motivated two applications. First, it is shown that density-dependent cooperative investment can evolve to have a qualitatively different, monotone or non-monotone, form depending on modelling details. The last study investigates the evolution of investing into two public-goods resources. The results suggest one general path by which labour division can arise via evolutionary branching. In addition to applications, two novel methodological derivations of fitness measures in structured metapopulations are given.

Design and implementation of a production synchronization extension for Microsoft Dynamics AX

In a just-in-time, assemble-to-order production environments the scheduling of material requirements and production tasks - even though difficult - is of paramount importance. Different enterprise resource planning solutions with master scheduling functionality have been created to ease this problem and work as expected unless there is a problem in the material flow. This case-based candidate’s thesis introduces a tool for Microsoft Dynamics AX multisite environment, that can be used by site managers and production coordinators to get an overview of the current open sales order base and prioritize production in the event of material shortouts to avoid part-deliveries.

School Bullies’ Quest for Power: Implications for Group Dynamics and Intervention

Bullying is characterized by an inequality of power between perpetrator and target. Findings that bullies can be highly popular have helped redefine the old conception of the maladjusted school bully into a powerful individual exerting influence on his peers from the top of the peer status hierarchy. Study I is a conceptual paper that explores the conditions under which a skillful, socially powerful bully can use the peer group as a means of aggression and suggests that low cohesion and low quality of friendships make groups easier to manipulate. School bullies’ high popularity should be a major obstacle for antibullying efforts, as bullies are unlikely to cease negative actions that are rewarding, and their powerful position could discourage bystanders from interfering. Using data from the Finnish program KiVa, Study II supported the hypothesis that antibullying interventions are less effective with popular bullies in comparison to their unpopular counterparts. In order to design interventions that can address the positive link between popularity and aggression, it is necessary to determine in which contexts bullies achieve higher status. Using an American sample, Study III examined the effects of five classroom features on the social status that peers accord to aggressive children, including classroom status hierarchy, academic level and grade level, controlling for classroom mean levels of aggression and ethnic distribution. Aggressive children were more popular and better liked in fifth grade relative to fourth grade and in classrooms of higher status hierarchy. Surprisingly, the natural emergence of status hierarchies in children’s peer groups has long been assumed to minimize aggression. Whether status hierarchies hinder or promote bullying is a controversial question in the peer relations’ literature. Study IV aimed at clarifying this debate by testing the effects of the degree of classroom status hierarchy on bullying. Higher hierarchy was concrrently associated with bullying and predictive of higher bullying six months later. As bullies’ quest for power is increasingly acknowledged, some researchers suggest teaching bullies to attain the elevated status they yearn for through prosocial acts. Study V cautions against such solutions by reviewing evidence that prosocial behaviors enacted with the intention of controlling others can be as harmful as aggression.

Flexible multibody dynamics and intelligent control of a hydraulically driven hybrid redundant robot machine

The assembly and maintenance of the International Thermonuclear Experimental Reactor (ITER) vacuum vessel (VV) is highly challenging since the tasks performed by the robot involve welding, material handling, and machine cutting from inside the VV. The VV is made of stainless steel, which has poor machinability and tends to work harden very rapidly, and all the machining operations need to be carried out from inside of the ITER VV. A general industrial robot cannot be used due to its poor stiffness in the heavy duty machining process, and this will cause many problems, such as poor surface quality, tool damage, low accuracy. Therefore, one of the most suitable options should be a light weight mobile robot which is able to move around inside of the VV and perform different machining tasks by replacing different cutting tools. Reducing the mass of the robot manipulators offers many advantages: reduced material costs, reduced power consumption, the possibility of using smaller actuators, and a higher payload-to-robot weight ratio. Offsetting these advantages, the lighter weight robot is more flexible, which makes it more difficult to control. To achieve good machining surface quality, the tracking of the end effector must be accurate, and an accurate model for a more flexible robot must be constructed. This thesis studies the dynamics and control of a 10 degree-of-freedom (DOF) redundant hybrid robot (4-DOF serial mechanism and 6-DOF 6-UPS hexapod parallel mechanisms) hydraulically driven with flexible rods under the influence of machining forces. Firstly, the flexibility of the bodies is described using the floating frame of reference method (FFRF). A finite element model (FEM) provided the Craig-Bampton (CB) modes needed for the FFRF. A dynamic model of the system of six closed loop mechanisms was assembled using the constrained Lagrange equations and the Lagrange multiplier method. Subsequently, the reaction forces between the parallel and serial parts were used to study the dynamics of the serial robot. A PID control based on position predictions was implemented independently to control the hydraulic cylinders of the robot. Secondly, in machining, to achieve greater end effector trajectory tracking accuracy for surface quality, a robust control of the actuators for the flexible link has to be deduced. This thesis investigates the intelligent control of a hydraulically driven parallel robot part based on the dynamic model and two schemes of intelligent control for a hydraulically driven parallel mechanism based on the dynamic model: (1) a fuzzy-PID self-tuning controller composed of the conventional PID control and with fuzzy logic, and (2) adaptive neuro-fuzzy inference system-PID (ANFIS-PID) self-tuning of the gains of the PID controller, which are implemented independently to control each hydraulic cylinder of the parallel mechanism based on rod length predictions. The serial component of the hybrid robot can be analyzed using the equilibrium of reaction forces at the universal joint connections of the hexa-element. To achieve precise positional control of the end effector for maximum precision machining, the hydraulic cylinder should be controlled to hold the hexa-element. Thirdly, a finite element approach of multibody systems using the Special Euclidean group SE(3) framework is presented for a parallel mechanism with flexible piston rods under the influence of machining forces. The flexibility of the bodies is described using the nonlinear interpolation method with an exponential map. The equations of motion take the form of a differential algebraic equation on a Lie group, which is solved using a Lie group time integration scheme. The method relies on the local description of motions, so that it provides a singularity-free formulation, and no parameterization of the nodal variables needs to be introduced. The flexible slider constraint is formulated using a Lie group and used for modeling a flexible rod sliding inside a cylinder. The dynamic model of the system of six closed loop mechanisms was assembled using Hamilton’s principle and the Lagrange multiplier method. A linearized hydraulic control system based on rod length predictions was implemented independently to control the hydraulic cylinders. Consequently, the results of the simulations demonstrating the behavior of the robot machine are presented for each case study. In conclusion, this thesis studies the dynamic analysis of a special hybrid (serialparallel) robot for the above-mentioned special task involving the ITER and investigates different control algorithms that can significantly improve machining performance. These analyses and results provide valuable insight into the design and control of the parallel robot with flexible rods.

WHEAT HERBAGE AMENDMENTS ALTER EMERGENCE DYNAMICS, SEEDLING GROWTH OF LAMBSQUARTER AND SOIL PROPERTIES

ABSTRACT Crop allelopathy is a potential tool for weed management but allelopathic potential often varies among cultivars and developmental stages of crop. Bioassays were conducted to appraise the allelopathic potential of herbage (incorporated at 8 g kg-1 soil) of different hexaploid wheat (Triticum aestivum) cultivars (Millat-2011, AARI-2011, Lasani-2008 and Faisalabad-2008) collected at different crop growth stages [tillering (Z-30), anthesis (Z-60) and maturity (Z-90)] against lambsquarter (Chenopodium album). Mean emergence time taken by lambsquarter was prolonged over control by anthesis and maturity stage herbage of all wheat cultivars. Final emergence percentage was dropped by 3-17% in response to different growth stages of herbage collection. Maximum suppression in shoot (45 and 78%) and root (60 and 90%) length, and seedling dry biomass (65 and 96%) of lambsquarter over control was recorded under the amendment of anthesis and maturity stages herbage of wheat cultivars. Total chlorophyll contents declined in response to herbage collected at anthesis and maturity stage of all wheat cultivars over control. Phenolic contents on the other hand were increased. Activities of enzymatic antioxidants also varied among all wheat cultivars, and declined by the incorporation of tillering, anthesis and maturity stage herbage. Wheat herbage induced lipid peroxidation in lambsquarter seedling and higher malondialdehyde content (0.56 and 0.77 nmol g-1 FW) was observed by the incorporation of wheat cultivars herbage collected at anthesis and maturity stage, respectively. Anthesis and maturity stage herbage of wheat cultivars Millat-2011, AARI-2011 and Lasani-2008 was more phytotoxic than Faisalabad-2008. Moreover, tillering stage herbage of all wheat cultivars had less inhibitory potential against emergence, seedling growth and biochemical attributes of lambsquarter. Wheat herbage amendment increased the soil pH, phenolic, organic carbon and nitrogen contents as compared to control.

Temporal dynamics of two species of Chaetophoraceae (Chlorophyta) in tropical streams of São Paulo State, Southeastern Brazil

Temporal dynamics of the chaetophoracean green algae Chaetophora elegans (Roth) C.A. Agardh and Stigeoclonium amoenum Kützing populations was investigated biweekly during late autumn trhough early spring (April to October) in two tropical streams from northwestern São Paulo State, southeastern Brazil. Abundances of one population of each species was evaluated by the quadrat technique in terms of percent cover and frequency. The fluctuations were related to the following stream variables: temperature, turbidity, specific conductance, pH, oxygen saturation, depth, substratum type, current velocity, irradiance and nutrients. Percent cover and frequency of C. elegans had lower values throughout the study period and was positively correlated to rainfall. Other correlations (i.e. positive of percent cover with depth and current velocity and negative with irradiance) were consistently found, reinforcing the strong influence of rainfall. On the other hand, percent cover and frequency of S. amoenum had higher values, with maximum growth from June to September. Percent cover was negatively correlated to rainfall. Results suggest the precipitation regime as the most important driving force to temporal changes in both populations, but playing different roles in each one. The gelatinous thallus of C. elegans seem to be favored by the increment of current velocity, since higher flows can improve the nutrient uptake by means of reduction in diffusion shell without promoting excessive drag force. In contrast, tufts of S. amoenum are, presumably, more exposed to drag force, and, consequently, more susceptible to mechanical damage effects due to higher current velocities.

The succession dynamics of a macroalgal community after a flood disturbance in a tropical stream from São Paulo State, southeastern Brazil

The succession dynamics of a macroalgal community in a tropical stream (20º58' S and 49º25' W) was investigated after disturbance by a sequence of intensive rains. High precipitation levels caused almost complete loss of the macroalgal community attached to the substratum and provided a strong pressure against its immediate re-establishment. After this disturbance, a weekly sampling program from May 1999 to January 2000 was established to investigate macroalgal recolonization. The community changed greatly throughout the succession process. The number of species varied from one to seven per sampling. Global abundance of macroalgal community did not reveal a consistent temporal pattern of variation. In early succession stages, the morphological form of tufts dominated, followed by unbranched filaments. Latter succession stages showed the almost exclusive occurrence of gelatinous forms, including filaments and colonies. The succession trajectory was mediated by phosphorus availability in which community composition followed a scheme of changes in growth forms. However, we believe that deterministic and stochastic processes occur in lotic ecosystems, but they are dependent on the length of time considered in the succession analyses.

Tree population and community dynamics in a Brazilian tropical semideciduous forest

The dynamics of the tree community and 30 tree populations were examined in an area of tropical semideciduous forest located on the margin of the Rio Grande, SE Brazil, based on surveys done in 1990 and 1997 in three 0.18 ha plots. The main purpose was to assess whether variations in dynamics were related to topography and the effects of a catastrophic flood in 1992. Rates of mortality and recruitment of trees and gain and loss of basal area in two topographic sites, lower (flooded) and upper (non-flooded), were obtained. Projected trajectories of mean and accelerated growth in diameter were obtained for each species. In both topographic sites, mortality rates surpassed recruitment rates, gain rates of basal area surpassed loss rates, and size distributions changed, with declining proportions of smaller trees. These overall changes were possibly related to increased underground water supply after the 1992 flood as well as to a c. 250-year-old process of primary succession on abandoned gold mines. Possible effects of the 1992 flood showed up in the higher proportions of dead trees in the flooded sites and faster growth rates in the flood-free sites. Species of different regeneration guilds showed particular trends with respect to their demographic changes and diameter growth patterns. Nevertheless, patterns of population dynamics differed between topographic sites for only two species.

Juvenile dynamics of the endemic and rare Enterolobium glaziovii Benth. (Mimosaceae) around reproductive trees in the Atlantic forest, Brazil

Studies on the regeneration and seedling mortality of rare tree species are important, but scarce. The aim of this study was to investigate the annual variation in recruitment, growth and mortality of juveniles of Enterolobium glaziovii Benth., a rare tree species from the Brazilian Atlantic Rain Forest. All seedlings and juveniles around four reproductive trees were labeled and their fate was followed from 1996 to 1999. There were no annual differences in juveniles' recruitment below and beyond the parental crown, but juveniles' survival and growth were lower below than beyond of the parental tree crowns. Small individuals (< 15 cm tall) showed the greatest mortality and the lowest growth, followed by medium (from 15 to 50 cm tall) and large ones (> 50 cm tall). Large juveniles were more widely dispersed from the conspecific parental tree than were medium and small ones. This suggests that distance dependent mortality of juveniles mediated by the parental tree is an important cause of spacing shifts associated with the growth of small individuals of E. glaziovii into large ones. Widely dispersed juveniles may escape the high mortality associated with pathogens, herbivores or seed predators concentrated around adult conspecifics. The negative influence of the parental tree on its juveniles may explain the sparse distribution of its adults in the forest.

Woody community dynamics in two fragments of "cerrado" stricto sensu over a seven-year period (1995-2002), MA, Brazil

This study was conducted in two fragments of "cerrado" stricto sensu in the Gerais de Balsas Colonization Project, located in southern Maranhão, Brazil. The objective was to evaluate the dynamics of the woody plant community, over seven years (1995-2002). Four transects of 160 × 20 m were monitored. All woody plants with a stem diameter > 3 cm, at 0.30 m above ground level, were recorded. In 1995, 983 and 1,177 stems were sampled in fragments 1 and 2, respectively; in 2002, 1057 and 1406 stems were sampled in the same fragments. In 1995, the Shannon diversity indices (H') were 3.07 and 3.33, in fragments 1 and 2, respectively, reaching their maximum value in 2002 of 3.11 and 3.35. The community of fragment 1 showed an increase of 7.5% in density and 4.4% in basal area between 1995 and 2002, while in fragment 2 there was an increment of 19.4% in density and 23.5% in basal area, over the same period. The annual increment in diameter was 0.13 cm year-1 and 0.17 cm year-1 in fragments 1 and 2, respectively. The mortality rate was 2.73% per year in fragment 1 and 4.88% per year in fragment 2, while the recruitment rate was 3.25% per year and 5.86% per year, respectively. The community presented high recruitment and mortality rates compared to the studies conducted in other sites, indicating a community that was highly dynamic in the period studied.