Investigation of the Impacts of Large-Scale Wind Power Penetration on the Angle and Voltage Stability of Power Systems

The complexity of power systems has increased in recent years due to the operation of existing transmission lines closer to their limits, using flexible AC transmission system (FACTS) devices, and also due to the increased penetration of new types of generators that have more intermittent characteristics and lower inertial response, such as wind generators. This changing nature of a power system has considerable effect on its dynamic behaviors resulting in power swings, dynamic interactions between different power system devices, and less synchronized coupling. This paper presents some analyses of this changing nature of power systems and their dynamic behaviors to identify critical issues that limit the large-scale integration of wind generators and FACTS devices. In addition, this paper addresses some general concerns toward high compensations in different grid topologies. The studies in this paper are conducted on the New England and New York power system model under both small and large disturbances. From the analyses, it can be concluded that high compensation can reduce the security limits under certain operating conditions, and the modes related to operating slip and shaft stiffness are critical as they may limit the large-scale integration of wind generation.

The impact of healing time before loading on orthodontic mini-implant stability: a histomophometric study in minipigs

Objective: To evaluate healing time before loading, areas compression and tension and location of insertion on mini-implant stability. Design: Six minipigs were used. Each animal received 3 mini-implants in each quadrant: 1 mini-implant was used as an unloaded control (G1, n = 24); the other 2 were loaded with 150 g-force at three time intervals (G2: immediate loading, G3: after 15 days and G4: after 30 days), with 16 mini-implant in each experimental group. After 120 days, tissue blocks of the areas of interest were harvested. Clinical analysis (exact Fisher test) determined the survival rate. Histological analysis (Kontron KS 300TM, Zeiss) quantified the fractional bone-toimplant contact (%BIC) and bone area (%BA) at each healing time point, areas of interest, and insertion site (ANOVA and t tests for dependent and independent samples). Results: The mini-implant survival rates were G1: 71%, G2: 50%, G3: 75% and G4: 63%, with no statistical differences between them. The groups presented similar %BIC and %BA. There were no differences between the compression and tension sides or maxillary and mandibular insertion sites. Conclusions: These results suggest that low-intensity immediate or early orthodontic loading does not affect mini-implant stability, because similar histomorphometric results were observed for all the groups, with partial osseointegration of the mini-implants present.

Biological and physicochemical stability of ceftazidime and aminophylline on glucose parenteral solution

Ceftazidime is a broad spectrum antibiotic administered mainly by the parenteral route, and it is especially effective against Pseudomonas aeruginosa. The period of time in which serum levels exceed the Minimum Inhibitory Concentration (MIC) is an important pharmacodynamic parameter for its efficacy. One of the forms to extend this period is to administer the antibiotic by continuous infusion, after prior dilution in a Parenteral Solution (PS). The present work assessed the stability of ceftazidime in 5% glucose PS for 24 hours, combined or not with aminophylline, through High Performance Liquid Chromatography (HPLC). The physicochemical evaluation was accompanied by in vitro antimicrobial activity compared MIC test in the 24-hour period. Escherichia coli and Pseudomonas aeruginosa were the microorganisms chosen for the MIC comparison. The HPLC analysis confirmed ceftazidime and aminophylline individual stability on PS, while the MIC values were slightly higher than the mean described in the literature. When both drugs were associated in the same PS, the ceftazidime concentration by HPLC decreased 25% after 24 hours. Not only did the MIC values show high loss of antibiotic activity within the same period, but also altered MIC values immediately after the preparation, which was not detected by HPLC. Our results indicate that this drug combination is not compatible, even if used right away, and that PS might not be the best vehicle for ceftazidime, emphasizing the importance of the MIC evaluation for drug interactions.

Her2p molecular modeling, mutant analysis and intramitochondrial localization

Bacterial GatCAB amidotransferases are responsible for the transamidation of mischarged glutamyl-tRNA(Gln) into glutaminyl-tRNA(Gln). Mitochondria matrix also has a multienzymatic complex necessary for the transamidation of glutamyl-tRNA(Gln). Gtf1p, Her2p and Pet112p are the constituents of mitochondrial GatFAB amidotransferase complex. Her2p is subunit A of GatFAB complex, while Gtf1p is subunit F, a connector protein between Pet112p (subunit B) and Her2p. Here we evaluate through molecular modeling and amino acid correlation analysis the HER2 protein family. Localization studies indicated that Her2p is predominantly localized in the mitochondrial outer membrane, but it is also located in the mitochondrial matrix where together with Pet112p and Gtf1p constitutes the GatFAB complex. Finally, HER2 random mutagenesis unveiled important residues that provide thermo stability for the complex and are differently suppressed by overexpression of GTF1 or PET112. For instance, her2/ts11 mutant showed its fermentative growth impaired, and poorly rescued by GTF1 indicating that Her2p unknown function in the mitochondria outer membrane affects cell viability.

Structural stability of flexible lines in catenary configuration under torsion

Catenary risers can present during installation a very low tension close to seabed, which combined with torsion moment can lead to a structural instability, resulting in a loop. This is undesirable once it is possible that the loop turns into a kink, creating damage. This work presents a numerical methodology to analyze the conditions of loop formation in catenary risers. Stability criteria were applied to finite element models, including geometric nonlinearities and contact constraint due to riser-seabed interaction. The classical Greenhill's formula was used to predict the phenomenon and parametric analysis shows a “universal plot” able to predict instability in catenaries using a simple equation that can be applied for typical risers installation conditions and, generically, for catenary lines under torsion.

Biological and physicochemical stability of ceftazidime and aminophylline on glucose parenteral solution

Ceftazidime is a broad spectrum antibiotic administered mainly by the parenteral route, and it is especially effective against Pseudomonas aeruginosa. The period of time in which serum levels exceed the Minimum Inhibitory Concentration (MIC) is an important pharmacodynamic parameter for its efficacy. One of the forms to extend this period is to administer the antibiotic by continuous infusion, after prior dilution in a Parenteral Solution (PS). The present work assessed the stability of ceftazidime in 5% glucose PS for 24 hours, combined or not with aminophylline, through High Performance Liquid Chromatography (HPLC). The physicochemical evaluation was accompanied by in vitro antimicrobial activity compared MIC test in the 24-hour period. Escherichia coli and Pseudomonas aeruginosa were the microorganisms chosen for the MIC comparison. The HPLC analysis confirmed ceftazidime and aminophylline individual stability on PS, while the MIC values were slightly higher than the mean described in the literature. When both drugs were associated in the same PS, the ceftazidime concentration by HPLC decreased 25% after 24 hours. Not only did the MIC values show high loss of antibiotic activity within the same period, but also altered MIC values immediately after the preparation, which was not detected by HPLC. Our results indicate that this drug combination is not compatible, even if used right away, and that PS might not be the best vehicle for ceftazidime, emphasizing the importance of the MIC evaluation for drug interactions.

Topics in geometry, analysis and inverse problems

The thesis consists of three independent parts. Part I: Polynomial amoebas We study the amoeba of a polynomial, as de ned by Gelfand, Kapranov and Zelevinsky. A central role in the treatment is played by a certain convex function which is linear in each complement component of the amoeba, which we call the Ronkin function. This function is used in two di erent ways. First, we use it to construct a polyhedral complex, which we call a spine, approximating the amoeba. Second, the Monge-Ampere measure of the Ronkin function has interesting properties which we explore. This measure can be used to derive an upper bound on the area of an amoeba in two dimensions. We also obtain results on the number of complement components of an amoeba, and consider possible extensions of the theory to varieties of codimension higher than 1. Part II: Differential equations in the complex plane We consider polynomials in one complex variable arising as eigenfunctions of certain differential operators, and obtain results on the distribution of their zeros. We show that in the limit when the degree of the polynomial approaches innity, its zeros are distributed according to a certain probability measure. This measure has its support on the union of nitely many curve segments, and can be characterized by a simple condition on its Cauchy transform. Part III: Radon transforms and tomography This part is concerned with different weighted Radon transforms in two dimensions, in particular the problem of inverting such transforms. We obtain stability results of this inverse problem for rather general classes of weights, including weights of attenuation type with data acquisition limited to a 180 degrees range of angles. We also derive an inversion formula for the exponential Radon transform, with the same restriction on the angle.

Primary stability in cementless total hip replacement: measurement techniques and aided-surgery

Primary stability of stems in cementless total hip replacements is recognized to play a critical role for long-term survival and thus for the success of the overall surgical procedure. In Literature, several studies addressed this important issue. Different approaches have been explored aiming to evaluate the extent of stability achieved during surgery. Some of these are in-vitro protocols while other tools are coinceived for the post-operative assessment of prosthesis migration relative to the host bone. In vitro protocols reported in the literature are not exportable to the operating room. Anyway most of them show a good overall accuracy. The RSA, EBRA and the radiographic analysis are currently used to check the healing process of the implanted femur at different follow-ups, evaluating implant migration, occurance of bone resorption or osteolysis at the interface. These methods are important for follow up and clinical study but do not assist the surgeon during implantation. At the time I started my Ph.D Study in Bioengineering, only one study had been undertaken to measure stability intra-operatively. No follow-up was presented to describe further results obtained with that device. In this scenario, it was believed that an instrument that could measure intra-operatively the stability achieved by an implanted stem would consistently improve the rate of success. This instrument should be accurate and should give to the surgeon during implantation a quick answer concerning the stability of the implanted stem. With this aim, an intra-operative device was designed, developed and validated. The device is meant to help the surgeon to decide how much to press-fit the implant. It is essentially made of a torsional load cell, able to measure the extent of torque applied by the surgeon to test primary stability, an angular sensor that measure the relative angular displacement between stem and femur, a rigid connector that enable connecting the device to the stem, and all the electronics for signals conditioning. The device was successfully validated in-vitro, showing a good overall accuracy in discriminating stable from unstable implants. Repeatability tests showed that the device was reliable. A calibration procedure was then performed in order to convert the angular readout into a linear displacement measurement, which is an information clinically relevant and simple to read in real-time by the surgeon. The second study reported in my thesis, concerns the evaluation of the possibility to have predictive information regarding the primary stability of a cementless stem, by measuring the micromotion of the last rasp used by the surgeon to prepare the femoral canal. This information would be really useful to the surgeon, who could check prior to the implantation process if the planned stem size can achieve a sufficient degree of primary stability, under optimal press fitting conditions. An intra-operative tool was developed to this aim. It was derived from a previously validated device, which was adapted for the specific purpose. The device is able to measure the relative micromotion between the femur and the rasp, when a torsional load is applied. An in-vitro protocol was developed and validated on both composite and cadaveric specimens. High correlation was observed between one of the parameters extracted form the acquisitions made on the rasp and the stability of the corresponding stem, when optimally press-fitted by the surgeon. After tuning in-vitro the protocol as in a closed loop, verification was made on two hip patients, confirming the results obtained in-vitro and highlighting the independence of the rasp indicator from the bone quality, anatomy and preserving conditions of the tested specimens, and from the sharpening of the rasp blades. The third study is related to an approach that have been recently explored in the orthopaedic community, but that was already in use in other scientific fields. It is based on the vibration analysis technique. This method has been successfully used to investigate the mechanical properties of the bone and its application to evaluate the extent of fixation of dental implants has been explored, even if its validity in this field is still under discussion. Several studies have been published recently on the stability assessment of hip implants by vibration analysis. The aim of the reported study was to develop and validate a prototype device based on the vibration analysis technique to measure intra-operatively the extent of implant stability. The expected advantages of a vibration-based device are easier clinical use, smaller dimensions and minor overall cost with respect to other devices based on direct micromotion measurement. The prototype developed consists of a piezoelectric exciter connected to the stem and an accelerometer attached to the femur. Preliminary tests were performed on four composite femurs implanted with a conventional stem. The results showed that the input signal was repeatable and the output could be recorded accurately. The fourth study concerns the application of the device based on the vibration analysis technique to several cases, considering both composite and cadaveric specimens. Different degrees of bone quality were tested, as well as different femur anatomies and several levels of press-fitting were considered. The aim of the study was to verify if it is possible to discriminate between stable and quasi-stable implants, because this is the most challenging detection for the surgeon in the operation room. Moreover, it was possible to validate the measurement protocol by comparing the results of the acquisitions made with the vibration-based tool to two reference measurements made by means of a validated technique, and a validated device. The results highlighted that the most sensitive parameter to stability is the shift in resonance frequency of the stem-bone system, showing high correlation with residual micromotion on all the tested specimens. Thus, it seems possible to discriminate between many levels of stability, from the grossly loosened implant, through the quasi-stable implants, to the definitely stable one. Finally, an additional study was performed on a different type of hip prosthesis, which has recently gained great interest thus becoming fairly popular in some countries in the last few years: the hip resurfacing prosthesis. The study was motivated by the following rationale: although bone-prosthesis micromotion is known to influence the stability of total hip replacement, its effect on the outcome of resurfacing implants has not been investigated in-vitro yet, but only clinically. Thus the work was aimed at verifying if it was possible to apply to the resurfacing prosthesis one of the intraoperative devices just validated for the measurement of the micromotion in the resurfacing implants. To do that, a preliminary study was performed in order to evaluate the extent of migration and the typical elastic movement for an epiphyseal prosthesis. An in-vitro procedure was developed to measure micromotions of resurfacing implants. This included a set of in-vitro loading scenarios that covers the range of directions covered by hip resultant forces in the most typical motor-tasks. The applicability of the protocol was assessed on two different commercial designs and on different head sizes. The repeatability and reproducibility were excellent (comparable to the best previously published protocols for standard cemented hip stems). Results showed that the procedure is accurate enough to detect micromotions of the order of few microns. The protocol proposed was thus completely validated. The results of the study demonstrated that the application of an intra-operative device to the resurfacing implants is not necessary, as the typical micromovement associated to this type of prosthesis could be considered negligible and thus not critical for the stabilization process. Concluding, four intra-operative tools have been developed and fully validated during these three years of research activity. The use in the clinical setting was tested for one of the devices, which could be used right now by the surgeon to evaluate the degree of stability achieved through the press-fitting procedure. The tool adapted to be used on the rasp was a good predictor of the stability of the stem. Thus it could be useful for the surgeon while checking if the pre-operative planning was correct. The device based on the vibration technique showed great accuracy, small dimensions, and thus has a great potential to become an instrument appreciated by the surgeon. It still need a clinical evaluation, and must be industrialized as well. The in-vitro tool worked very well, and can be applied for assessing resurfacing implants pre-clinically.

Application of numerical methods to earthquake stability assessment of slopes

Questo documento descrive gran parte del lavoro svolto durante un periodo di studio di sei mesi all’International Centre for Geohazards (ICG) di Oslo. Seguendo la linea guida dettata nel titolo, sono stati affrontati diversi aspetti riguardanti la modellazione numerica dei pendii quali l’influenza delle condizioni al contorno e delle proporzioni del modello, la back-analysis di eventi di scivolamento e l’applicazione delle analisi di stabilità monodimensionali. La realizzazione di semplici modelli con il programma agli elementi finiti PLAXIS (Brinkgreve et al., 2008) ha consentito di analizzare le prestazioni dei modelli numerici riguardo all’influenza delle condizioni al contorno confrontandoli con un calcolo teorico del fattore di amplificazione. Questa serie di test ha consentito di stabilire alcune linee guida per la realizzazione di test con un buon livello di affidabilità. Alcuni case-history, in particolare quello di Las Colinas (El Salvador), sono stati modellati allo scopo di applicare e verificare i risultati ottenuti con i semplici modelli sopracitati. Inoltre sono state svolte analisi di sensitività alla dimensione della mesh e ai parametri di smorzamento e di elasticità. I risultati hanno evidenziato una forte dipendenza dei risultati dai parametri di smorzamento, rilevando l’importanza di una corretta valutazione di questa grandezza. In ultima battuta ci si è occupati dell’accuratezza e dell’applicabilità dei modelli monodimensionali. I risultati di alcuni modelli monodimensionali realizzati con il software Quiver (Kaynia, 2009) sono stati confrontati con quelli ottenuti da modelli bidimensionali. Dal confronto è risultato un buon grado di approssimazione accompagnato da un margine di sicurezza costante. Le analisi monodimensionali sono poi state utilizzate per la verifica di sensitività. I risultati di questo lavoro sono qui presentati e accompagnati da suggerimenti qualitativi e quantitativi per la realizzazione di modelli bidimensionali affidabili. Inoltre si descrive la possibilità di utilizzare modelli monodimensionali in caso d’incertezze sui parametri. Dai risultati osservati emerge la possibilità di ottenere un risparmio di tempo nella realizzazione di importanti indagini di sensitività.

Structural and functional analysis of centromeric chromatin

Animal neocentromeres are defined as ectopic centromeres that have formed in non-centromeric locations and avoid some of the features, like the DNA satellite sequence, that normally characterize canonical centromeres. Despite this, they are stable functional centromeres inherited through generations. The only existence of neocentromeres provide convincing evidence that centromere specification is determined by epigenetic rather than sequence-specific mechanisms. For all this reasons, we used them as simplified models to investigate the molecular mechanisms that underlay the formation and the maintenance of functional centromeres. We collected human cell lines carrying neocentromeres in different positions. To investigate the region involved in the process at the DNA sequence level we applied a recent technology that integrates Chromatin Immuno-Precipitation and DNA microarrays (ChIP-on-chip) using rabbit polyclonal antibodies directed against CENP-A or CENP-C human centromeric proteins. These DNA binding-proteins are required for kinetochore function and are exclusively targeted to functional centromeres. Thus, the immunoprecipitation of DNA bound by these proteins allows the isolation of centromeric sequences, including those of the neocentromeres. Neocentromeres arise even in protein-coding genes region. We further analyzed if the increased scaffold attachment sites and the corresponding tighter chromatin of the region involved in the neocentromerization process still were permissive or not to transcription of within encoded genes. Centromere repositioning is a phenomenon in which a neocentromere arisen without altering the gene order, followed by the inactivation of the canonical centromere, becomes fixed in population. It is a process of chromosome rearrangement fundamental in evolution, at the bases of speciation. The repeat-free region where the neocentromere initially forms, progressively acquires extended arrays of satellite tandem repeats that may contribute to its functional stability. In this view our attention focalized to the repositioned horse ECA11 centromere. ChIP-on-chip analysis was used to define the region involved and SNPs studies, mapping within the region involved into neocentromerization, were carried on. We have been able to describe the structural polymorphism of the chromosome 11 centromeric domain of Caballus population. That polymorphism was seen even between homologues chromosome of the same cells. That discovery was the first described ever. Genomic plasticity had a fundamental role in evolution. Centromeres are not static packaged region of genomes. The key question that fascinates biologists is to understand how that centromere plasticity could be combined to the stability and maintenance of centromeric function. Starting from the epigenetic point of view that underlies centromere formation, we decided to analyze the RNA content of centromeric chromatin. RNA, as well as secondary chemically modifications that involve both histones and DNA, represents a good candidate to guide somehow the centromere formation and maintenance. Many observations suggest that transcription of centromeric DNA or of other non-coding RNAs could affect centromere formation. To date has been no thorough investigation addressing the identity of the chromatin-associated RNAs (CARs) on a global scale. This prompted us to develop techniques to identify CARs in a genome-wide approach using high-throughput genomic platforms. The future goal of this study will be to focalize the attention on what strictly happens specifically inside centromere chromatin.

An Analysis of Living Conditions in Rural Villages in China. A New Geography of the Country.

Analysts, politicians and international players from all over the world look at China as one of the most powerful countries on the international scenario, and as a country whose economic development can significantly impact on the economies of the rest of the world. However many aspects of this country have still to be investigated. First the still fundamental role played by Chinese rural areas for the general development of the country from a political, economic and social point of view. In particular, the way in which the rural areas have influenced the social stability of the whole country has been widely discussed due to their strict relationship with the urban areas where most people from the countryside emigrate searching for a job and a better life. In recent years many studies have mostly focused on the urbanization phenomenon with little interest in the living conditions in rural areas and in the deep changes which have occurred in some, mainly agricultural provinces. An analysis of the level of infrastructure is one of the main aspects which highlights the principal differences in terms of living conditions between rural and urban areas. In this thesis, I first carried out the analysis through the multivariate statistics approach (Principal Component Analysis and Cluster Analysis) in order to define the new map of rural areas based on the analysis of living conditions. In the second part I elaborated an index (Living Conditions Index) through the Fuzzy Expert/Inference System. Finally I compared this index (LCI) to the results obtained from the cluster analysis drawing geographic maps. The data source is the second national agricultural census of China carried out in 2006. In particular, I analysed the data refer to villages but aggregated at province level.

Banking Regulation in Turkey and Russia: An Economic Analysis

The importance of the banks and financial markets relies on the fact that they promote economic efficiency by allocating savings efficiently to profitable investment opportunities.An efficient banking system is a key determinant for the financial stability.The theory of market failure forms the basis for understanding financial regulation.Following the detrimental economic and financial consequences in theaftermath of the crisis, academics and policymakers started to focus their attention on the construction of an appropriate regulatory and supervisory framework of the banking sector. This dissertation aims at understanding the impact of regulations and supervision on banks’ performance focusing on two emerging market economies, Turkey and Russia. It aims at examining the way in which regulations matter for financial stability and banking performance from a law & economics perspective. A review of the theory of banking regulation, particularly as applied to emerging economies, shows that the efficiency of certain solutions regarding banking regulation is open to debate. Therefore, in the context of emerging countries, whether a certain approach is efficient or not will be presented as an empirical question to which this dissertation will try to find an answer.

The atmospheric stable boundary layer: Data analysis and comparison with similarity theories

The objective of this dissertation is to study the structure and behavior of the Atmospheric Boundary Layer (ABL) in stable conditions. This type of boundary layer is not completely well understood yet, although it is very important for many practical uses, from forecast modeling to atmospheric dispersion of pollutants. We analyzed data from the SABLES98 experiment (Stable Atmospheric Boundary Layer Experiment in Spain, 1998), and compared the behaviour of this data using Monin-Obukhov's similarity functions for wind speed and potential temperature. Analyzing the vertical profiles of various variables, in particular the thermal and momentum fluxes, we identified two main contrasting structures describing two different states of the SBL, a traditional and an upside-down boundary layer. We were able to determine the main features of these two states of the boundary layer in terms of vertical profiles of potential temperature and wind speed, turbulent kinetic energy and fluxes, studying the time series and vertical structure of the atmosphere for two separate nights in the dataset, taken as case studies. We also developed an original classification of the SBL, in order to separate the influence of mesoscale phenomena from turbulent behavior, using as parameters the wind speed and the gradient Richardson number. We then compared these two formulations, using the SABLES98 dataset, verifying their validity for different variables (wind speed and potential temperature, and their difference, at different heights) and with different stability parameters (zita or Rg). Despite these two classifications having completely different physical origins, we were able to find some common behavior, in particular under weak stability conditions.

Flow Field–Flow Fractionation for size analysis and characterization of nanoparticles for applications in Life Sciences

Nanotechnologies are rapidly expanding because of the opportunities that the new materials offer in many areas such as the manufacturing industry, food production, processing and preservation, and in the pharmaceutical and cosmetic industry. Size distribution of the nanoparticles determines their properties and is a fundamental parameter that needs to be monitored from the small-scale synthesis up to the bulk production and quality control of nanotech products on the market. A consequence of the increasing number of applications of nanomaterial is that the EU regulatory authorities are introducing the obligation for companies that make use of nanomaterials to acquire analytical platforms for the assessment of the size parameters of the nanomaterials. In this work, Asymmetrical Flow Field-Flow Fractionation (AF4) and Hollow Fiber F4 (HF5), hyphenated with Multiangle Light Scattering (MALS) are presented as tools for a deep functional characterization of nanoparticles. In particular, it is demonstrated the applicability of AF4-MALS for the characterization of liposomes in a wide series of mediums. Afterwards the technique is used to explore the functional features of a liposomal drug vector in terms of its biological and physical interaction with blood serum components: a comprehensive approach to understand the behavior of lipid vesicles in terms of drug release and fusion/interaction with other biological species is described, together with weaknesses and strength of the method. Afterwards the size characterization, size stability, and conjugation of azidothymidine drug molecules with a new generation of metastable drug vectors, the Metal Organic Frameworks, is discussed. Lastly, it is shown the applicability of HF5-ICP-MS for the rapid screening of samples of relevant nanorisk: rather than a deep and comprehensive characterization it this time shown a quick and smart methodology that within few steps provides qualitative information on the content of metallic nanoparticles in tattoo ink samples.

Displacement Analysis of Under-Constrained Cable-Driven Parallel Robots

This dissertation studies the geometric static problem of under-constrained cable-driven parallel robots (CDPRs) supported by n cables, with n ≤ 6. The task consists of determining the overall robot configuration when a set of n variables is assigned. When variables relating to the platform posture are assigned, an inverse geometric static problem (IGP) must be solved; whereas, when cable lengths are given, a direct geometric static problem (DGP) must be considered. Both problems are challenging, as the robot continues to preserve some degrees of freedom even after n variables are assigned, with the final configuration determined by the applied forces. Hence, kinematics and statics are coupled and must be resolved simultaneously. In this dissertation, a general methodology is presented for modelling the aforementioned scenario with a set of algebraic equations. An elimination procedure is provided, aimed at solving the governing equations analytically and obtaining a least-degree univariate polynomial in the corresponding ideal for any value of n. Although an analytical procedure based on elimination is important from a mathematical point of view, providing an upper bound on the number of solutions in the complex field, it is not practical to compute these solutions as it would be very time-consuming. Thus, for the efficient computation of the solution set, a numerical procedure based on homotopy continuation is implemented. A continuation algorithm is also applied to find a set of robot parameters with the maximum number of real assembly modes for a given DGP. Finally, the end-effector pose depends on the applied load and may change due to external disturbances. An investigation into equilibrium stability is therefore performed.