A detailed modelling of contact dynamics involving general flexible multi-body systems of arbitrary kinematic architecture is considered. The components undergoing direct contact (e.g., the end-effector of a manipulator and a satellite) are modelled using the finite element method and the Lagrange multiplier technique. Special attention is paid to dynamic fidelity of contact dynamics. Contact geometric constraints and corresponding contact forces are analysed and incorporated into the dynamical equations. This model takes into account structural deformations and oscillations, friction, time-varying contact area, and repeated contact/impact. Multi-body systems, on the other hand, are handled by a modified Euler-Lagrange method based on the Natural Orthogonal Complement (NOC). Thus, the system dynamics is composed of a set of differential equations (either multi-body formulations or finite element nodal displacement formulations) subjected to sets of algebraic equations expressing kinematic or contact constraints. A systematic procedure for solving this system of equations is formulated with special emphasis on computational efficiency. / This dynamic model is then used to design a composite controller which must simultaneously achieve three goals: (1) trajectory tracking, (2) force control, and (3) stabilization of the flexible degrees of freedom of the multibody system. The singular perturbation method is used to obtain two reduced order models. Subsequently, the slow subsystem is used to design a simultaneous position/force controller based on impedance control, where an optimization method is incorporated to accommodate manipulator redundancy. The fast subsystem is used to design a Linear Quadratic Regulator (LQR) to suppress structural vibrations. / A simulation environment is developed based on the above procedures and formulations for the planar case. It is used to perform dynamic and control simulations of a variety of contact scenarios involving multi-body systems. A comparative study of the results indicates that a detailed contact dynamics model may be essential for a realistic simulation of contact/impact, capture, and force control operations.

An analysis and comprehensive solution to the direct kinematics problem (DK) of all planar 3-legged platforms with lower pairs, called general planar Stewart-Gough platform (PSGP), is presented. There are 10 types of PSGP DK problem formulation including those with mixed leg architecture. / Planar kinematic mapping expresses pole position and rotation angle of a planar displacement as a point in 3-dimensional projective space represented by 4 homogeneous coordinates. This provides a universal tool for kinematic analysis. Its application will be demonstrated in the derivation of a general algorithm for planar DK. For each type of PSGP, the problem is reduced to a 6th order univariate polynomial whose roots reveal all solutions. An example of a PSGP with 6 real assembly configurations is presented. Furthermore, this algorithm was implemented and tested exhaustively. A complete self-contained version, coded in C, is available at http://www.cim.mcgill.ca/∼paul/. It should be easy to customize and adapt to any given real time micro-controller application.

Kinematic design and performance evaluation of serial-type robotic manipulators is the main focus of this thesis with due attention being paid to redundant manipulators. The thesis provides a review of the existing contributions made to the subject, identifying those areas that can be advanced in depth or breadth and making theoretical contributions to some of these areas. The design, manufacturing and commissioning of a full-scale representative example of a redundant manipulator designed for kinematic isotropy is also discussed. Although various theoretical methods of analysis and characterization of the kinematic performance have been reported in the past two decades, the kinematic architecture of industrial manipulators has not changed very much. The design requirements for these manipulators, have been mostly driven by issues such as kinematic simplicity and mechanical constructibility. These criteria have thus led to the existence of a particular class of manipulators whose axes are either parallel or perpendicular, i.e., orthogonal manipulators. / It is believed that, in order to fully exploit the redundancy of the new generation of industrial manipulators, it is advantageous to consider general architectures. If improved kinematic performance can be achieved by examining novel manipulator architectures, then it becomes necessary to explore new design requirements. The aim of this thesis is to contribute to the above-mentioned exploration. In Chapter 2, the singularity and workspace of regional structures (i.e., three-axis manipulators) are discussed. Regional structures forming the positioning part of most industrial manipulators, they have been regarded as representatives of nonredundant manipulators. / Chapter 3 contains a detailed review of the proposed measures of dexterity together with an extensive discussion on the invariance properties of these indices. Chapter 4 is devoted to the investigation of the condition numbers of matrices in general, and of the Jacobian matrix of the robotic manipulators in particular. In Chapter 5, the isotropic design of redundant manipulators is discussed in detail whereby several isotropic seven-axis designs are introduced. Anthropomorphic requirements are also included where, it is shown that seven- and eight-axis manipulators cannot possess isotropy and anthropomorphism simultaneously. Optimum postures of hyperredundant manipulators are then investigated and finally, singularity distributions in the workspace of isotropic manipulators are compared to those of their nonisotropic counterparts. In Chapter 6, kinematic performance of serial manipulators is discussed from a geometric point of view. A novel measure of conditioning based on an index of isotropy, defined elsewhere, is examined in detail, and several interesting features of this measure are provided. With the aid of this measure, explicit expressions for the determination of the characteristic length, and the characteristic point are derived. In Chapter 7, the kinematic and mechanical design of a full-scale seven-axis isotropic manipulator called REDIESTRO 1 are introduced. REDIESTRO 1 was designed, manufactured and commissioned during the course of this thesis at the McGill Centre for Intelligent Machines (CIM) of McGill University.

This thesis introduces a new approach to the problem of estimating the parameters of a dynamic model of a robotic manipulator using force-and-motion data collected from the manipulator. / As an alternative to commonly used least-square estimation techniques, bounded-error estimation is proposed, whereby worst-case bounds on the parameter estimates are computed based upon non-restrictive assumptions on the total error in the data, which can include systematic errors arising from unmodelled dynamics of the robot. It is argued that computing such worst-case bounds gives one a direct assessment of the accuracy, not only the precision, of the parameter estimates and offers insight into the usefulness of the model itself. / As a means of dealing with the complexity of the robot dynamics equations, the use of special test motions is adopted. By considering a very general definition of a test motion, it is shown how a large number of simplified dynamics equations can be generated in symbolic form for a given robot dynamics model, each of which may have unique properties beneficial in the context of robot parameter estimation. The use of a sequence of test motions for estimating all identifiable parameters of a dynamic model is then discussed. The "best" test-motion sequence is defined as one that minimizes an objective function that is the average of the uncertainties in the parameters it estimates. / An evolutionary-type algorithm for estimating the identifiable parameters in a robot dynamics model is then described. This algorithm searches for the "best" test-motion sequence described above. The algorithm maintains a population of individuals, each of which is a test-motion sequence. As the algorithm runs, test-motion sequences grow and recombine into larger test-motion sequences, and undergo a selection process whereby only the better test-motion sequences survive, as defined by the above-mentioned objective function. In order to sample a broad but manageable area of the search space of test-motion sequences, the algorithm features the use of a heuristic initial population generation algorithm that produces an initial population of "good" test-motion sequences based upon qualitative symbolic properties of the test-motion equations. / A new method for determining "exciting" trajectories for robot parameter estimation experiments is described. This method is distinguished from methods reported in the literature in that it is purely symbolic and is geared to the use of special test motions. The method is demonstrated on a stand-alone example. Then, it is described how the method can be incorporated in the preceding heuristic initial population generation algorithm. / The evolutionary robot parameter estimation algorithm is then tested experimentally using data from an actual Puma 560 industrial robot. The algorithm is run separately using both the joint-torque model and the base-reaction models. It is shown that meaningful estimate bounds can be obtained for many of the parameters, and correspond with previous estimates reported in the literature.

Small groups of circular cylinders of equal diameter, in tandem, side-by-side and staggered configurations, were investigated in steady mean cross-flow, and under conditions of an impulsive start, for Reynolds numbers from 500 to 6000. Experiments were conducted in water in three facilities, using flow visualization, hot-film anemometry and particle image velocimetry (PIV). The emphasis was on acquiring an improved physical understanding of the fluid behaviour, and the dynamics of the vortical structures in the flow, as the number of cylinders, the spacing between the cylinders, and the angle of incidence with respect to the oncoming flow, were varied. / For tandem cylinders in impulsively started flow, the development showed constrained streamwise growth and lateral expansion of the gap recirculation zones at small and intermediate pitch ratios. Under steady cross-flow conditions, reattachment of the free shear layers from the upstream cylinder, onto the surface of the downstream cylinder, was found to occur in an alternating, non-continuous, and non-simultaneous fashion, in a process synchronized with Karman vortex shedding from the downstream cylinder. Within the gap between the cylinders, bounded on either side by the reattaching shear layers, was found weakly rotating or stagnant fluid, with vorticity concentrations only near the points of reattachment. / The temporal development of the side-by-side configuration was dominated by strong flow through the gaps between the cylinders, rapid breakup of the recirculation zones behind the outer cylinders, gap vortex shedding, and the formation of a counter-rotating vortex pair in the combined wake. Under steady mean cross-flow conditions, the PIV vorticity data showed instantaneous variation in the base-bleed flows, the gap flow deflection angles and the vortex formation lengths. In the three-cylinder side-by-side configuration, vortex shedding frequency measurements were sensitive to the measurement location. / For the two-cylinder staggered configuration in steady cross-flow, nine flow patterns were identified, and processes of vortex pairing, enveloping, impingement and induced separation were observed. Some new insight was gained into previously published force coefficient and Strouhal number data, by considering the flow patterns responsible. The study revealed that vortex shedding frequencies are more properly associated with the individual shear layers, rather than with the individual cylinders.

Many practical problems in engineering can be modelled as linear dynamical systems with periodically varying coefficients. This thesis proposes a new design method for the control of these linear time-periodic systems. / First, Floquet-Lyapunov theory is used to derive the Floquet factors of the state-transition matrix of a given system. We introduce a novel approach to obtain every real representation. It is demonstrated that the periodicity of the periodic factor can be determined a priori using a constant matrix, which we call the Yakubovich matrix, based upon the signs of the eigenvalues of the monodromy matrix. We then introduce a novel method for the numerical computation of the Floquet factors, relying upon a boundary-value problem formulation and the Yakubovich matrix. / In the second part, we use the invertibility of the controllability Gramian and a specific form for the feedback gain matrix to build a novel control law for the closed-loop system. The new controller can be full-state or observer-based and allows the control engineer to assign all the invariants of the system, i.e. the full monodromy matrix. Deriving the feedback matrix requires first solving a matrix integral equation for the periodic Floquet factor of the new state-transition matrix of the closed-loop system. This is achieved via a spectral method, which can then be further refined by a boundary-value problem formulation. Computational efficiency of the scheme may be further improved by performing the controller synthesis on the transformed system obtained from the reducibility theorem. / Finally, the effectiveness of the method is illustrated with an application to a quick-return mechanism using a software toolbox developed for MATLAB(TM).

Photopyroelectric spectroscopy (PPES) is a relatively new nondestructive photothermal technique that uses a pyroelectric sensor placed in intimate contact with thin film samples to record the photogenerated thermal waves transmitted by the sample. In this thesis it is demonstrated that photopyroelectric spectroscopy is capable of recovering profiles of optical absorptivity in micron scale thick polymer laminates with submicron depth resolution. The pyroelectric method has also been used to characterize adhesion at polymer/metal interfaces from the photothermal impulse response using both the transmission and inverse detection geometries. The PPES technique can also map the distribution of polyene bands created during photodegradation of polyvinyl chloride. Results are obtained in the frequency and time domains using conventional lock-in detection, excitation with wideband time domain sweep waveforms and wideband homodyne techniques. The experimental photothermal results can be modeled using the linear properties of heat conduction to obtain quantitative values of the optical and thermal properties of the samples.

An equal-order co-located Control Volume Finite Element Method (CVFEM) for the prediction of multidimensional combined conduction, convection, and radiation heat transfer in emitting, absorbing, and isotropically scattering media has been formulated, implemented, and tested. The focus of this work is on a CVFEM for the prediction of multidimensional radiation heat transfer in participating media, and the amalgamation of this method with available CVFEMs, and their extensions, for conduction and convection heat transfer. / In the proposed CVFEM, the calculation domain is divided into two-node linear, three-node triangular, and four-node tetrahedral finite elements in one, two, and three dimensions, respectively. Each element is further subdivided in such a way that upon assembly of all elements, complete control volumes are formed about each node in the calculation domain. To account for the directional nature of radiation heat transfer, a spherical envelope, surrounding each node in the calculation domain, is discretized into adjacent non-overlapping solid angles. Two different schemes for the interpolation of dependent variables in the approximation of the convective fluxes, across control-volume surfaces, are investigated. The intensity of radiation in any given direction is interpolated within each element using a scheme based on a particular solution of the one-dimensional radiative transfer equation (RTE). Appropriate conservation laws are imposed on the control volumes associated with the nodes. The resulting sets of integral conservation equations are then approximated by algebraic discretization equations, using the previously-mentioned interpolation functions. These nonlinear, coupled, algebraic equations are solved by a sequential solution procedure which incorporates Picard iterations. / The suggested method has been implemented into computer programs, and used to solve several test problems. These include convection-diffusion problems, radiation heat transfer problems, and combined conduction, convection, and radiation heat transfer problems, in one, two, and three dimensions. The results demonstrate the ability of the proposed CVFEM to accurately solve the mathematical model used in this thesis. / The proposed CVFEM has been applied successfully to radiation heat transfer in homogeneous gray media bounded by gray-diffuse walls. However, the gray and the above-mentioned isotropic conditions can be relaxed using a band model and anisotropic phase-functions. This is suggested as a possible extension of the CVFEM put forward in this thesis.

An internal combustion engine was instrumented in view of developing automatic diagnosis methods based on the analysis of PV diagrams. / The pressure signal is unstable over successive cycles. Consequently, pressure must be averaged over several consecutive cycles to produce valid data. / Due to instrumentation problems the data obtained was insufficient to allow the development of diagnostics. The investigation reported in this work is thus limited to the development of a microprocessor-based system for the acquisition of pressure-volume data on high speed, spark ignition internal combustion engines. / Several instrumentation problems were identified and solutions applied or proposed. The information presented here can form the basis for further research on the original project.

The cross-flow past a pair of staggered circular cylinders is investigated numerically at a Reynolds number of 800 using a 2-D random vortex method. The numerical model was validated at a Reynolds number of 200. A flow around two stationary cylinders was investigated at a Reynolds number of 800 for comparison. Besides staggered configurations, tandem and side-by-side arrangements were also studied for better understanding of a flow around two cylinders.For staggered arrangements, four different cylinder configurations were discussed in the stationary cylinders case. For a small pitch ratio, P/D = 2, at α = 16° the upstream cylinder's inner shear-layer was deflected between the two cylinders and included the separation of the gap shear layer of the downstream cylinder. One Strouhal number of 0.159 was observed in the present study. For a large pitch ratio, P/D = 3.25, at α = 16°, the vortices shed from the upstream cylinder impinge on the downstream one. A single Kármán vortex street is formed behind the downstream cylinder, and therefore, the obtained Strouhal number is very close to that in a single stationary cylinder. At moderate incidence angles, 20° ≤ α ≤ 45°, a pair of vortices was shed via the inner shear-layers of the two cylinders, and then enveloped by the outer shear-layer from the upstream cylinder. This process yields a large combined vortex, which is followed by a vortex shed from the downstream cylinder's outer shear-layer, and multiple Strouhal numbers with an integral relationship. In general, the mean drag coefficient of the downstream cylinder was smaller than that of the upstream cylinder. The negative mean lift coefficients were observed for the downstream cylinder for all configurations considered in this study. / L'écoulement transversal a passé une paire de cylindres circulaires quiconces, avec soit un sujet à forcer une oscillation harmonique dans la direction transversale, est étudié numériquement au nombre Reynolds de 800 utilisant une méthode de tourbillonnement en 2 dimensions. Le modèle numérique a été validé au nombre Reynolds de 200. Un écoulement autour de 2 cylindres stationnaires a aussi été étudié au nombre Reynolds de 800 comme comparaison. À part les dispositions quiconces, les dispositions tandem et côte à côte ont aussi été examinées afin de mieux comprendre l'écoulement à l'entour des deux cylindres.Pour les dispositions quiconces, quatre configurations différentes de cylindres ont été préparées dans le cas des cylindres stationnaires. Pour un petit degré de ratio, P / D = 2, à α = 16°, l'intérieur de la couche cisaillée du cylindre en amont a été dévié entre les deux cylindres et a provoqué la séparation de l'écart de la couche cisaillée du cylindre en aval. Un nombre Strouhal de 0,159 a été observé dans la présente étude. Pour un plus grand degré de ratio, P / D = 3,25, à α = 16°, les tourbillons se sont répandus du cylindre en amont pour ensuite empiéter sur celui en aval. Un seul tourbillon de Kàrmàn est formé derrière le cylindre en aval, et donc, le nombre de Strouhal obtenu est très proche de celui d'un seul cylindre stationnaire. Aux angles d'incidence modérée, 20° ≤ α ≤ 45°, une paire de tourbillons s'est répandue via le les couches cisaillées internes des deux cylindres, puis a été enveloppée par le la couche cisaillée externe du cylindre en amont. Cette procédure donne un grand tourbillonnement combiné, qui est suivi par un tourbillonnement répandu par le cylindre de la couche cisaillée externe en aval et les multiples nombres de Strouhal avec une relation intégrale. En général, le coefficient de traînée moyen du cylindre en aval a été plus petit que celui du cylindre en amont. Des coefficients de levage négatifs ont été observés pour le cylindre en aval pour toutes les configurations considérées dans cette étude.