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.

Chaos in a Two-Degree of Freedom Duffing Oscillator

High dimensional dynamical systems has intricate behavior either on temporal or on spatial evolution properties. Nevertheless, most of the work on chaotic dynamics has been concentrated on temporal behavior of low-dimensional systems. This contribution is concerned with the chaotic response of a two-degree of freedom Duffing oscillator. Since the equations of motion are associated with a five-dimensional system, the analysis is performed by considering two Duffing oscillators, both with single-degree of freedom, coupled by a spring-dashpot system. With this assumption, it is possible to analyze the transmissibility of motion between the two oscillators.

Application of the center manifold theory to the study of slewing flexible Non-ideal structures with nonlinear curvature: a case study

In this paper is Analyzed the local dynamical behavior of a slewing flexible structure considering nonlinear curvature. The dynamics of the original (nonlinear) governing equations of motion are reduced to the center manifold in the neighborhood of an equilibrium solution with the purpose of locally study the stability of the system. In this critical point, a Hopf bifurcation occurs. In this region, one can find values for the control parameter (structural damping coefficient) where the system is unstable and values where the system stability is assured (periodic motion). This local analysis of the system reduced to the center manifold assures the stable / unstable behavior of the original system around a known solution.

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.

Functional changes of human quadriceps muscle injured by eccentric exercise

The present study evaluated functional changes of quadriceps muscle after injury induced by eccentric exercise. Maximal isometric torque of quadriceps and the surface electromyography (root mean square, RMS, and median frequency, MDF) of the vastus medialis oblique (VMO) and vastus lateralis (VL) muscles were examined before, immediately after and during the first 7 days after injury. Serum creatine kinase (CK) levels and magnetic resonance imaging (MRI) were used to identify muscle injury. The subject was used as her own control and percent refers to pre-injury data. Experiments were carried out with a sedentary 23-year-old female. Injury was induced by 4 bouts of 15 maximal isokinetic eccentric contractions (angular velocity of 5º/s; range of motion from 40º to 110º of knee flexion). The isometric torque of the quadriceps (knee at 90º flexion) decreased 52% immediately after eccentric exercise and recovered on the 5th day. The highest reduction of RMS occurred on the 2nd day after injury in both VL (63%) and VMO (66%) and only VL recovered to the pre-injury level on the 7th day. Immediately after injury, the MDF decreased by 5 and 3% (VMO and VL, respectively) and recovered one day later. Serum CK levels increased by 109% on the 2nd day and were still increased by 32% on the 7th day. MRI showed large areas of injury especially in the deep region of quadriceps. In conclusion, eccentric exercise decreased the isometric torque and electromyographic signals of quadriceps muscle, which were recovered in one week, despite the muscle regeneration signals.

Effect of frequency of static stretching on flexibility, hamstring tightness and electromyographic activity

We compared the effect of the number of weekly repetitions of a static stretching program on the flexibility, hamstring tightness and electromyographic activity of the hamstring and of the triceps surae muscles. Thirty-one healthy subjects with hamstring tightness, defined as the inability to perform total knee extension, and shortened triceps surae, defined by a tibiotarsal angle wider than 90° during trunk flexion, were divided into three groups: G1 performed the stretching exercises once a week; G2, three times a week, and G3, five times a week. The parameters were determined before and after the stretching program. Flexibility improved in all groups after intervention, from 7.65 ± 10.38 to 3.67 ± 12.08 in G1, from 10.73 ± 12.07 to 0.77 ± 10.45 in G2, and from 14.20 ± 10.75 to 6.85 ± 12.19 cm in G3 (P < 0.05 for all comparisons). The increase in flexibility was higher in G2 than in G1 (P = 0.018), while G2 and G3 showed no significant difference (G1: 4 ± 2.17, G2: 10 ± 5.27; G3: 7.5 ± 4.77 cm). Hamstring tightness improved in all groups, from 37.90 ± 6.44 to 29 ± 11.65 in G1, from 39.82 ± 9.63 to 21.91 ± 8.40 in G2, and from 37.20 ± 6.63 to 26.10 ± 5.72° in G3 (P < 0.05 for all comparisons). During stretching, a statistically significant difference was observed in electromyographic activity of biceps femoris muscle between G1 and G3 (P = 0.048) and G2 and G3 (P = 0.0009). No significant differences were found in electromyographic activity during maximal isometric contraction. Stretching exercises performed three times a week were sufficient to improve flexibility and range of motion compared to subjects exercising once a week, with results similar to those of subjects who exercised five times a week.

The effects of stretching on the flexibility, muscle performance and functionality of institutionalized older women

Stretching has been widely used to increase the range of motion. We assessed the effects of a stretching program on muscle-tendon length, flexibility, torque, and activities of daily living of institutionalized older women. Inclusion/exclusion criteria were according to Mini-Mental State Examination (MMSE) (>13), Barthel Index (>13) and Lysholm Scoring Scale (>84). Seventeen 67 ± 9 year-old elderly women from a nursing home were divided into 2 groups at random: the control group (CG, N = 9) participated in enjoyable cultural activities; the stretching group (SG, N = 8) performed active stretching of hamstrings, 4 bouts of 1 min each. Both groups were supervised three times per week over a period of 8 weeks. Peak torque was assessed by an isokinetic method. Both groups were evaluated by a photogrammetric method to assess muscle-tendon length of uni- and biarticular hip flexors and hamstring flexibility. All measurements were analyzed before and after 8 weeks by two-way ANOVA with the level of significance set at 5%. Hamstring flexibility increased by 30% in the SG group compared to pre-training (76.5 ± 13.0° vs 59.5 ± 9.0°, P = 0.0002) and by 9.2% compared to the CG group (76.5 ± 13.0° vs 64.0 ± 12.0°, P = 0.0018). Muscle-tendon lengths of hip biarticular flexor muscles (124 ± 6.8° vs 118.3 ± 7.6°, 5.0 ± 7.0%, P = 0.031) and eccentric knee extensor peak torque were decreased in the CG group compared to pre-test values (-49.4 ± 16.8 vs -60.5 ± 18.9 Nm, -15.7 ± 20%, P = 0.048). The stretching program was sufficient to increase hamstring flexibility and a lack of stretching can cause reduction of muscle performance.

Real-time simulation of multibody systems with applications for working mobile vehicles

This dissertation describes an approach for developing a real-time simulation for working mobile vehicles based on multibody modeling. The use of multibody modeling allows comprehensive description of the constrained motion of the mechanical systems involved and permits real-time solving of the equations of motion. By carefully selecting the multibody formulation method to be used, it is possible to increase the accuracy of the multibody model while at the same time solving equations of motion in real-time. In this study, a multibody procedure based on semi-recursive and augmented Lagrangian methods for real-time dynamic simulation application is studied in detail. In the semirecursive approach, a velocity transformation matrix is introduced to describe the dependent coordinates into relative (joint) coordinates, which reduces the size of the generalized coordinates. The augmented Lagrangian method is based on usage of global coordinates and, in that method, constraints are accounted using an iterative process. A multibody system can be modelled as either rigid or flexible bodies. When using flexible bodies, the system can be described using a floating frame of reference formulation. In this method, the deformation mode needed can be obtained from the finite element model. As the finite element model typically involves large number of degrees of freedom, reduced number of deformation modes can be obtained by employing model order reduction method such as Guyan reduction, Craig-Bampton method and Krylov subspace as shown in this study The constrained motion of the working mobile vehicles is actuated by the force from the hydraulic actuator. In this study, the hydraulic system is modeled using lumped fluid theory, in which the hydraulic circuit is divided into volumes. In this approach, the pressure wave propagation in the hoses and pipes is neglected. The contact modeling is divided into two stages: contact detection and contact response. Contact detection determines when and where the contact occurs, and contact response provides the force acting at the collision point. The friction between tire and ground is modelled using the LuGre friction model, which describes the frictional force between two surfaces. Typically, the equations of motion are solved in the full matrices format, where the sparsity of the matrices is not considered. Increasing the number of bodies and constraint equations leads to the system matrices becoming large and sparse in structure. To increase the computational efficiency, a technique for solution of sparse matrices is proposed in this dissertation and its implementation demonstrated. To assess the computing efficiency, augmented Lagrangian and semi-recursive methods are implemented employing a sparse matrix technique. From the numerical example, the results show that the proposed approach is applicable and produced appropriate results within the real-time period.

Variational Monte Carlo study of core-valence separation schemes for first-row atoms and positive ions /

All-electron partitioning of wave functions into products ^core^vai of core and valence parts in orbital space results in the loss of core-valence antisymmetry, uncorrelation of motion of core and valence electrons, and core-valence overlap. These effects are studied with the variational Monte Carlo method using appropriately designed wave functions for the first-row atoms and positive ions. It is shown that the loss of antisymmetry with respect to interchange of core and valence electrons is a dominant effect which increases rapidly through the row, while the effect of core-valence uncorrelation is generally smaller. Orthogonality of the core and valence parts partially substitutes the exclusion principle and is absolutely necessary for meaningful calculations with partitioned wave functions. Core-valence overlap may lead to nonsensical values of the total energy. It has been found that even relatively crude core-valence partitioned wave functions generally can estimate ionization potentials with better accuracy than that of the traditional, non-partitioned ones, provided that they achieve maximum separation (independence) of core and valence shells accompanied by high internal flexibility of ^core and Wvai- Our best core-valence partitioned wave function of that kind estimates the IP's with an accuracy comparable to the most accurate theoretical determinations in the literature.

Anaerobic performance in ice hockey : the effect of skate blade radius of hollow

The purpose of the study was to investigate the effect of skate blade radius of hollow (ROH) on anaerobic performance, specifically during the acceleration and stopping phases of an on-ice skating test. Fifteen, male Junior B hockey players (mean age 19 y ± 1.46) were recruited to participate. On-icc testing required each participant to complete an on-ice anaerobic performance test [Reed Repeat Skate (RRS)) on three separate days. During each on-ice test, the participant's skate blades were sharpened to one of three, randomly assigned, ROH values (0.63 cm, 1.27 cm, 1.90 cm). Performance times were recorded during each RRS and used to calculate anaerobic variables [anaerobic power (W), anaerobic capacity (W), and fatigue index (s, %)). Each RRS was video recorded for the purpose of motion analysis. Video footage was imported into Peak Motus™ to measure kinematic variables of the acceleration and stopping phases. The specific variables calculated from the acceleration phase were: average velocity over 6 m (m/s), average stride length (m), and mean stride rate (strides/s). The specific variables calculated from the stopping phase were: velocity at initiation of stopping (rn/s), stopping distance (m), stopping time (s). A repeated measures ANOV A was used to assess differences in mean performance and kinematic variables across the three selected hollows. Further analysis was conducted to assess differences in trial by trial performance and kinematic variables for all hollows. The primary findings of the study suggested that skate blade ROH can have a significant effect on kinematic variables, namely stride length and stride rate during the acceleration phase and stopping distance and stopping time during the stopping phase of an on-ice anaerobic performance test. During the acceleration phase, no significant difdifferences were found in SR and SL across the three selected hollows. Mean SR on the 1.27 cm hollow was significantly slower than both the 0.63 cm and 1.90 cm hollows and SL was significantly longer when skating on the 1.27 cm hollow in comparison to the 1.90 cm hollow. During the stopping phase, stopping distance on the 0.63 cm hollow (4.12 m ± 0.14) was significantly shorter than both the 1.27 cm hollow (4.43 m ± 0.08) (p < 0.05) and the 1.90 cm ho])ow (4.35 m ± 0.12) (p < 0.05). Mean ST was also significantly shorter when stopping on the 0.63 cm hollow then both the 1.27 cm and 1.90 cm hollows. Trial by trial results clearly illustrated the affect of fatigue on kinematic variables; AV, SR, IV decreased from trial 1 to 6. There was no significant effect on anaerobic performance variables during the RRS. Altering the skate blade ROH has a significant and practical affect on accelerating and stopping performance will be discussed in this paper.

The impact of tobacco control policies on university students' smoking in Ontario

Objective. Despite steady declines in the prevalence of tobacco use among Canadians, young adult tobacco use has remained stubbornly high over the past two decades (CTUMS, 2005a). Currently in Ontario, young adults have the highest proportion of smokers of all age cohorts at 26%. A growing body of evidence shows that smoking restrictions and other tobacco control policies can reduce tobacco use and consumption among adults and deter initiation among youth; whether young adult university students' smoking participation is influenced by community smoking restrictions, campus tobacco control policies or both remains an empirical question. The purpose of this study is to examine the relationship among current smoking status of students on university campuses across Ontario and various tobacco control policies, 3including clean air bylaws of students' home towns, clean air by-laws of the community where the university is situated, and campus policies. Methods. Two data sets were used. The 200512006 Tobacco Use in a Representative Sample of Post-Secondary Students data set provides information about the tobacco use of 10,600 students from 23 universities and colleges across Ontario. Data screening for this study reduced the sample to 5,114 17-to-24 year old undergraduate students from nine universities. The second data set is researcher-generated and includes information about strength and duration of, and students' exposure to home town, local and campus tobacco control policies. Municipal by-laws (of students' home towns and university towns) were categorized as weak, moderate or strong based on criteria set out in the Ontario Municipal By-law Report; campus policies were categorized in a roughly parallel fashion. Durations of municipal and campus policies were calculated; and length of students' exposure to the policies was estimated (all in months). Multinomial logistic regression analyses were used to examine the relationship between students' current smoking status (daily, less-than-daily, never-smokers) and the following policy measures: strength of, duration of, and students' exposure to campus policy; strength of, duration of, and students' exposure to the by-law in the university town; and, strength of, duration of, and students' exposure to the by-law in the home town they grew up in. Sociodemographic variables were controlled for. Results. Among the Ontario university students surveyed, 7.0% currently use tobacco daily and 15.4% use tobacco less-than-daily. The proportions of students experiencing strong tobacco control policies in their home town, the community in which their university is located and at their current university were 33.9%,64.1 %, and 31.3% respectively. However, 13.7% of students attended a university that had a weak campus policy. Multinomial logistic regressions suggested current smoking status was associated with university town by-law strength, home town by-law strength and the strength of the campus tobacco control policy. In the fmal model, after controlling for sociodemographic factors, a strong by-law in the university town and a strong by-law in students' home town were associated with reduced odds of being both a less-than-daily (OR = 0.64, 95%CI: 0.48-0.86; OR = 0.80, 95%CI: 0.66-0.95) and daily smoker (OR = 0.59, 95%CI: 0.39-0.89; OR = 0.76, 95%CI: 0.58-0.99), while a weak campus tobacco control policy was associated with higher odds of being a daily smoker (OR = 2.08, 95%CI: 1.31-3.30) (but unrelated to less-than-daily smoking). Longer exposure to the municipal by-law (OR = 0.93; 95%CI: 0.90-0.96) was also related to smoking status. Conclusions. Students' smoking prevalence was associated with the strength of the restrictions in university, and with campus-specific tobacco control policies. Lessthan- daily smoking was not as strongly associated with policy measures as daily smoking was. University campuses may wish to adopt more progressive campus policies and support clean air restrictions in the broader community. More research is needed to determine the direction of influence between tobacco control policies and students' smoking.

Active isolated stretching : an investigation of the mechanical mechanisms

The Active Isolated Stretching (AIS) technique proposes that by contracting a muscle (agonist) the opposite muscle (antagonist) will relax through reciprocal inhibition and lengthen without increasing muscle tension (Mattes, 2000). The clinical effectiveness of AIS has been reported but its mechanism of action has not been investigated at the tissue level. Proposed mechanisms for increased range of motion (ROM) include mechanical or neural changes, or an increased stretch tolerance. The purpose of the study was to investigate changes in mechanical properties, i.e. stiffness, of skeletal muscle in response to acute and long-term AIS stretching for the hamstring muscle group. Recreationally active university-aged students (female n=8, male n=2) classified as having tight hamstrings, by a knee extension test, volunteered for the study. All stretch procedures were performed on the right leg, with the left leg serving as a control. Each subject was assessed twice: at an initial session and after completing a 6-week AIS hamstring stretch training program. For both test sessions active knee extension (ROM) to a position of "light irritation", passive resisted torque and stiffness were determined before and after completion of the AIS technique (2x10 reps). Data were collected using a Biodex System 3 Pro (Biodex Medical Systems, NY, USA) isokinetic dynamometer. Surface electromyography (EMG) was used to monitor vastus lateralis (VL) and hamstring muscle activity during the stretching movements. Between test sessions, 2x10 reps of the AIS bent knee hamstring stretch were performed daily for 6-weeks.

Collection of Canadian periodical clippings and Peninsular Game Club of St. Catharines broadside, 1874, [1910-1950]

Items include: 13 small poems clipped from newspapers. None of the poems list authors. Most of the poems are based on life lessons. Clippings of short stories which appear to have come from a St. Catharines newspaper. The stories include anecdotes, humour and medical advice. There is no author listed on any of the stories. 2 coloured sewing machine advertisements each measuring 9 cm. x 13 cm. and 9 cm. x 14 cm. 1 broadside measuring 27 cm. x 37 cm. and posted by the Peninsular Game Club of St. Catharines. The broadside is a copy of the game laws of 1874 with a warning that breach of these laws will bring rigorous prosecution.

Studies on the dynamics and rheology of dilute suspensions of Brownian particles in simple shear flow under the action of an external force

We present a novel approach to computing the orientation moments and rheological properties of a dilute suspension of spheroids in a simple shear flow at arbitrary Peclct number based on a generalised Langevin equation method. This method differs from the diffusion equation method which is commonly used to model similar systems in that the actual equations of motion for the orientations of the individual particles are used in the computations, instead of a solution of the diffusion equation of the system. It also differs from the method of 'Brownian dynamics simulations' in that the equations used for the simulations are deterministic differential equations even in the presence of noise, and not stochastic differential equations as in Brownian dynamics simulations. One advantage of the present approach over the Fokker-Planck equation formalism is that it employs a common strategy that can be applied across a wide range of shear and diffusion parameters. Also, since deterministic differential equations are easier to simulate than stochastic differential equations, the Langevin equation method presented in this work is more efficient and less computationally intensive than Brownian dynamics simulations.We derive the Langevin equations governing the orientations of the particles in the suspension and evolve a procedure for obtaining the equation of motion for any orientation moment. A computational technique is described for simulating the orientation moments dynamically from a set of time-averaged Langevin equations, which can be used to obtain the moments when the governing equations are harder to solve analytically. The results obtained using this method are in good agreement with those available in the literature.The above computational method is also used to investigate the effect of rotational Brownian motion on the rheology of the suspension under the action of an external force field. The force field is assumed to be either constant or periodic. In the case of con- I stant external fields earlier results in the literature are reproduced, while for the case of periodic forcing certain parametric regimes corresponding to weak Brownian diffusion are identified where the rheological parameters evolve chaotically and settle onto a low dimensional attractor. The response of the system to variations in the magnitude and orientation of the force field and strength of diffusion is also analyzed through numerical experiments. It is also demonstrated that the aperiodic behaviour exhibited by the system could not have been picked up by the diffusion equation approach as presently used in the literature.The main contributions of this work include the preparation of the basic framework for applying the Langevin method to standard flow problems, quantification of rotary Brownian effects by using the new method, the paired-moment scheme for computing the moments and its use in solving an otherwise intractable problem especially in the limit of small Brownian motion where the problem becomes singular, and a demonstration of how systems governed by a Fokker-Planck equation can be explored for possible chaotic behaviour.

Mathematical Modelling of the Dynamics of Granular Materials in a Rotating Cylinder

The current study is aimed at the development of a theoretical simulation tool based on Discrete Element Method (DEM) to 'interpret granular dynamics of solid bed in the cross section of the horizontal rotating cylinder at the microscopic level and subsequently apply this model to establish the transition behaviour, mixing and segregation.The simulation of the granular motion developed in this work is based on solving Newton's equation of motion for each particle in the granular bed subjected to the collisional forces, external forces and boundary forces. At every instant of time, the forces are tracked and the positions velocities and accelarations of each partcle is The software code for this simulation is written in VISUAL FORTRAN 90 After checking the validity of the code with special tests, it is used to investigate the transition behaviour of granular solids motion in the cross section of a rotating cylinder for various rotational speeds and fill fraction.This work is hence directed towards a theoretical investigation based on Discrete Element Method (DEM) of the motion of granular solids in the radial direction of the horizontal cylinder to elucidate the relationship between the operating parameters of the rotating cylinder geometry and physical properties ofthe granular solid.The operating parameters of the rotating cylinder include the various rotational velocities of the cylinder and volumetric fill. The physical properties of the granular solids include particle sizes, densities, stiffness coefficients, and coefficient of friction Further the work highlights the fundamental basis for the important phenomena of the system namely; (i) the different modes of solids motion observed in a transverse crosssection of the rotating cylinder for various rotational speeds, (ii) the radial mixing of the granular solid in terms of active layer depth (iii) rate coefficient of mixing as well as the transition behaviour in terms of the bed turnover time and rotational speed and (iv) the segregation mechanisms resulting from differences in the size and density of particles.The transition behaviour involving its six different modes of motion of the granular solid bed is quantified in terms of Froude number and the results obtained are validated with experimental and theoretical results reported in the literature The transition from slumping to rolling mode is quantified using the bed turnover time and a linear relationship is established between the bed turn over time and the inverse of the rotational speed of the cylinder as predicted by Davidson et al. [2000]. The effect of the rotational speed, fill fraction and coefficient of friction on the dynamic angle of repose are presented and discussed. The variation of active layer depth with respect to fill fraction and rotational speed have been investigated. The results obtained through simulation are compared with the experimental results reported by Van Puyvelde et. at. [2000] and Ding et at. [2002].The theoretical model has been further extended, to study the rmxmg and segregation in the transverse direction for different particle sizes and their size ratios. The effect of fill fraction and rotational speed on the transverse mixing behaviour is presented in the form of a mixing index and mixing kinetics curve. The segregation pattern obtained by the simulation of the granular solid bed with respect to the rotational speed of the cylinder is presented both in graphical and numerical forms. The segregation behaviour of the granular solid bed with respect to particle size, density and volume fraction of particle size has been investigated. Several important macro parameters characterising segregation such as mixing index, percolation index and segregation index have been derived from the simulation tool based on first principles developed in this work.