Engineering Mechanics: Dynamics
... Let assume that the principal axes of the rigid body are coincident with the body fixed frame, then Euler angles ψ, θ and φ in the z-y-x form can be used to describe instantaneous orientation of a rigid body with respect to a fixed coordinate system : 19) ω x =ψ sin θ sin φ +θ cos φ ω y =ψ sin θ cos φ −θ sin φ (4) ω z =ψ cos θ +φ which can also be written in the matrix form: ...
... (1). We note that the sum of the moments about the center of mass of a rigid body due to external forces and couples equals to the rate of change of the angular momentum about the center of mass : 19) ...
... (17)], associated with the "flipping" motion, to its final stable configuration [as per Eq. (18) or (19) and Solution-1 or 2 in Fig. 5], are shown in Fig. 7, where masses for the initial configuration are shown in white, whereas the masses for the final configuration are shown in black color. ...
This paper is dedicated to the numerical simulation and analysis of the "Dzhanibekov's Effect" - non-stable "flipping" motion of the rigid body with periodic change by 180° of the direction of the main axis of its rotation, always occurring when the body is provided with the main rotation about its axis with intermediate principal moment of inertia. In this work we are proposing and developing a new concept of "inertial morphing" of the spacecraft for the versatile control of the "Dzhanibekov's Effect", enabling manipulations with the attitude of the spacecraft without employing classical gyroscopes. We are demonstrating that applying controlled changes to the inertial properties of the system, the "Dzhanibekov's Effect" flipping motion can be completely stopped, if this motion is undesirable. Similarly, the "Dzhanibekov's Effect" flipping motion can be activated on the stable, non-tumbling spacecraft, if this is desired for the purposes of the mission. We are also showing that the frequency of the flipping motion can be controlled within a wide range. For the implementation of the transformations between stable and unstable modes of motion, we are proposing two main conceptual solutions, involving changes to the system, resulting in the intermediate moment of inertia becoming the smallest or largest principal moment of inertia of the body. Development of the conceptual 6-mass model of the spacecraft enabling controllable switching OFF of the "Dzhanibekov's Effect" flipping is presented. Furthermore, we also exploring the possibilities of utilization of the "Dzhanibekov's Effect" for possible future new space missions, employing periodic change in the attitude orientation of the spacecraft. It is believed, that new results of this research may have multiple applications for possible future space missions. In particular, we are suggesting assistance in establishing formation flight; thruster direction control and control of the period of the "flipping" motion of the spacecraft.
... Each of the terms in equation (11) has been derived with reference to an inertial frame, and each has a direct physical interpretation. The first term is the stretch acceleration due to a change in magnitude of the stretch velocity. ...
... The third term, Most notable, however, is the way in which the process has revealed the physical meaning of the second term in eqn. (11); i.e., ...
... Fig. 3, and Fig. 4, may be used to explain the physical basis of the Coriolis acceleration calculated as a part of kinematic analyses in rigid body dynamics. Students should apply relative velocity equation (4) and relative acceleration equation (11) to a large variety of problems to gain confidence and establish a solid foundation of understanding. After this foundation is established, they are in a position to consider one last question -how does the physical interpretation developed in the context of an inertial frame connect with the "effects" commonly presented for rotating frames? ...
The subject of dynamics is fundamental to engineering programs in general, and can be challenging to teach. In particular, the topic of Coriolis acceleration and the “Coriolis effect” may present the greatest challenge of all. Although mathematical formulations and physical explanations are available in many textbooks and technical articles, undergraduate students still have trouble making meaningful and long-lasting connections between the mathematical expressions and the physical manifestations of the phenomenon. In our opinion, a significant part of the problem can be attributed to the traditional formulation of kinematic equations using rotating frames of reference. Normally, the Coriolis acceleration is defined, derived, and explained using at least one noninertial frame. At the University of Saskatchewan, our approach is to express the equations of rigid body dynamics solely with respect to a single inertial frame of reference, and to thereby solve all the problems that would otherwise be solved using rotating frames. We also use this approach for deriving and explaining the Coriolis effect. Although our approach is, in a sense, equivalent to the traditional method, we have found that students are better able to understand and apply the principles of dynamics when working within a single inertial frame. In this paper, our pedagogical approach will be presented and then applied to the question of “what’s going on” with the Coriolis effect
... The present model generalizes both of the previous models of the RP [14,15] in addition to the non-relativistic projectile (NRP) discussed in text books [1,2]. The horizontal and vertical velocities for the RP will be analytically obtained. ...
... In the literature, the projectile problem (PP) has been extensively discussed in text books [1,2]. Further, it was investigated in Newtonian mechanics using classical calculus [3][4][5][6][7][8] and also in view of fractional calculus [9][10][11][12][13]. ...
The projectile motion (PP) in a vacuum is re-examined in this paper, taking into account the relativistic mass in special relativity (SR). In the literature, the mass of the projectile was considered as a constant during motion. However, the mass of a projectile varies with velocity according to Einstein’s famous equation m=m01−v2/c2, where m0 is the rest mass of the projectile and c is the speed of light. The governing system consists of two-coupled nonlinear ordinary differential equations (NODEs) with prescribed initial conditions. An analytical approach is suggested to treat the current model. Explicit formulas are determined for the main characteristics of the relativistic projectile (RP) such as time of flight, time of maximum height, range, maximum height, and the trajectory. The relativistic results reduce to the corresponding ones of the non-relativistic projectile (NRP) in Newtonian mechanics, when the initial velocity is not comparable to c. It is revealed that the mass of the RP varies during the motion and an analytic formula for the instantaneous mass in terms of time is derived. Also, it is declared that the angle of maximum range of the RP depends on the launching velocity, i.e., unlike the NRP in which the angle of maximum range is always π/4. In addition, this angle lies in a certain interval [π/4,π/6) for any given initial velocity (<c). The obtained results are discussed and interpreted. Comparisons with a similar problem in the literature are performed and the differences in results are explained.
... Due to the fact that there are many papers [2,5,6,8] that provide information on capabilities and suitability of MCSA it was decided to invent own diagnostic system. This paper presents concept of condition monitoring and diagnosing system dedicated for industrial press line based on data coming from different sources like vibration, electrical and thermal measurements what makes the system hybrid and allows improve diagnostic inference process. ...
... Criticality analysis gave a good basis for further design process of condition monitoring system. There are many methods that can be implemented for that purpose, like AHP (Analytic Hierarchy Process) [17], ABC (Activity Based Costing) [18] or MFMEA (Machinery Failure Mode and Effects Analysis) [2]. During designing of condition monitoring systems of press line the authors were basing on MFMEA which allows to assign the problem to particular element of the analysed object. ...
Idea of Industry 4.0 indicate Condition Based Maintenance (CBM) and Predictive Maintenance
(PdM) as fundamental maintenance strategies in modern factories. CBM and PdM could be implemented with use of on-line continuous monitoring and diagnostic systems as well as program of systematic
examinations of asset condition done by maintenance personnel. Using data collected from hand held
instruments and from on-line systems is possible to build full image of current asset condition and predict
probably faults in the future. This paper presents system of condition monitoring and diagnosing of main
drive of industrial press line. The system use diagnostic data coming from different sources like vibration,
electrical and thermal measurements. Application of different types of data makes the system hybrid and
allows improve diagnostic inference process. The article describes the way of system design and its
implementation.
... In more complex geometries, such as lattice filled cylinders, the member can be split into more simple geometries then analyzed as a summation of the part. For the situation where the member's surface thickness is thin compared to the overall geometry, the moment of inertia can be computed as the mass moment of inertia divided by the area density [15]. As the lattice structure varies significantly throughout the test specimens, but can be considered thin surfaced, the second method was utilized in this analysis. ...
... The area density can be computed through two different methods, either mass divided by total surface area, Eq 13, or as the specimen density multiplied by the average cross-sectional thickness, Eq 14 [15]. ...
This paper describes in detail the background, laboratory setup, and experimental results associated with the mechanical testing and observations of three different Triply Periodic Minimal Surface (TPMS) structures. The purpose of this study is to examine the variation in mechanical properties through structural design and relative density. The material chosen for this study was Inconel 718, and the TPMS structures were constructed utilizing a General Electric Concept Laser M2 Cusing additive manufacturing machine. Compression testing was conducted utilizing an MTS Model 810 universal testing machine following the recommended compression testing procedures outlined in American Society for Testing and Materials (ASTM) E9-19 Standard Test Methods of Compression Testing of Metallic Materials at Room Temperature. Analysis was performed to determine the modulus of elasticity for the tested designs, with additional analysis required the determination of the area moment of inertia for the TPMS structures. This provided the stress required for failure of the first cell within the specimen utilizing beam theory calculations. These results are to be included in further research aimed at investigating the time dependent characteristics of lattice structural designs under high strain rate impact with a hard target.
... . A recent comprehensive list of FC applications can be found in [7][8][9][10][11][12]. The projectile problem (PP) is a classical issue in Newtonian mechanics [13][14][15][16][17][18][19][20]. Recently, the PP was revisited in the perspective of FC, but the proposed models require some improvement to achieve more accurate descriptions. ...
... Applying the Laplace transform for the first equation in (14) leads to ...
This paper addresses the modeling of projectile motion using fractional models vis-a-vis experimental data. Recently, it was shown that an auxiliary parameter () needs to be included in the fractional modeling to preserve the dimensionality of the physical quantities. In previous studies, was subjected to several restrictions without considering clear and meaningful reasons. Such problems are overcome here and a method for estimating using the experimental data is introduced. A new solution for the two-dimensional projectile motion using the Caputo’s fractional derivative is obtained. An explicit formula for the trajectory of the projectile in vacuum is first derived. Then, the projectile parametric equations in a resistant medium are expressed in terms of the Mittag–Leffler function. The transcendental equations for the time of flight and the time of maximum height are solved numerically. The model agrees with the classical one as the fractional order tends to 1. In view of the superior results, the current numerical modeling approach is validated for this real-world application.
... The former is found with trigonometry (eqs. 9 and 10) and the latter is derived from the instantaneous center of rotation method [22] (eq. 11) (9) (10) (11) where is the distance between the instantaneous center and the moving joint and is the angular speed of the coupler (12) ...
... The derivatives of regarding (designated as ) are also necessary (22) where (23) ...
Dynamic Joint-Forces in a mechanism produce vibration and wear, decreasing its life span. Many studies have been carried out on optimization of mechanisms dynamic behaviour; however, few of it are focused on the reduction of Joint-Forces. Therefore, this work presents a method to obtain the link lengths of Function Generation Four-Bar Linkages, minimizing the maximum dynamic force in the joints. The study assumes that the crank rotates with constant angular velocity and the rocker moves a high amount of inertia between two positions. Hence, the mechanism mass and inertia is considered negligible. The equations of motion are set up together with Dead-Center Construction method after Alt. To analyze the behaviour of the Joint-Forces, all the equations are parametrized, finding out that the maximum Joint-Force is minimizable for every task given. The minimization of the Joint-Forces is achieved by using simple algorithms as Bisection and Regula-Falsi Illinois. The results show that this method reduces the maximal Joint-Force by a mean value of 8.5%, with respect to the Dead-Center Construction method with Transmission Angle Minimization. Moreover, for some tasks, the force reduction could reach up to 60%. Furthermore, this method solves the problem of null-length crank and rocker for centric crank-rocker mechanisms, generated by the Transmission Angle minimization.
... Additionally, collision interaction is provided by stoppers 6. Outside different drag interactions are provided by the axial elements 5 and 8. In object translated motion (without rotation) equation of motion is [1][2][3][4]: ...
... As the weight mg and Archimedes forces are constant, then from the vector equation (1) it can be concluded that only the force R ̅ can generate controlled propulsion action and move the object. ...
... Traditional descriptions of kinematics tend to use the angular and linear components of a link's velocity separately in most works, e.g., [79] and [80]. The remaining derivation of the recursive Newton-Euler algorithm will be easier however if one combines these components into a spatial velocity, ˆ v , per Eqn. ...
... This model is derived from the motion of a point mass, which has position and velocity but has no orientation or angular velocity, which is discussed in many dynamics texts, e.g. [79] . The model represents the system state as the linear position, x, and linear velocity, ˙ x, of the vehicle body with respect to the global frame of reference per Eqn. ...
This thesis addresses Nonlinear Model Predictive Controller (NMPC) of multi-rotor Unmanned Aerial Vehicles (UAVs). It presents two primary contributions: i) a novel method of numerically analyzing flight controller performance, and ii) two novel NMPC components: an optimization algorithm and a UAV model. These contributions are assessed in a case study comparing a set of five NMPC systems on flight performance in nine tests including impulse response, periodic wind disturbances, and obstacle avoidance.
The Performance Analysis Methodology (PAM) proposed in this work calculates the probability of a controller maintaining a UAV's state output within a set of user defined benchmark values during flight tests. These tests can take many forms, but this thesis considers initial state errors, reference changes, disturbing winds, and obstacles. To estimate this probability, the PAM simulates multiple flights under each set of test conditions, analyzes each test flight individually to determine whether tracking error was within the desired benchmark values, and combines the analyzed data via statistical analysis. To generate accurate flight test data, a novel formulation of recursive Newton-Euler multibody dynamics is proposed, and models for commonly encountered vehicle subsystems are provided. To appropriately analyze the test flight data, a novel pseudo-Laplace transform is proposed capable of accounting for time-varying elements within the tracking error signals. Finally, to combine flight test data from multiple tests, two methods of statistical analysis, mean/variance analysis and binomial probability analysis, are provided. Combined into the PAM, these techniques form a novel means to determine how likely a control system is to safely maintain a UAV in a desired state despite disruption.
Two NMPC components are proposed in this thesis: i) an E-greedy kinodynamic tree algorithm for optimization, and ii) a derivative multi-rotor UAV model for cost prediction. The E-greedy tree algorithm expands the concept of random kinodynamic trees to incorporate game theory as a means of focusing tree growth. This produces an optimization algorithm that can identify low-cost control inputs faster than typical NMPC optimization techniques. The derivative multi-rotor model is designed to account for a wider range of dynamic effects in predicting the cost of control inputs. Where typical multi-rotor models in MPC literature assume that control signals directly specify the joint velocities of propellers and joint angles propeller blades, the derivative model models the propeller velocity and blade angle rates of change. As a result, the derivative multi-rotor model produces better prediction of future vehicle motion and, correspondingly, better predictions of cost. This thesis presents these two new components alongside three other NMPC optimization algorithms and two other NMPC multi-rotor vehicle models for comparison.
As a demonstration of both PAM and NMPC, the case study uses a large variable-pitch propeller quadrotor as the basis for analyzing the performance of six NMPCs (each a combination of an optimization algorithm and a multi-rotor model), and a PID reference tracking controller. Each controller is tested for performance on nine different tests covering a range of control challenges. The results from each test are used to create flight envelopes depicting the range of conditions within which each controller met selected performance benchmarks. The new NMPC optimization algorithm shows immediate advantages, achieving the goal of identifying low-cost control inputs faster. The new NMPC model shows promise, but was hindered by the computational capacity of the quadrotor's onboard processor. Finally, the PAM proves capable of performing a diverse set of tests, while producing data that can be quickly and easily interpreted.
... If the generalized coordinate q i is an angular displacement, p i is the angular momentum [33,35]. The rate of angular momentum in recursive form can be written as [36] ...
... The impulsive force is defined as a force of relatively large magnitude that acts over a small interval of time. Determining the actual history of such a force is often impractical, but its average value can be estimated [36]. Therefore, the impulse at foot strike I strk can be calculated as ...
The optimization-based dynamic prediction of 3D human running motion is studied in this paper. A predictive dynamics method is used to formulate the running problem, and normal running is formulated as a symmetric and cyclic motion. Recursive Lagrangian dynamics with analytical gradients for all the constraints and objective function are incorporated in the optimization process. The dynamic effort is used as the performance measure, and the impulse at the foot strike is also included in the performance measure. The joint angle profiles and joint torque profiles are calculated for the full-body human model, and the ground reaction force (GRF) is determined. Several cause-and-effect cases are studied, and the formulation for upper-body yawing motion is proposed and simulated. Simulation results from this methodology show good correlation with experimental data obtained from human subjects and the existing literature.
... Among topics covered in the course, the one that appears to present a challenge to some students is the concept of "conservative forces" versus "non-conservative forces." The topic is covered in all respected and popular textbooks [1][2][3][4] in a nearly similar fashion. For example, Bedford ...
... The rotational dynamics of the aircraft is described by the Euler's equation of motion [36,37] ...
This paper addresses the actuator fault detection and isolation in the case of a total loss of a powertrain of Fleasy’s VTOL (Vertical Take-Off and Landing) aircraft in Multi-Copter mode for safety purposes. A static and dynamic characterization of the powertrain is first performed on a test bench, followed by a parameter identification of the aircraft rotational dynamics using flight data, while preserving the non-linear structure of the system. A real-time prediction of the output is then constructed, relying on the knowledge of the identified model, along with the inertial unit measurements. A fault-detection algorithm is developed based on a likelihood test applied to the residuals and on an appropriate choice of normal probability distribution parameters, the isolation being achieved by an innovative implementation of the signs of the
residuals in the detection algorithm. The contribution of this work is twofold. First, we apply the theoretical work on identification and fault detection to our VTOL tail-sitter aircraft subject to uncertainties (unmodeled aerodynamic effects), disturbances (wind gusts) and non-linearities. Second, and most importantly, we show a very good real-time prediction of the output, and
we validate the developed algorithm through flight experiments where the failure of a motor is intentionally triggered by a switch on the remote controller. The results show a successful detection and isolation of the faulty motor within less than 1 second. This work is considered a step forward in safe aerial transportation and for obtaining an aircraft type certification.
... The spear energy and velocity at distance can be determined given the muzzle velocity using the generic drag force equation and Newton's equations for constant acceleration [22]. ...
This investigation outlines the current technical state of spearguns and key
performance concepts. Testing of natural rubber was conducted to determine
dissipation losses given an assumed 30 minute load case. This data was then
used to develop a function that determines the potential energy stored by 14, 16,
17 or 18mm natural rubber bands given any speargun geometry.
Momentum and energy balances were used to derive equations of motion for the
dynamic behaviour of conventional, roller and inverted spearguns. The system
energy from the rubber function and component masses calculated from
speargun geometry are used to solve for component velocities.
Shaft velocity at various ranges was then calculated using an estimated drag
coefficient and penetration at these ranges was calculated using an estimated
fish tissue cavity strength. COVID-19 prevented testing to empirically determine
these coefficients and increase simulator accuracy; Part 11 outlines the testing
still outstanding.
Shaft buckling and bending were compared and discussed to a limited extent.
Parts 10 & 11 summarise the findings and performance trends uncovered by the
simulation and demonstrated how the simulator could be used to improve
speargun design. Part 12 outlines three areas of research and one survey that
would further expand understanding of speargun dynamics and simulator
capability.
The simulator was published as a website running Python 3; it can be accessed
and used by anyone with a web browser at no cost. Work to complete testing and
evaluate simulator accuracy is ongoing.
... If one object is a particle, and the second one is a wall sample, then the particle-wall coefficient of restitution (e w ) is obtained. Bedford and Fowler (2008) showed that the coefficient of restitution may be obtained from Eq. (5) if the objects involved in the collision are not subjected to rotation, and both wood pellets have similar dimensions, therefore they have similar masses. Subscripts 1 and 2 refer to the objects involved in the collision, while u and v represent the velocity of the objects just before and after the collision, respectively: ...
Wood pellets are increasingly being used to produce energy as a part of the decarbonization process of the economy, but their handling is associated with several problems, which usually requires that the equipment used has to be modified and improved. The discrete element method is a numerical technique suitable for simulating individual particles and handling systems. This paper focuses on the determination of the mechanical and physical parameters for wood pellet particles which are required to develop a discrete element method model to improve handling and transport systems. This study reports the experimentally determined values for wood pellet particles with respect to particle density, modulus of elasticity, particle-particle and particle-wall coefficients of restitution, and particle-particle and particle-wall coefficients of friction. Following the previous findings by other researchers with large samples of bulk material , it has been found that the modulus of elasticity for individual wood pellets depends on the water content, and the particle-wall coefficient of restitution depends on the impact velocity.
... The most successful books currently available on the market [3][4][5][6][7][8][9][10][11][12] all have outstanding features and have been responsible for educating many generations of students, including the authors of this paper. However, it has been our experience that these textbooks, with the exception of the recent books by Tongue and Sheppard [11,12] (more on these books below), do not explicitly present a structured problem solving approach that can guide a student through any problem they will encounter in mechanics, not just statics and dynamics. ...
... The mass remains stationary relative to the circular bar. Choose the KD for finding the value of the constant angular velocity [7]. ...
... The mathematical definition of impulse loading and the subsequent solution of the impulse response are ordinarily addressed within the differential equation course 1 . The physical nature of impulse and momentum are usually covered in a classical dynamics course 2,3 . Yet, even with this redundant coverage (and potentially more in specific programs) students often possess little intuition regarding impulse loading. ...
... A theory course in dynamics is typically included at the sophomore level of most mechanical engineering programs 1,2 . It is common for the content of such a course to begin with particle dynamics. ...
... We can simplify these terms further using the following two relationships. Firstly, for any vector u (for details, see Bedford and Fowler (1995) and Love (1944)) ...
As oil production moves to deeper water and marginal fields, it is necessary to critically consider the merits and drawbacks of different subsea pipelaying techniques. The pipeline tow method is one of these. The basic concept of the tow method is to tow and lay the pipeline at an off-shore location after joining and testing the system at an on-shore fabrication site. This method, therefore, assures improved production quality of pipelines and can be applied economically and easily to all kinds of pipe. It does, however, pose a greater risk of failure due to ocean wave loads during its towing phase. As a consequence, the tow method requires very careful design to achieve a very small submerged weight and maintain a nearly horizontal catenary that is then directly exposed to wave action. The physical problem of towed pipelines in currents and waves is exceedingly complex. The static component of the problem has a significant structural nonlinearity whereas the dynamic component is complicated by the quadratic nonlinearity of the hydrodynamic drag force and the unusual nature of the inertia force under a high near-tangential flow. Such an inertia force was first identified by Sir James Lighthill as applicable to circular cylinders with near- tangential incident flow in waves. The analysis must also account for the axial dynamics of the pipeline, towlines and the tow vessels. The research described in this thesis is aimed at investigating these issues and to obtain a quantitative understanding of their effects on the responses of typical towed pipelines. Initially, the governing equations for towed pipelines and the analytical solutions for simplified cases are presented. In order to tackle a full, representative problem, the finite element method (FEM) is used both for static and dynamic analysis. For the static analysis, full nonlinear algorithms are implemented for the pipeline with simple support boundary condition at each end. To improve convergence performance during this nonlinear analysis, an enhanced catenary equation, which can consider the effect of a uniform normal component of current load, is used to obtain an initial configuration for the nonlinear analysis. To consider deformation-dependent loading from currents and hydrostatic pressure, an improved version of the direct iteration method is applied using a conventional inner iteration approach with constant external load and an outer iteration to ensure that the residual forces resulting from the deformation-dependent loading are equilibrated. Both tow vessels and towlines are added to the static analysis model to form a dynamic analysis model with the initial stiffness method being employed during a direct integration procedure. The dynamic analysis is done in the time domain for regular waves with either the Morison equation or Lighthill's inertia loading formulation. The results from this complete FEM are verified by comparison with those from another finite element package (ABAQUS) for simplified models. The results show that towed pipelines are highly influenced by external loads because their submerged weight must be kept very small. Therefore, an accurate application of deformation-dependent loading and hydrostatic pressure force is essential during the static analysis. In dynamic cases, high lateral responses are concentrated around the ends of the pipeline due to their proximity to the water surface and the soft constraints from towlines. The dynamic bending moment is mainly influenced by wave forces on the pipeline and increases rapidly as the pipeline approaches the water surface. The axial interaction between tow vessels and a pipeline is highly influenced by the property of the towline. Therefore, too stiff towlines may induce large dynamic axial force and give transient compressive axial force. The Morison formulation gives slightly less inertia force and response than that obtained from Lighthill's approach. Considering this slight difference and the uncertainties in wave kinematics and drag forces, it can be said that the Morison formulation still provides reasonable results for towed pipelines.
... So let's first examine how many new items may occur when use the traditiona l approach to solve projectile problems with the example below. The solution to this problem is taken from the solution manual provided by the publisher [3]. Without an explicit note, all examples used in this paper use a Cartesian coordinate system with the origin at the initial position and upward as the positive -direction. ...
... Consider for example two impact points, 1 and 2, located on a rigid body. Using classical rigid-body dynamics [77], the difference between the velocities of these two impact points is found as ...
This work proposes an analytic method for resolving planar multi-point indeterminate impact problems for rigid-body systems. An event-based approach is used to detect impact events, and constraints consistent with the rigid-body assumption are used to resolve the indeterminacy associated with multi-point impact analysis. The work-energy relation is utilized to determine post-impact velocities based on an energetic coefficient of restitution to model energy dissipation, thereby yielding an energetically consistent set of post-impact velocities based on Stronge’s energetic coefficient of restitution for the treatment of rigid impacts. The effect of stick–slip transition is analyzed based on Coulomb friction. This paper also discusses the transition from impact to contact. This analysis is essential for considering the rocking block problem that is used as an example herein. The predictions of the model for the rocking block problem are compared to experimental results published in the literature. An example of a planar ball undergoing two-point impact is also presented.
... Comparison between total soils bearing capacity [6] with total human pressure force has shown that minimum size that suitable to use for the based tool is 15 times 10 inch. Meanwhile, for pusher tools, shear force diagram, shear force formula [5], [7], and first class lever formula [2] were used to obtain the suitable minimum size for the tools. From this formula, we obtained 30mm diameter and 31 inch long for the pusher minimum size. ...
Dynamic probing is a continuous soil investigation technique, which is one of the simplest soil penetration test. It basically consist of repeatedly driving a metal tipped probe into the ground using a drop weight of fixed mass and travel. Testing was carried out continuously from ground level to the final penetration depth. Once the soil investigation work done, it is difficult to pull out the probe rod from the ground, due to strong soil structure grip against probe cone and prevent the probe rod out from the ground. Thus, in this case, a tool named Extracting Probe was created to assist in the process of retracting the probe rod from the ground. In addition, Extracting Probe also can reduce the time to extract the probe rod from the ground compare with the conventional method. At the same time, it also can reduce manpower cost because only one worker involve to handle this tool compare with conventional method used two or more workers. From experiment that have been done we found that the time difference between conventional tools and extracting probe is significant, average time difference is 155 minutes. In addition the extracting probe can reduce manpower usage, and also labour cost for operating the tool. With all these advantages makes this tool has the potential to be marketed.
... This equation has some extra terms compared to previous work, 8 because the gyroscopic and angular momentum effects of the rotors are included. Now a Taylor expansion can be applied to equation 8 resulting in equation 13. ...
... The center of gravity is located in the origin of the axis system and the distance to each of the rotors along the X axis is given by l and along the Y axis by b. If the angular velocity vector of the vehicle is denoted by Ω = [p, q, r] T and its derivative byΩ, the rotational dynamics are given by Euler's equation of motion [13], more specifically the one that describes rotation. If we consider the body axis system as our coordinate system we get Eq. ...
Incremental nonlinear dynamic inversion is a sensor-based control approach that promises to provide high-performance nonlinear control without requiring a detailed model of the controlled vehicle. In the context of attitude control of micro air vehicles, incremental nonlinear dynamic inversion only uses a control effectiveness model and uses estimates of the angular accelerations to replace the rest of the model. This paper provides solutions for two major challenges of incremental nonlinear dynamic inversion control: how to deal with measurement and actuator delays, and how to deal with a changing control effectiveness. The main contributions of this article are 1) a proposed method to correctly take into account the delays occurring when deriving angular accelerations from angular rate measurements; 2) the introduction of adaptive incremental nonlinear dynamic inversion, which can estimate the control effectiveness online, eliminating the need for manual parameter estimation or tuning; and 3) the incorporation of the momentum of the propellers in the controller. This controller is suitable for vehicles that experience a different control effectiveness across their flight envelope. Furthermore, this approach requires only very coarse knowledge of model parameters in advance. Real-world experiments show the high performance, disturbance rejection, and adaptiveness properties.
Read More: http://arc.aiaa.org/doi/abs/10.2514/1.G001490
... However, many simplifications can be made, especially concerning rotations. The information in Section 2.1.1 is retrieved from Bedford et al. [2008] while the main sources of Section 2.1.2 is Servin [2010] and Millington [2010] unless otherwise stated. ...
Games are becoming increasingly realistic. Real-time physics simulation were almost unimaginable just decades ago but are now a vital part of many games. Even dynamic physics simulation e.g. interactive fluids has found a place in game development. This paper investigates and evaluates three methods of simulating fluids with the purpose of testing these in a 2d game environment. These methods are all Lagrangian i.e. particlebased, Sph methods, and chosen because of their differences but also their importance to the field of interactive fluid simulation. In order to integrate the methods, they will be implemented with use of the 2d mechanics engine Box2d which is a popular choice in 2d game development. To evaluate the methods, water is the fluid of choice. Water is the most abundant of fluids and is bound to be found in most games containing fluids. Water is almost incompressible, therefore, the methods ability to withhold incompressibility is tested. Also, the convergence properties of kinetic energy is tested in order to find out more about stability. The results showed that the method based on Müller et al. [2003] demanded a prohibitively
Research into head impacts, in order to understand brain affectation, has been considered of great importance since ancient times. In this paper it is shown, from the biomechanics point of view, the mechanical ability of the skull bone structure to support a high velocity impact (specifically 100 m/s) with the application of numerical computer tools. An skull’s numerical model was developed from a patient’s tomography scan to achieve a nearness to reality evaluation. For the development of this research, it was necessary to include the bases of biomechanics, particularly impact biomechanics, the principle of impulse and momentum from classical dynamics. The elastic and plastic behavior of materials in general is explained, in order to achieve a better understanding of the behavior of the osseous material that is exposed to a sudden load. Having a prior knowledge, the idealized shell structure was used to model the mechanical structure of the human skull. The numerical model of the skull was developed by a three steps shell idealization; A first idealization considered a perfectly plastic material. Next, it was considered an elastic perfectly plastic material. Finally, the model consisted of a rigid perfectly plastic material. For the three models considerations on the energy dynamics and impulsive loads were discussed. Knowing the mechanical part of the study, it was necessary then to complement the theoretical framework with knowledge regarding the human skull anatomy. Within the core of the present study, the numerical analysis methods are described, along with the methodology for modelling the skull. Impact loads were calculated for two different loading cases; frontal and lateral. Results were obtained for total displacements and maximum principal stresses. Additionally, energy analyses were performed for each study including total energy, kinetic energy, internal energy and plastic work.KeywordsImpact loadingFinite element analysisSkullEnergy evaluation
Hoy en día el ahorro de energía eléctrica es un elemento fundamental de las políticas públicas para el cuidado de los recursos energéticos no renovables, la pluralización energética, la defensa del medio ambiente, el incremento de productividad, y la competencia y el ahorro económico familiar. Dentro
de esto se ha movilizado el desarrollo de nuevos sistemas que coadyuven a lograr realizar dicho ahorro, uno de estos es el uso del diagnóstico energético, y con ello los instrumentos digitales que lo soporten. Este trabajo presenta un sistema desarrollado en código abierto en la plataforma NetBeans, que ayuda
en la contabilización y cálculo de cargas eléctricas de forma mensual para que realice diagnósticos energéticos residenciales, preocupándose específicamente de las medidas que se deben tomar una vez realizado dicho diagnostico residencial y no en lo secundario que será hacer conteo y cálculo, que se puede realizar con el sistema, de esto se presenta el desarrollo del código pasando por una plantilla
realizada en una hoja de cálculo, puesto a punto por medio de diversas pruebas, las cuales fueron realizar el conteo de cargas en dos residencias, evaluando así su funcionamiento, el desempeño de la herramienta cumple con lo requerido, jerarquiza las cargas de acuerdo a su localización y se obtiene un
cálculo correcto en kWh/mes.
In simulations of granular mixtures with real-shaped particles, fine particles are mostly simplified to spheres to improve computational efficiency. The basis for simplification is that the shape effect of fine particles is negligible when compared with coarse particles. However, existing simplifications are usually arbitrary without considering the size ratio between coarse and fine particles, causing fine shapes to be ignored unreasonably. Therefore, what size ratio can simplify the shape of fine particles? To solve this problem, the real model with real-shaped fines and the simplified model with simplified-shaped fines were established to explore the difference between the two models affected by size ratios. The real-shaped particles were constructed based on representative sand and gravel grains, and contact parameters were calibrated by a series of physical tests. The simulation results show that the permanent deformation of real models can be reproduced by simplified models with a large SR, while the resilient deformation cannot be reproduced no matter what SR is. Although there are some differences between the two models at macro- and mesoscales, the fine shapes can be simplified under the condition of SR ≥ 11, the computational efficiency of which can be greatly improved compared with real models. This study aims to provide a quantitative basis for the shape simplification of fine particles from the perspective of simulation accuracy and computational efficiency.
Swimming and flying animals across diverse taxa rely on the ability to maneuver for feeding1-6, escaping predation7-9, finding mates10-13, and navigating complex physical environments14-16. As such, the evolutionary success of these animals depends in part on propulsor designs that can efficiently change the orientation of the body during locomotion. We show that across 292 species of swimming and flying animals—including birds, fish, cetaceans, bats, insects, and sea turtles—the location of lateral maneuvering propulsors is tightly constrained at a location approximately 1/3 of the body length from the anterior end. A theoretical model for optimal turning is consistent with these observations, and it makes a further prediction of a non-trivial relationship between propulsor placement and body center of mass. That prediction is also confirmed by an additional, detailed morphometric analysis of 38 species. The present observations are notable in that a simple physical model appears sufficient to explain observed morphological diversity, and it suggests that propulsor placement in swimming and flying metazoans favors structural solutions that are adapted to enable efficient maneuvering in fluids.
This chapter presents a new method for analysing and modeling the flow in the pipe networks. Furthermore, new theorems are proposed that give a way to test the observability and controllability of a given system.
Engineering educators express concern that undergraduate engineering students solve problems procedurally without the necessary conceptual understanding. While research in engineering dynamics has focused on using technology to improve student performance, this article focuses on using representations for modelling problem solving in the lecture. This is an in-depth, qualitative case study of the pedagogy of an experienced lecturer in a dynamics course in a professional undergraduate engineering programme at a South African university. Social semiotic multimodality is used to analyse the lecturer’s purposeful, contextual language choices. The analysis shows how the lecturer creates – using the available space, media and time of the lecture – multiple opportunities for students to access the valued practice of using a complex dynamics concept meaningfully in a heuristic to problem solve as a student and engineer-in-training. The findings from the case study surface points of engagement on problem solving pedagogy in the lecture space.
The mathematical modelling and simulation of natural phenomena is considered the art of science. In this investigation, we review the modelling and simulation of dynamic system from the very beginning steps to the complicated and more advanced systems. This chapter may serve as a concise supplementary learning material for any course related to dynamic systems, modelling and simulations, deterministic dynamics, system of linear ordinary differential equations, etc. It will present guidelines and recommendations for modelling of various engineering systems. The basic concepts are illustrated with selection of several illustrative case studies with detailed diagrams and associate MATLAB scripts. This work will show that, with use of modern simulation tools and computer environments, modelling and simulation process of complex systems is structurally doable. The wide spectrum of the presented examples in mechanical, aerospace, civil, electrical, environmental and other engineering areas makes this work useful for a very wide audience, including engineers, scientists, students and enthusiasts of science and technology.
In the present work, a new design of power screw jack with ball bearing is presented. The Acme thread or trapezoidal thread was used which is consider the best type, since it gives high power transmission, also its simple in manufacturing compared with the other types. A computer program is developed in Quick basic language to calculates the dimensions of all parts for power screw jack (depend on the given load and materials). Revit MEP 2008 software program was used to design of power screw jack. The validity of results is verified and shows that there is a good agreement between the results of the present solution and the correlation related to it.
This paper presents advanced techniques used to reconstruct a motor vehicle accident involving a fully loaded tractor-trailer and school bus with 30 young students. The accident investigation included analysis of the physical evidence using photogrammetry and high-definition laser scanning, application of engine control module (ECM) and global positioning system (GPS) data, and analyzing onboard video footage from the bus. Momentum-based crash simulation software (PC-Crash) was used to simulate the accident. The simulation data was compared with National Transportation Safety Board (NTSB) data and with the onboard bus video footage. Further, rigid-body kinematic equations were used to determine occupant kinematics (velocities) and dynamics (accelerations). Multiple graphics are used to demonstrate the accident reconstruction and occupant kinematics and dynamics.
Adaptive Front-Lighting System (AFLS) is a system which assists driver's field of vision by automatically controlling its brightness and illumination angle to adapt various driving conditions such as climate, traffic, road changes and so forth. This paper aims to propose novel model-based PID gain design method to improve the performances of Dynamic Bending Light (DBL) module that change horizontal angle of a system by applying Brent-Dekker algorithm that finds the root of nonlinear function and implementing Nelder-Mead simplex algorithm to the system reduction process. Along with the linear system model-based control theory, motor dynamics were modeled with frequency response. Validation of the prototype resulted in having less than 3 % error from the simulation, where position initialization and the real-time status monitoring function is available due to the closed loop control which enables over 3 times faster response than the conventional open-loop system. © 2018, The Korean Society of Automotive Engineers and Springer-Verlag GmbH Germany, part of Springer Nature.
This paper presents a review on student misconceptions of general plane motion (GPM), one of the most difficult yet important concepts in engineering dynamics and a foundational course that civil and mechanical engineering students are required to take in their undergraduate study. The paper discusses student misconceptions of GPM reported in the literature. Five reasons that cause student misconceptions of GPM are proposed and analyzed: lack of fundamental understanding of basic concepts, basic mathematics skills, knowledge transfer skills, spatial skills, and hand-sketching skills. Some remedial strategies for correcting student misconceptions of GPM are also discussed.
Today, greater emphasis is being placed on a component’s ‘machinability’ , but this term is an ambiguous one, having a variety of different meanings, depending upon the production engineer’s requirements. In fact, the machinability expression does not have an authoritative definition, despite the fact that it has been used for decades. In 1938, Ernst in his book on the ‘Physics of Metal Cutting’ , defined machinability in the following manner: ‘As a complex physical property of a metal involving:
• True machinability, a function of the tensile strength,
• Finishability, or ease of obtaining a good finish,
• Abrasiveness, or the abrasion undergone by the tool during cutting.’
This work is about planar rigid-body kinematics and, in particular, the principle of the instantaneous center of rotation (IC). Using a computer simulated approach, a workflow is presented that results in a visual representation of the locus of the IC, based on particle imagevelocimetry(PIV). Here, a small number of digital animations of textured objects are created with multibody dynamicssoftware, and later imported in PIVsoftware to extract the velocity field (magnitude and direction) of objects moving within a plane. We believe the workflow presented may help learners improve their understanding of the concept of the IC, thus enhancing their knowledge of rigid body kinematics.
Mechanics is a branch of physics that is concerned with the motion and deformation of bodies that are acted on by mechanical disturbances called forces. Mechanics is the oldest of all physical sciences, dating back to the times of Archimedes (287–212 BC). Galileo (1564–1642) and Newton (1642–1727) were the most prominent contributors to this field. Galileo made the first fundamental analyses and experiments in dynamics, and Newton formulated the laws of motion and gravity.
In which we find that a rigid body has six degrees of freedom, learn how to describe the orientation of a rigid body in terms of Euler angles, define inertial and body coordinates and find the Euler-Lagrange equations for a single rigid body…
One of the major problems facing solar energy systems is the efficiency as the sun moves on the celestial sphere. The solar tracker is a device that tracks the position of the sun and set the solar energy conversion system focusing normal to the sunbeams. This paper presents a design focused on harnessing the maximum available solar radiation using dual-axis tracking mechanism. The tracking mechanism is designed to focus the solar conversion system perpendicular to the rays of the sun (sunbeams) at all time of the day relative to the position of the sun in the sky dome. The driving mechanism for the motion are two direct current linear actuators of 12V each, which one of the actuators tracks the east to west motion of the sun while the second linear actuator tracks the seasonal motion/daily altitude of the sun. The main task of the tracking mechanism is to focus solar energy conversion system perpendicular to the sun to maximize the absorbed solar radiation and minimize the energy consumption for tracking system. The movement of the sun on the celestial sphere was the bases of the tracking mechanisms angles design. The azimuth angle at sunrise and sunset for the year was calculated and the maximum value for both situations was used for the design of the east to west tracking of the sun at Universiti Kebangsaan Malaysia – 3 oN, 101.8 oE. For the north to south tracking process which is related to the altitude, the altitude angles was calculated for a period of one year and the maximum value was used to decide the design for the north-south tracking on the second axis of the tracker. Analytical study of clear sky solar radiation at the location for the tracking system and 15o fixed solar system was conducted, it was found that the performance of the solar system increased by over 20% assuming the tracker is 80% efficient.
In the evaluation of crashworthiness of roadside safety features, full-scale impact tests are generally required according to the established test protocols. Since the tests are expensive, it is useful to predict the crash responses of a vehicle from the other size test vehicles. This concept was used in the Manual for Assessing Safety Hardware (MASH) of American Association of State Highway and Transportation Officials (AASHTO) to decide whether mid-size vehicle tests are necessary for an attenuator system design in addition to the small car and pickup truck tests. The general applicability of this procedure in the estimation of impact responses of one vehicle from the tested vehicle is studied using the crash test data of 11 crash cushions tested by the Korea Expressway Corporation Research Institute (KECRI). Each of the 11 crash cushions has two sets of test data from 1.3 and 0.9 ton vehicles tested with an impact speed of 80 or 100 km/h depending on the class of each system. Using the procedure, for each of the 11 systems, 1.3 ton crash data were transformed into the 0.9 ton crash data, then the estimated 0.9 ton crash data were compared with the 0.9 ton test data. It was found that the crash data predictions deviated from the test data, leading to overly conservative estimation of safety risk factors. The procedure was also found inapplicable in estimating crash data of a large vehicle (1.3 ton) from the test data of a small vehicle (0.9 ton). New procedure to estimate the crash data of a vehicle from the test vehicle regardless of their relative mass size was developed and the method was validated using the crash test data of 11 different crash cushions. In the new procedure developed, pivoting the velocity trace of test vehicle was utilised. The new procedure showed favourable results in estimating the crash data of a small vehicle (0.9 ton) from the crash data of a large test vehicle (1.3 ton). It can also be applied in reverse case estimation where the predicting vehicle (1.3 ton) was larger than the test vehicle (0.9 ton).
This paper presents optimization-based dynamic three-dimensional (3D) human running prediction. A predictive dynamics method is used to formulate the running problem, and normal running is formulated as a symmetric and cyclic motion. In addition, a slow jog along curved paths has been formulated. It is a non-symmetric running motion, so a stride formulation has been used. The dynamic effort and impulse are used as the performance measure, and the upper body yawing moment is also included in the performance measure. The joint angle profiles and joint torque profiles are calculated for the full-body human model, and the ground reaction force is determined. The effects of foot location and orientation on the running motion prediction are simulated and studied. Simulation results from this methodology show good correlation with experimental data obtained from human subjects.
ResearchGate has not been able to resolve any references for this publication.