Dynamics of Multibody Systems With Spherical Clearance Joints

This work deals with a methodology to assess the influence of the spherical clearance joints in spatial multibody systems. The methodology is based on the Cartesian coordinates, being the dynamics of the joint elements modeled as impacting bodies and controlled by contact forces. The impacts and contacts are described by a continuous contact force model that accounts for geometric and mechanical characteristics of the contacting surfaces. The contact force is evaluated as function of the elastic pseudo-penetration between the impacting bodies, coupled with a nonlinear viscous-elastic factor representing the energy dissipation during the impact process. A spatial four bar mechanism is used as an illustrative example and some numerical results are presented, being the efficiency of the developed methodology discussed in the process of their presentation. The results obtained show that the inclusion of clearance joints in the modelization of spatial multibody systems significantly influences the prediction of components’ position and drastically increases the peaks in acceleration and reaction moments at the joints. Moreover, the system’s response clearly tends to be nonperiodic when a clearance joint is included in the simulation.

Modeling the Climber Fall Arrest Dynamics

Sports and mountaineering activities are becoming more and more popular. Equipment constructors seek to develop products and devices that are easy to use and that take into account all safety recommendations. PETZL and INSA have collaborated to develop a model for the simulation of displacements and efforts involved during the fall of a climber in the “safety chain”. The model is based on the classical equations of motion, in which climber and belayer are considered as rigid masses, while the rope is considered as a series of non-linear stiffness passing through several devices as brakes and runners. The main goal is to predict the forces in the rope and on the return anchor at the first rebound of the fall. Experiments were first performed in order to observe and determine the dynamic characteristics of the rope, and then to validate results stemming from simulations. Several fall configurations are simulated, and the model performs satisfactorily. It also provides a close approximation of the phenomena observed experimentally. The model enables the assessment of the existing equipments and the improved design of the future one.

Dynamics of a Two-DOF Parallel Pointing Mechanism

This paper presents kinematic and dynamic analyses of a two-degree-of-freedom pointing parallel mechanism. The mechanism consists of a moving platform, connected to a fixed platform by two legs of type PUS (prismatic-universal-spherical). At first a simplified kinematic model of the pointing mechanism is introduced. Based on this proposed model, the dynamics equations of the system using the Natural Orthogonal Complement method are developed. Numerical examples of the inverse dynamics results are presented by numerical simulation.

High Performance Low Cost Implementation of FPGA-Based Fractional-Order Operators

Hardware implementation of fractional-order differentiators and integrators requires careful consideration of issues of system quality, hardware cost, and speed. This paper proposes using field programmable gate arrays (FPGAs) to implement fractional-order systems, and demonstrates the advantages that FPGAs provide. As an illustration, the fundamental operators to a real power is approximated via the binomial expansion of the backward difference. The resulting high-order FIR filter is implemented in a pipelined multiplierless architecture on a low-cost Spartan-3 FPGA. Unlike common digital implementations in which all filter coefficients have the same word length, this approach exploits variable word length for each coefficient. Our system requires twenty percent less hardware than a system of comparable quality generated by Xilinx’s System Generator on its most area-efficient multiplierless setting. The work shows an effective way to implement a high quality, high throughput approximation to a fractional-order system, while maintaining less cost than traditional FPGA-based designs.

Contact Modeling Technique of a Flexible Piston and Cylinder Using Modal Synthesis Method

In this paper, contact modeling technique and dynamics analysis of piston and cylinder system are presented by using modal synthesis method. It is very important to select mode shapes representing a global or local behavior of a flexible body due to a specified loading condition. This paper proposes a technique to generate the static correction modes which are nicely representing a motion by a contact force between a piston and cylinder. First normal modes of piston and cylinder under a boundary condition are computed, and then static correction modes due to a contact force applied at contacted nodes are added to the normal modes. Also, this paper proposes an efficient dynamics analysis process while changing the shape of the piston and cylinder. In optimization process or design study, their geometric data can be changed a bit. The slight changes of their contact surfaces make a high variation of the magnitude of a contact force, and it can yield the different dynamic behavior of an engine system. But, since the variations of the normal and correction modes are very small, the re-computation of their normal and correction modes due to the change of contact surfaces can be useless. Until now, whenever their contact surfaces are changed at a design cycle, the modes have been recomputed. Thus, most engineers in industries have been spent many times in very tedious and inefficient design process. In this paper, the normal and correction modes from the basic geometry of the piston and cylinder are computed. If the geometry shape is changed, nodal positions of the original modal model are newly calculated from an interpolation method and changed geometry data. And then the updated nodes are used to compute a precise contact force. The proposed methods illustrated in this investigation have good agreement with results of a nodal synthesis technique and proved that it is very efficient design method.

Differential-Geometric Methods in Multibody Dynamics and Control

This paper presents a differential-geometric approach to the multibody system dynamics regarded as a point dynamics in a n-dimensional configuration space Rn. This configuration space becomes a Riemannian space Vn the metric of which is defined by the kinetic energy of the multibody system (MBS). Hence, all concepts and statements of the Riemannian geometry can be used to study the dynamics of MBS. One of the key points is to set up the non-linear Lagrangian motion equations of tree-like MBS as well as of constrained mechanical systems, the perturbed equations of motion, and the motion equations of hybrid MBS in a derivative-free manner. Based on this approach transformation properties can be investigated for application in real-time simulation, control theory, Hamilton mechanics, the construction of first integrals, stability etc. Finally, a general Lyapunov-stable force control law for underactuated systems is given that demonstrates the power of the approach in high-performance sports applications.

The “Fractional” Kinetic Equations and General Theory of Dielectric Relaxation

Based on the Mori-Zwanzig formalism it becomes possible to suggest a general decoupling procedure, which reduces a wide set of various micromotions distributed over a self-similar structure to a few collective/reduced motions describing the relaxation/exchange behavior of a complex system in the mesoscale region. The frequency dependence of the reduced collective motion contains real and pair of complex-conjugate power-law exponents in the frequency domain and explains naturally the “universal response” (UR) phenomenon discovered by A. Jonscher in a wide class of heterogeneous materials. This strict mathematical result allows in developing a consistent and general theory of dielectric relaxation that can describe wide set of dielectric spectroscopy (DS) data measured in some frequency/temperature range in many heterogeneous materials. Based on this result it becomes possible also to suggest a new set of two-pole elements, which generalizes the conventional RLC-elements and can constitute the basis of new theory of the linear electric circuits.

On the Dynamic Isotropy of Mechanisms With Two Degrees of Freedom

The comparison of mechanisms with different topology or with different geometry, but with the same topology, is a necessary operation during the design of a machine sized for a given task. Therefore, tools that evaluate the dynamic performances of a mechanism are welcomed. This paper deals with the dynamic isotropy of 2-dof mechanisms starting from the definition introduced in a previous paper. In particular, starting from the condition that identifies the dynamically isotropic configurations, it shows that, provided some special cases are not considered, 2-dof mechanisms have at most a finite number of isotropic configurations. Moreover, it shows that, provided the dynamically isotropic configurations are excluded, the geometric locus of the configuration space that collects the points associated to configurations with the same dynamic isotropy is constituted by closed curves. This results will allow the classification of 2-dof mechanisms from the dynamic-isotropy point of view, and the definition of some methodologies for the characterization of the dynamic isotropy of these mechanisms. Finally, examples of applications of the obtained results will be given.

A Dynamical Model for Studying the Stability of Thermo-Solutal Convection Under the Effect of Vertical Vibration

This paper concerns the thermal stability analysis of porous layer saturated by a binary fluid under the influence of mechanical vibration. The linear stability analysis of this thermal system leads us to study the following damped coupled Mathieu equations: BH¨+B(π2+k2)+1H˙+(π2+k2)−k2k2+π2RaT(1+Rsinω*t*)H=k2k2+π2(NRaT)(1+Rsinω*t*)Fε*BF¨+Bπ2+k2Le+ε*F˙+π2+k2Le−k2k2+π2NRaT(1+Rsinω*t*)F=k2k2+π2RaT(1+Rsinω*t*)H where RaT is thermal Rayleigh number, R is acceleration ratio (bω2/g), Le is the Lewis number, k is the dimensionless wave-number, ε* is normalized porosity and N is the buoyancy ratio (H and F are perturbations of temperature and concentration fields). In the follow up, the non-linear behavior of the problem is studied via a generalization of the Lorenz model (five coupled non-linear differential equations with periodic coefficients). In the presence or absence of gravity, the stability limit for the onset of stationary as well as Hopf bifurcations is determined.

Distribution of Sub and Super Harmonic Solution of Mathieu Equation Within Stable Zones

The third stable region of the Mathieu stability chart, surrounded by one π-transition and one 2π-transition curve is investigated. It is known that the solution of Mathieu equation is either periodic or quasi-periodic when its parameters are within stable regions. Periodic responses occur when they are on a “splitting curve”. Splitting curves are within stable regions and are corresponding to coexisting of periodic curves where an instability tongue closes. Distributions of sub and super-harmonics, as well as quasi-periodic solutions are analyzed using power spectral density method.