Rigid Body

Virtual reality applications refer to the use of com- puters to simulate a physical environment in such a way that humans can readily visualize, explore, and interact with "objects" in this environment. The design of virtual scenes requires realistic physically based simulation algorithms and in particular effi- cient collision detection routines. Collision detection prevent penetrations between objects. This paper presents an overview of the collision detection procedures for rigid bodies. It divides those procedures in two families that form a general hybrid collision detection algorithm. The first family is used in the first phase known as broad phase that roughly detects collision. The second family is used in the second one known as narrow phase that exactly detects if collision occurs.

A method is proposed for deriving dynamical equations for systems with both rigid and flexible components. During the derivation, each flexible component of the system is represented by a ``surrogate element'''' which captures the response characteristics of that component and is easy to mathematically manipulate. The derivation proceeds essentially as if each surrogate element were a rigid body. Application of an extended form of Lagrange''s equation yields a set of simultaneous differential equations which can then be transformed to be the exact, partial differential equations for the original flexible system. This method''s use facilitates equation generation either by an analyst or through application of software-based symbolic manipulation.

The authors examine some issues in the transfer function modeling of a single flexible link. Using the assumed-modes approach, it is possible to find the transfer function between the torque input and the net tip deflection. It is shown that when the number of modes is increased for more accurate modeling, the relative degree of the transfer function becomes ill-defined.

The network model approach for rigid and multi-rigid body systems developed recently [1,2] can also be used conveniently in formulating system equations or equations of motion of three-dimensional mechanical systems of interconnected rigid bodies. In this article, this method is further elaborated for establishing only the kinematics of spatial robotic bevel-gear trains. However the dynamic analysis of such systems using the same method is also possible and will be taken up in a future publication.

Abstract: In this article, we review some of the theoretical solutions used to describe swirl dominated flows in both unidirectional and bidirectional flow orientations. This short survey starts with the Rankine vortex and culminates in the presentation of a compressible solution of the bidirectional vortex. After classifying representative swirl motions as external or internal depending on physical boundary conditions, their commonalities are identified along with their relevance to either geophysical or industrial applications. We also identify ...

Macromolecular modeling and design are increasingly useful in basic research, biotechnology, and teaching. However, the absence of a user-friendly modeling framework that provides access to a wide range of modeling capabilities is hampering the wider adoption of computational methods by non-experts. RosettaScripts is an XML-like language for specifying modeling tasks in the Rosetta framework. RosettaScripts provides access to protocol-level functionalities, such as rigid-body docking and sequence redesign, and allows fast testing and deployment of complex protocols without need for modifying or recompiling the underlying C++ code. We illustrate these capabilities with RosettaScripts protocols for the stabilization of proteins, the generation of computationally constrained libraries for experimental selection of higher-affinity binding proteins, loop remodeling, small-molecule ligand docking, design of ligand-binding proteins, and specificity redesign in DNA-binding proteins.

Abstract: In this paper, we investigate the control and reduced-order synchronization in a new third-order chaotic system derived from the rigid body dynamics. A recursive backstepping control is designed based on Lyapunov stability theory to eliminate the chaotic behaviour. To ...

A significant portion of the Earth's surface consists of zones of diffuse deformation. The interior regions of these diffuse zones of deformation move at distinctly different velocities from that of adjacent plates, and, because of their complexities, have been ignored in previous no-net-rotation (NNR) models (e.g., NNR-NUVEL1A). We have calculated a new NNR model from a continuous velocity field that incorporates both rigid plate motion and velocity gradients within plate boundary zones. The velocity field is obtained through a bi-cubic Bessel interpolation of almost 3000 geodetic velocities and strain rates inferred from Quaternary faults. The geodetic velocities are taken from about 50 different, mainly published, studies. For each study we have not adopted the original reference frame. Instead, we have solved for a rigid body rotation for each study that rotate the vectors of each study into a model reference frame in the process of satisfying a least-squares fit between model and observed velocities and model and observed strain rates. When compared with earlier NNR models we find significantly different angular velocities for many plates in our model. Differences between the NNR model presented here and earlier NNR models can be attributed to both the effect of including velocity gradients in diffuse plate boundary zones, as well as actual differences between geodetically derived, present-day, surface motions and geologic estimates. We find that for the Indian, Arabian, Nazca, Cocos, Philippine Sea, and the Caribbean plate the differences between our model and the NNR-NUVEL1A model are mainly due to differences between geodetic and geologic plate velocities. For the Eurasian plate the discrepancy that we find between our result and NNR-NUVEL1A model can not only be ascribed to the difference between geodetic and geologic velocities, but also to the significant effect of including plate boundary zones. The significantly different NNR rotation vectors that we find for the majority of plates suggests that caution is warranted when using the NNR-NUVEL1A model to change from an ITRF to a tectonic reference frame. Our new NNR results indicate that such practice may result in significant discrepancies in crustal velocities with respect to the chosen reference plate. Finally, similar to earlier NNR models, we find a significant difference between the NNR velocities and velocities with respect to hotspots.

This work addresses the construction of a four- wheel, nonlinear vehicle dynamic bond graph model and its implementation in the 20sim modeling and simulation environment. Nonlinear effects arising from the coupling of vertical, longitudinal and lateral vehicle dynamics, as well as geometric nonlinearities coming from the suspension system are taken into account. Transmission and (a simplified) engine models are also

In this paper, we investigate power flow in compliant mechanisms that are employed in dynamic applications. More specifically, we identify various elements of the energy storage and transfer between the input, external load, and strain energy stored within the compliant transmission. The goal is to design compliant mechanisms for dynamic applications by exploiting the inherent energy storage capability of compliant mechanisms in the most effective manner. We present a detailed case study on a flapping mechanism, in which we compare the peak input power requirement in a rigid-body mechanism with attached springs versus a distributed compliant mechanism. Through this case study, we present two approaches: (1) generative-load exploitation and (2) reactance cancellation, to describe the role of stored elastic energy in reducing the peak input power requirement. We propose a compliant flapping mechanism and its evaluation using nonlinear transient analysis. The input power needed to driv...

Mechanics: Oldest of the Physical Sciences: Archimedes (287-212 BC): Principles of Lever and Buoyancy. Mechanics is a branch of the physical sciences that is concerned with the state of rest or motion of bodies subjected to the action of forces.
Statics: Deals with equilibrium of bodies under action of forces (bodies may be either at rest or move with a constant velocity).
Dynamics: Deals with motion of bodies (accelerated motion)

This work presents a comparative study of two different control strategies for a flexible single-link manipulator. The dynamic model of the flexible manipulator involves modeling the rotational base and the flexible link as rigid bodies using the Euler Lagrange's method. The resulting system has one Degree-Of-Freedom (one DOF) and it provide freedom to increase the degree as well. Two types of regulators are studied, the State-Regulator using Pole Placement, and the Linear-Quadratic regulator (LQR). The LQR is obtained by resolving the Ricatti equation, in this work, we apply and compare two strategies to control the tip of the flexible link: state-feedback and linear quadratic regulator. These regulators are designed to reduce tip vibrations and increase system stability due to the flexibility of the arm.

In this paper the dynamic analysis of the Macpherson strut motor-vehicle suspension system is presented. The equations of motion are formulated using a two-step transformation. Initially, the equations of motion are derived for a dynamically equivalent constrained system of particles that replaces the rigid bodies by applying Newton’s second law. The equations of motion are then transformed to a reduced set in terms of the relative joint variables. Use of both Cartesian and joint variables produces an efficient set of equations without loss of generality. For open chains, this process automatically eliminates all of the non-working constraint forces and leads to an efficient solution and integration of the equations of motion. For closed loops, suitable joints should be cut and few cut-joints constraint equations should be included for each closed chain. The chosen suspension includes open and closed loops with quarter-car model. The results of the simulation indicate the simplicity and generality of the dynamic formulation.