Velocity Of Rigid Body Research Articles

Fast frictional dynamics for rigid bodies

We describe an efficient algorithm for the simulation of large sets of non-convex rigid bodies. The algorithm finds a simultaneous solution for a multi-body system that is linear in the total number of contacts detected in each iteration. We employ a novel contact model that uses mass, location, and velocity information from all contacts, at the moment of maximum compression, to constrain rigid body velocities. We also develop a new friction model in the configuration space of rigid bodies. These models are used to compute the feasible velocity and the frictional response of each body. Implementation is simple and leads to a fast rigid body simulator that computes steps on the order of seconds for simulations involving over one thousand non-convex objects in high contact configurations.

Inertial phase separation in rotating self-gravitating media

The centrifugal separation of foreign inclusions (particles) in a rotating spherical volume of a self-gravitating medium is considered in the hydrodynamic approximation. Using the full Lagrangian approach, the particle trajectories and radial concentration profiles are studied for a rigid-body velocity distribution in the carrier phase. The regimes of continuum and free-molecular flow around the particles are considered. The cases of a “heavy” (with density greater than that of the carrier phase and traveling toward the center) and a “light-weight” (traveling toward the periphery) admixture are investigated. Analytical and numerical solutions corresponding to steady-state spherically symmetric boundary conditions for the dispersed phase are found. It is shown that the presence of rotation may result in a significant angular anisotropy of the radial particle concentration distributions and, in particular, in the formation of ring-shaped accumulation zones of “heavy” inclusions in the equatorial plane. The solutions obtained can be used to explain the mechanisms of onset of density nonuniformities in planet cores, the formation of planetary systems from gas-particle clouds, and the behavior of aerosol particles in atmospheric vortices.

Robots and Screw Theory: Applications of Kinematics and Statics to Robotics

<i>Robots and Screw Theory: Applications of Kinematics and Statics to Robotics</i>

Kinematic Synthesis of Adjustable RSSR-SS Mechanisms for Multi-Phase Finite and Multiply Separated Positions

This paper presents a new technique for synthesizing RSSR-SS mechanisms to achieve phases of rigid body positions, velocities and accelerations using the same hardware. This work considers two-phase fixed pivot adjustment problems with fixed crank and follower lengths. By specifying the R-S link joint axes, the constant length condition becomes the only design constraint for these links. The prescribed finite and multiply separated positions are then incorporated in the link constraint equations with respect to the prescribed coordinate frame for each link and the RSSR-SS mechanism joint variables and driving link parameters are calculated.

KINEMATIC SYNTHESIS OF RRSC MECHANISMS FOR MULTI-PHASE FINITE AND MULTIPLY SEPARATED POSITIONS

This paper presents a new technique for synthesizing RRSC mechanisms to achieve phases of rigid body positions, velocities and accelerations using the same hardware. This work considers two-phase moving pivot problems with constant R-R and C-S link lengths. By specifying the R-R and C-S link joint axes, the constant length condition becomes the only design constraint for these links. The prescribed finite and multiply separated positions are then incorporated in the link constraint equations with respect to the prescribed coordinate frame for each link and the mechanism joint variables and driving link parameters calculated. The rigid body velocities and accelerations were prescribed using instant screw axis (ISA) parameters.

Energy-Based Stabilization of Angular Velocity of Rigid Body in Failure Configuration

Energy-Based Stabilization of Angular Velocity of Rigid Body in Failure Configuration

A Constrained Multibody System Dynamics Avoiding Kinematic Singularities.

In the analysis of constrained multibody systems, the constraint reaction forces are normally expressed in terms of the constraint equations and a vector of Lagrange multipliers. Because it fails to incorporate conservation of momentum, the Lagrange multiplier method is deficient when the constraint Jacobian matrix is singular. This paper presents an improved dynamic formulation for the constrained multibody system. In our formulation, the kinematic constraints are still formulated in terms of the joint constraint reaction forces and moments; however, the formulations are based on a second-order Taylor expansion so as to incorporate the rigid body velocities. Conservation of momentum is included explicitly in this method; hence the problems caused by kinematic singularities can be avoided. In addition, the dynamic formulation is general and applicable to most dynamic analyses. Finally the 3-leg Stewart platform is used for the example of analysis.

Influence of Reference Conditions on the Analysis of Impact-Induced Elastic Waves

Impact problems involving flexible bodies that undergo largerotations and translations were solved by using the floating frame ofreference approach. Analytically defined modes were selected to describedeformation. Different mode shapes can be used depending on the type ofattachment between the body frames of reference and the flexible bodies.Evaluating the kinematic coefficient of restitution during impactentails using the equivalent rigid body velocities of the flexiblebodies. In general, however, such velocities cannot be identified withreference velocities. When the colliding bodies can undergo large translations, freeattachments allow the use of mode shapes that possess zero totalmomentum. In this case, reference motion coincides with the equivalentrigid body motion of the flexible bodies and is not coupled to elasticmotion. When the colliding solids can rotate freely, the use of modeshapes with a zero angular momentum does not uncouple reference andelastic motion. However, if small deformation occurs during freerotation of the flexible body, the derivative of the reference angleremains roughly constant. Such a derivative can be interpreted as theequivalent angular velocity of the flexible body. When using a rigidattachment between the body frames of reference and the flexible bodies,reference motion does not coincide with the equivalent rigid bodyvelocity of the flexible bodies, which leads to non-constant referencevelocities when the bodies move freely. As a result, the equivalentrigid body velocities must be evaluated as linear combinations ofreference and elastic velocities. As shown in this paper, the use of free or rigid attachments asreference conditions, and their corresponding mode shapes allows theaccurate description of impact-induced elastic waves. However, theevaluation of elastic efforts with rigid attachments provides spuriouselastic forces at the attachment point. Such forces decrease as thenumber of modes increases.

Full-scale crash test and simulation of a composite helicopter

A finite element model of the Sikorsky Advanced Composite Airframe Program (ACAP) helicopter was developed using the non-linear, explicit transient dynamic code, MSC.Dytran. Analytical predictions were correlated with experimental data obtained from a full-scale crash test of the Sikorsky ACAP helicopter flight test article that was conducted in June 1999 at the Impact Dynamics Research Facility of NASA Langley Research Centre, Hampton, Virginia, USA. The helicopter was impacted at 11.58 m/s vertical and 9.9-m/s forward velocity with an attitude of 6.25° pitch (nose up) and 3.5° left roll. Due to the relatively long crash pulse duration, a rigid-body helicopter model with an energy absorbing landing gear model was executed initially. Prior to fuselage contact, a deformable structural model was executed with the rigid-body nodal displacements and velocities used as initial conditions.

Objective and Frame-Invariant Kinematic Metric Functions for Rigid Bodies

Kinematic metric functions, which allow us to make metric measurements such as “distance,” “length,” and “angle,” are often needed in robotics. However, some commonly used metric functions are not well-defined because of their dependence on choice of reference frame. This paper presents formal and practical conditions for kinematic metric functions to be well-defined. To properly analyze this issue, we introduce an intrinsic formulation of the configuration space of a rigid body that does not depend on frames. Based on this intrinsic definition, the principle of objectivity, or observer indifference, is introduced to derive a formal condition for well-definedness of kinematic metric functions. The principle of objectivity is further used to gain physical insight into left, right, and bi-invariances on the Lie group SE(3). The abstract notion of objectivity is then related to the more practically useful notion of frame invariance, which is shown to be necessary and sufficient for objectivity. Thus, frame invariance can be used as a practical condition for determining objective functions, and we give an explicit formula to determine frame invariance of a given metric function. Finally, by use of examples, we present several frame-invariant norms of rigid body velocities and wrenches. These examples demonstrate that norms with interesting physical interpretations need not be derived from inner products of velocities or wrenches.

Robust output feedback stabilization of the angular velocity of a rigid body

The problem of semi-global stabilization of the angular velocity of an underactuated rigid body in the presence of model errors is addressed and solved using a smooth, time-varying, dynamic, output feedback control law. The proposed scheme improves some of the existing results and provides guidelines for a general stabilization strategy applicable to systems which are not exponentially stabilizable. Simulations results are included.

Robust output feedback stabilization of the angular velocity of a rigid body

The problem of semi-global stabilization of the angular velocity of an under-actuated rigid body in the presence of model errors is addressed and solved using a smooth, time-varying, dynamic, output feedback control law. The proposed scheme improves some of the existing results and provides guidelines for a general stabilization strategy applicable to systems which are not exponentially stabilizable. Simulations results are included.

Određivanje sile kojom se fluid suprotstavlja kretanju krutog tela

The paper investigates added mass quantity or, in other words, fluid inertia moment by which fluid resists to the change of its velocity. Fluid, as any other rigid substance, resists to the change of its velocity. In rigid substances the resistance equals the mass of rigid body while in fluids that mass cannot be known in advance, it has to be determined. Its determination is accompanied by certain difficulties due to fluid mass quantity, its physical and chemical properties as well as to the form and the law of rigid body velocity change while the body is moving through space filled with fluid.

Strict Control Lyapunov Functions for Homogeneous Jurdjevic-Quinn Type Systems

The decomposition of nonlinear output feedback control into an observer and a state feedback control This paper presents a method to design an explicit control Lyapunov function for affine and homogeneous systems that satisfy the so-called “Jurdjevic-Quinn conditions”. For these systems a positive definite function is known that can only be made non increasing by feedback; a control Lyapunov function is obtained via a deformation of this function. As an example of its applications, this method allows one to construct an explicit control Lyapunov function for the stabilization of the angular velocity of an underactuated rigid body.

On a class of limit states of frictional joints: formulation and existence theorem

The model dealt with is a linear elastic body in frictional contact with a rigid support. Limit states of such an assemblage are characterized by deformations and forces such that a small perturbation may introduce a large change in configuration. The class of limit states considered here is specified by the possibility of superposing a time constant rigid body velocity field to a static deformation. The problem of finding such states (i.e., forces and static deformations) for a prescribed rigid body velocity is formulated, and for the case when the geometrically admissible rigid body displacements form a linear space an existence result is given. It is proved that under restrictions on the magnitude of the friction coefficient and in the case that an intuitively clear condition on the direction of the forces is satisfied, there exist a load multiplier and a corresponding static displacement.

Decentralized sliding mode control for flexible link robots

A technique using augmented sliding mode control for robust, real-time control of flexible multiple link robots is presented. For the purpose of controller design, the n-link, n-joint robot is subdivided into n single joint, single link subsystems. A sliding surface for each subsystem is specified so as to be globally, asymptotically stable. Each sliding surface contains rigid-body angular velocity, angular displacement and flexible body generalized velocities. The flexible body generalized accelerations are treated as disturbances during the controller design. This has the advantage of not requiring explicit equations for the flexible body motion. The result is n single input, single output controllers acting at the n joints of the robot, controlling rigid body angular displacement and providing damping for flexible body modes. Furthermore, the n controllers can be operated in parallel so that compute speed is independent of the number of links, affording real-time, robust, control.

Grounding experiments on soft bottoms

To verify a theoretical analysis procedure for calculation of the hull girder response of ships running aground, a series of large-scale ship grounding experiments was performed on an artificial island made of engineered fill. The tests were conducted by running a condemned fishing vessel up on selected beaches of the island with velocities ranging between 2m/s and 5.5m/s. During the tests, surge, heave, and pitch accelerations were measured and also the deformations of the beach and the ship bow. Based on these accelerations, rigid body velocities and motions were determined. The forces arising from the interaction between the bow of the vessel and the seabed were determined by solving the equations of motions. This article describes the analysis of the measured results and a comparison of the results from the full-scale measurements with results from a recently developed analysis procedure for grounding on soft bottoms.

Analytic Solution of Euler’s Equations of Motion for an Asymmetric Rigid Body

The problem of the time evolution of the angular velocity of a spinning rigid body, subject to torques about three axes, is considered. An analytic solution is derived that remains valid when no symmetry assumption can be made. The solution is expressed as a first-order correction to a previous solution, which required a symmetry or near-symmetry assumption. Another advantage of the new solution (over the former) is that it remains valid for large initial conditions of the transverse angular velocities.

Nutational stability and passive control of spinning rockets with internal mass motion

Necessary and sufficient conditions for asymptotic stability are developed for a symmetric spinning rocket with axial forcing and dissipative internal mass motion. Results show that spin about the axis of least inertia is asymptotically stable provided that three conditions are satisfied: 1) the axial thrust magnitude is sufficiently large, 2) the restoring forces for the internal mass motion are sufficiently large, and 3) the internal mass motion occurs aft of the system mass center. Under these same conditions, spin about the axis of largest inertia may be unstable. Numerical studies show that a passive control device with these characteristics can be used to attenuate the coning of prolate spinners such as those transfer orbit boost vehicles that have been plagued by unexpectedly pronounced coning instabilities. Nomenclature c = damping constant for particle motion F = magnitude of thrust (assumed constant) /i, /i, 73 = moments of inertia of (symmetric) rigid body for axes #1, #2, and 53, respectively k = spring constant for elastic restraint on particle M = mass of rigid body m = mass of particle li = m/(m -f M) Q = nominal spin rate of rigid body about #3 0)1,0)2 = components of rigid-body angular velocity for axes B and B2, respectively

Determination of First and Second Order Instant Screw Parameters from Landmark Trajectories

Least squares methods were developed to determine instant screw axis (ISA) and angular acceleration axis (AAA) parameters in experimental and analytical studies. The algorithms provide linear relationships for rigid body velocity and acceleration descriptors based on position, velocity, and acceleration data for individual points on the body. Weighted least squares estimators are presented for statistical weighting on individual landmarks as well as for variance weighting to reduce systematic measurement effects. The methods include instantaneous second order screw motion which describes differential geometry of screw axodes. Two spatial mechanism examples provide recommendations for landmark count, distribution, and placement.