Large Angular Rotations Research Articles

Multi-scale cold embossing of CoCrFeNiMn high entropy alloy with ultra-high temperature durability

Ultra-precision machining and forming of metallic materials is of great significance in the fields of catalysts, sensors, and biomedical devices. In present work, the multi-scale cold embossing of CoCrFeNiMn high entropy alloy (HEA) with structures ranging from macro-scale to nano-scale was investigated at room temperature. In less 7 s, the macro patterns, the shapes of Arabic numerals, 5 μm wide gratings, 30 μm diameter hemispherical arrays, and ∼270 nm nanowires were formed rapidly. The highest replication of the HEA cold embossing was up to 98%. A series of slip bands were detected in the cold embossed HEA structures, which can accommodate more dislocations and facilitate the plastic deformation process. Moreover, dislocation pile-up and large angular rotation within grains are observed in the deformation areas, which is favorable to contain dislocation cells, leading to grain refinement and an increase in hardness. In addition, the multi-scale HEA can be used as a high-temperature resistant mold for forming thermoplastic materials such as plastics and metallic glasses at temperatures up to 900 °C. Our researches provide candidate materials and novel methods for the facile preparation and various applications of hyperfine structures.

Deep Sensor Fusion Between 2D Laser Scanner and IMU for Mobile Robot Localization

Multi-sensor fusion plays a key role in 2D laser-based robot location and navigation. Although it has achieved great success, there are still some challenges, e.g., being fragile when having a large angular rotation. In this paper, we present a deep learning-based approach to localizing a mobile robot using a 2D laser and an inertial measurement unit. A novel recurrent convolutional neural network (RCNN)-based architecture is developed to fuse laser and inertial data for scan-to-scan pose estimation. A scan-to-submap optimization is also introduced to optimize the poses estimated by the RCNN for enhanced robustness and accuracy. Extensive experiments have been conducted in both simulation and practice with a real mobile robot, verifying the effectiveness of the proposed deep sensor fusion system.

Failure analysis and performance comparison of Triple-LET and LET flexure hinges

Abstract A new type of flexure hinge named the Triple Lamina Emergent Torsional (Triple-LET) was proposed in this paper. Its 3D structure was designed, and its equivalent bending stiffness was also derived. Based on the equivalent formula and the finite element simulation analysis, the equivalent bending stiffness of the Triple-LET and the LET flexure hinge with the same overall dimensions were analyzed and compared. It was concluded that under the same torque, the Triple-LET flexure hinge can realize larger deformation than the LET flexure hinge. Thus, the proposed new flexure hinge is presented as a compliant joint suitable for applications where large angular rotation is desired. Failure analyses of the Triple-LET and the LET flexure hinges were also carried out, respectively. The analysis results show that the Triple-LET flexure hinge made of polypropylene can reach 180° with no plastic deformation, while the LET flexure hinge with the same overall dimensions will plastically deform once the bending angle is greater than 161.4°. The results also indicate that the range of bending angles of the Triple-LET flexure hinge made of beryllium bronze is from 0° to 128.2°, which is two times larger than that of the LET flexure hinge.

An orthogonal return method for linearly polarized beam based on the Faraday effect and its application in interferometer.

Correct return of the measuring beam is essential for laser interferometers to carry out measurement. In the actual situation, because the measured object inevitably rotates or laterally moves, not only the measurement accuracy will decrease, or even the measurement will be impossibly performed. To solve this problem, a novel orthogonal return method for linearly polarized beam based on the Faraday effect is presented. The orthogonal return of incident linearly polarized beam is realized by using a Faraday rotator with the rotational angle of 45°. The optical configuration of the method is designed and analyzed in detail. To verify its practicability in polarization interferometry, a laser heterodyne interferometer based on this method was constructed and precision displacement measurement experiments were performed. These results show that the advantage of the method is that the correct return of the incident measuring beam is ensured when large lateral displacement or angular rotation of the measured object occurs and then the implementation of interferometric measurement can be ensured.

The nonholonomic and chaotic nature of a rolling isolation system

This paper presents the modeling of a rolling isolation platform used to protect objects from the hazards of horizontal shaking. The platform is built from four pairs of recessed steel bowls: four concave-up, attached to a shaking floor via a steel frame, and four concave-down, attached to the isolated object via a steel frame. Four steel ball-bearings, located between these bowls, allow the bottom- and top-frames to roll with respect to one another. In order for the four ball-bearings to remain in contact with the bowls during times of large angular rotation, the top-frame is assumed to conform to a saddle shape. The kinematics of the rolling contact impose a set of eight nonholonomic constraints to the translational and rotational dynamics of the platform center. The nonholonomic equations of state are found from the fundamental form of Lagrange's equation, which incorporates velocity constraints via Lagrange multipliers. A viscous damping model calibrated to experimental free-responses depends upon the mass of the isolated object. Precise photogrammetric measurements of a sample of these steel bowls provide the data required to calibrate the potential energy function for this system. It is shown that for the non-quadratic potential energy function of this particular system, free response trajectories are strongly sensitive to slight perturbations in initial conditions, and that the system is, in fact, chaotic. Even in the absence of any mass or stiffness eccentricity, translational and rotational motions are nonlinearly coupled through the constraint of slip-free rolling. Uni-axial models cannot be used to predict responses of these systems.

Lamina Emergent Torsional (LET) Joint

Part of the challenge in designing compliant mechanisms is finding suitable joints that provide the needed motion and force–deflection characteristics. The Lamina Emergent Torsional (LET) Joint is presented as a compliant joint suited for applications where large angular rotation is desired, but high off-axis stiffness is not as critical. The joint is introduced and the equations necessary for determining the force–deflection characteristics are presented. Since the LET Joint can be fabricated from a single planar layer, it is well suited for macro and micro applications. Illustrative examples are provided with devices fabricated from materials as diverse as steel, polypropylene, and polycrystalline silicon.

Time-resolved x-ray studies of the dynamics of smectic-Alayer realignment by magnetic fields

While the rotation of smectic layers under an applied field may at first appear to be a relatively simple problem, the dynamic processes involved are rather complex. An applied field produces a torque on the liquid crystal director, but has no direct influence on the smectic layers. If the director is reoriented significantly, however, the layers must also reorient in order to accommodate this (the layered structure is produced by short-range molecular interactions). Indeed, if the liquid crystalline order is not maintained during the realignment then matters become even more complex. In this paper we use time-resolved x-ray scattering to investigate the realignment of smectic- A layers in thin-film devices using a magnetic field. No evidence is found for continuous rotation of the smectic layers under any circumstances in such devices, a result that is not found when using bulk samples. No evidence indicating the formation of the nematic phase is observed during realignment. A molecular-dynamics technique is used to model the system which indicates that the sample becomes significantly disorganized during the realignment process when large angular rotations are induced.

Viewer-Centered Object Representation in the Human Visual System Revealed by Viewpoint Aftereffects

Are there neurons representing specific views of objects in the human visual system? A visual selective adaptation method was used to address this question. After visual adaptation to an object viewed either 15 or 30 degrees from one side, when the same object was subsequently presented near the frontal view, the perceived viewing directions were biased in a direction opposite to that of the adapted viewpoint. This aftereffect can be obtained with spatially nonoverlapping adapting and test stimuli, and it depends on the global representation of the adapting stimuli. Viewpoint aftereffects were found within, but not across, categories of objects tested (faces, cars, wire-like objects). The magnitude of this aftereffect depends on the angular difference between the adapting and test viewing angles and grows with increasing duration of adaptation. These results support the existence of object-selective neurons tuned to specific viewing angles in the human visual system.

Near-minimum-time eigenaxis rotation maneuvers using reaction wheels

A near-minimum-t ime (near-maximum-acceleration/deceleration) control technique is presented to rotate a spacecraft around its eigenaxis (shortest angular path). Practical control constraints such as wheel torque and wheel speed are also taken into account. In this paper a nominally nadir pointing satellite in a circular low Earth orbit under passive gravity gradient stabilization and active reaction wheel control will be used as an example. A standard linear feedback quaternion regulator will be used to three-axis stabilize the spacecraft before and after each large angular rotation. Robustness against inertia modeling errors is ensured by tracking the reference maneuver. The algorithm presented can easily be adapted to be used on inertially stabilized spacecraft.

Dynamics of flexible multibody systems using loaded-interface substructure synthesis approach

A simple numerical method for dynamic simulation of multibody systems consisting of rigid and flexible bodies is presented. This paper investigates the multibody systems with inertia properties of flexible components that undergo large angular rotations. The equation of motion is derived using the finite element/Lagrange formulation. A substructure synthesis method is employed to reduce the number of elastic coordinates of the multibody system. A modification to the traditional boundary conditions at the free interface has been incorporated. An example is given to demonstrate the accuracy of the computed results which obtained from this new free interface method. This example has been analyzed using the present free interface method and also the finite element method in order to compare the efficient and accuracy of both methods. It was shown that the new free interface substructure synthesis method provides accurate results even with lesser elements.

Thermoelastic Analysis of Flexible Multibody Machine-Tool Mechanisms

This investigation is concerned with the thermoelastic analysis of flexible multibody machine-tool mechanisms using the finite-element method. Thermoelastic response of the machine tool is obtained by discretizing the machine tool into a number of simple elements and calculating the thermal stress and strain of each element under the average temperature rise. The generalized thermoelastic forces associated with the generalized elastic coordinates are then determined using the virtual work. The nonlinear dynamic behavior of the machine-tool mechanism due to the application of a constant cutting force as well as a chattering (dynamic) force, with and without thermal effects, is analyzed. The chattering force is obtained by considering the cutting force variations due to the variation of undeformed chip thickness and the rate of penetration of the tool, as a result of tool deformation. In this investigation, the machine-tool mechanism is considered as a multibody system consisting of interconnected rigid and flexible bodies that undergo large angular rotations. Bending and axial deformation of the elastic bodies in the system are considered. Component mode synthesis techniques are employed in order to reduce the number of elastic coordinates and the system differential equations of motion and nonlinear algebraic constraint equations are written in terms of a coupled set of reference and modal elastic coordinates. The formulation is exemplified using a crank-shaper mechanism wherein the flexibility of the tool as well as the flexibility of the mechanism links are considered.

Timoshenko beams and flexible multibody system dynamics

A method for the dynamic analysis of flexible multibody systems that accounts for rotary inertia and shear deformation effects is presented. Flexible components in the system are discretized by using the finite element method. Because of the large rotations of the system components, a set of reference co-ordinates are employed to describe the motion of a selected body reference. Kinetic and strain energies are derived for each element, thus identifying the element mass and stiffness matrices which account for the rotary inertia and shear deformation effects. A new set of time invariant element matrices that describe the coupling between the reference motion and elastic deformations is developed. These matrices need be evaluated only once in advance for the dynamic analysis. It has been, shown that the form of these matrices as well as the mass and stiffness matrices are significantly affected by the inclusion of rotary inertia and shear deformation. The formulation presented in this paper is exemplified by a two-dimensional flexible multibody aircraft. Numerical results indicate that rotary inertia and shear have a significant effect on the dynamic response of large scale flexible multibody systems with large angular rotations and in which the reference motion and elastic deformation are coupled.

Application of perturbation techniques to flexible multibody system dynamics

In this paper, a matrix perturbation technique is developed for flexible bodies (substructures) that undergo large reference translational and rotational displacements. Although the governing dynamic equations of motion of such systems are highly nonlinear because of the large angular rotations and the resulting nonlinear inertia coupling between the reference motion and the elastic deformation, a generalized linear eigenvalue problem that defines the deformation mode shapes of the body with respect to the selected body reference is identified. This eigenvalue problem is solved only once and the variations in the body stiffness and inertia properties due to a change in selected design parameters are evaluated by using perturbation analysis techniques. The main advantage of using the proposed technique is to avoid a new finite element discretization when some design parameters are changed. This, in turn, substantially reduces the computational time, especially when large scale flexible bodies with complex geometry are considered. A numerical example is presented in order to demonstrate the use of the perturbation techniques developed in this paper in the design of flexible multibody systems.

Effect of using composites on the dynamic response of multi-body systems

A finite element scheme is presented for studying the dynamic response of multi-body systems with components manufactured from orthotropic materials. The formulation presented is exemplified by using fiber-reinforced cornposite laminates. The multi-body system considered in this investigation consists of interconnected rigid and flexible components, each undergoing large angular rotations. The configuration of the elastic components is identified by using two sets of generalized co-ordinates, reference and elastic co-ordinates. Reference co-ordinates describe the location and orientation of a selected body reference while elastic co-ordinates describe the deformation with respect to the body reference. Component modes of elastic components in the system are used to reduce the number of generalized co-ordinates. The system differential equations of motion and the algebraic constraint equations describing mechanical joints in the system are written in terms of mixed sets of reference and modal co-ordinates. Two numerical examples, for a slider crank mechanism and a Peaucellier mechanism, are presented in order to demonstrate the effect of the use of the composites on the dynamic response of multi-body systems. Numerical results showed that the use of composites represents an effective passive control strategy.

Impact responses of multi-body systems with consistent and lumped masses

A method is presented for the dynamic analysis of inertia-variant constrained mechanical systems of interconnected rigid and flexible components which may be impacting on one another. The flexible bodies are permitted to undergo large angular rotations. Elastic co-ordinaets of flexible components are described by using sets of shape functions or shape vectors, resulting in consistent or lumped mass formulations that account for the non-linear inertia coupling between the reference motion and elastic deformations. The consistent formulation allows the use of the Rayleigh-Ritz method or the finite element method, while the lumped mass formulation allows the direct use of assumed shape vectors or experimentally identified data. The generalized impulse momentum relations for all bodies of the constrained mechanical system are formulated and solved to account for jump discontinuities in system velocities and constraint reaction forces resulting from impact. Numerical examples illustrate the effect of using estimated dynamic characteristics as well as using truncated sets of elastic co-ordinates to represent the elastic motion of flexible bodies on the accuracy of the dynamic model of a multi-body system subjected to shock loading conditions due to the impacts.

Transient analysis of flexible multi-body systems. Part II: Application to aircraft landing

This investigation presents a method for transient analysis of a large-scale multi-body aircraft consisting of interconnected rigid and flexible bodies that undergo large angular rotations. Elastic components of the aircraft are discretized using the finite element method. The system equations of motion and nonlinear algebraic constraint equations describing joints between different components are written in the Lagrangian formulation using a finite set of coupled reference and modal coordinates. The system differential equations of motion and algebraic constraint equations are computer-generated and integrated forward in time using an explicit-implicit direct numerical integration algorithm coupled with a Newton-Raphson type iteration in order to check on constraint violations. Impact and intermittent motion events are accounted for by using a generalized momentum balance that predict jump discontinuities in the generalized velocities as well as jump discontinuities in the system reaction forces. The formulation presented and the computer program developed are used to simulate the impact between the landing gear and the runway. The method is also used to predict the dynamic behavior of the aircraft during the traverse of an abrupt elevation change in the runway.

Automated Analysis of Constrained Systems of Rigid and Flexible Bodies

This paper is concerned with modeling inertia properties of flexible components that undergo large angular rotations. Consistent, lumped and hybrid mass techniques are presented in detail and used to model the inertia properties of flexible bodies. The consistent formulation allows using the finite-element method as well as Rayleigh-Ritz method to describe the deformation of elastic components. Lumped mass techniques allow using shape vectors or experimentally identified data. In the hybrid mass formulation, the flexibility mass matrix is evaluated using a consistent mass formulation, while the inertia coupling between gross rigid body motion and elastic deformation is formulated using a lumped mass technique. Different mass formulations require the evaluation of similar sets of time-invariant matrices that represent the inertia coupling. Consequently, these matrices have to be evaluated only once in advance for the dynamic analysis. A unified mathematical model, and accordingly a unified computer program (DAMS: Dynamic Analysis of Multibody Systems), that deal with different formulations are developed. A comparative study is presented in order to study the effect of the mass formulation on the dynamic response of elastodynamic constrained systems. The validity of the linear theory that neglects the effect of small oscillations on large rigid body motion is also discussed.

Viscoelastic analysis of multi-body systems using the finite element method

A study of the effect of viscoelastic material damping on the dynamic response of multibody systems, consisting of interconnected rigid, elastic and viscoelastic components, is presented. The motion of each elastic or viscoelastic body is identified by using three sets of modes: rigid body, reference and normal modes. Rigid body modes describe translation and large angular rotation of a body reference. Reference modes are the result of imposing the body-axis conditions. Normal modes define the deformation of the body relative to the body reference. Constraints between different components are formulated by using a set of non-linear algebraic equations that can be introduced to the dynamic formulation by using a Lagrange multiplier technique or can be utilized to eliminate dependent co-ordinates by partitioning the constraint Jacobian matrix. In developing the system equations of motion of the viscoelastic component, an assumption of a linear viscoelastic model is made. A Kelvin-Voigt model is employed, wherein the stress is assumed to be proportional to the strain and its time derivative. The formulation yields a constant damping matrix and the damping forces depend only on the local deformation; thus, no additional coupling between the reference and elastic co-ordinates appears in the formulation when considering the viscoelastic effects. It is demonstrated, by a numerical example, that the viscoelastic material damping can have a significant effect on the dynamic response of multibody systems.

Spatial Transient Analysis of Inertia-Variant Flexible Mechanical Systems

An analytical method for transient dynamic simulation of large-scale inertia-variant spatial mechanical and structural systems is presented. Multibody systems consisting of interconnected rigid and flexible substructures which may undergo large angular rotations are analyzed. A finite element technique is used to characterize the elastic properties of deformable substructures. A component mode technique is then employed to eliminate insignificant substructure modes. Nonlinear holonomic constraint equations are used to define joints between different substructures. The system equations of motion are written in terms of a mixed set of modal and physical coordinates. A generalized coordinate partitioning technique is then employed to eliminate redundant differential equations. An implicit-explicit numerical integration algorithm solves the remaining set of differential equations and the approximate physical system state is recovered. The transient analysis of a spatial vehicle with flexible chassis is presented to demonstrate the method.

A Coordinate Reduction Technique for Dynamic Analysis of Spatial Substructures with Large Angular Rotations∗

ABSTRACT A substructuring technique is presented for transient dynamic analysis of systems composed of interconnected rigid and elastic bodies that undergo large angular displacements. Displacement of elastic bodies is represented by superposition of local linear elastic deformation on large displacement of body reference coordinate systems. Elastic bodies are thus represented by combined sets of reference and local elastic generalized coordinates. Modal analysis and substructuring of individual elastic components allow for elimination of insignificant modes. Equations of motion and constraint are formulated in terms of mixed sets of modal and reference generalized coordinates. Planar and spatial linkages with flexible elements are presented to illustrate use of the method developed.