Linear Degrees Of Freedom Research Articles

Linear Degrees of Freedom of the MIMO X-Channel With Delayed CSIT

We study the degrees of freedom (DoFs) of the multiple-input multiple-output X-channel (MIMO XC) with delayed channel state information at the transmitters (delayed CSITs), assuming linear coding strategies at the transmitters. We present two results: 1) the linear sum DoF for MIMO XC with general antenna configurations and 2) the linear DoF region for MIMO XC with symmetric antennas. The converse for each result is based on developing a novel rank-ratio inequality that characterizes the maximum ratio between the dimensions of received linear subspaces at the two multiple-antenna receivers. The achievability of the linear sum DoF is based on a three-phase strategy, in which during the first two phases only the transmitter with fewer antennas exploits delayed CSIT in order to minimize the dimension of its signal at the unintended receiver. During the third phase, both transmitters use delayed CSIT to send linear combinations of past transmissions, such that each receiver receives a superposition of desired message data and known interference, thus simultaneously serving both receivers. We also derive other linear DoF outer bounds for the MIMO XC that, in addition to the outer bounds from the sum DoF converse and the proposed transmission strategy, allow us to characterize the linear DoF region for symmetric antenna configurations.

Linear Degrees of Freedom of MIMO Broadcast Channels With Reconfigurable Antennas in the Absence of CSIT

The K-user multiple-input and multiple-output (MIMO) broadcast channel (BC) with no channel state information at the transmitter (CSIT) is considered, where each receiver is assumed to be equipped with reconfigurable antennas capable of choosing a subset of receiving modes from several preset modes. Under general antenna configurations, the sum linear degrees of freedom (LDoF) of the K-user MIMO BC with reconfigurable antennas is completely characterized, which corresponds to the maximum sum DoF achievable by linear coding strategies. The LDoF region is further characterized for a class of antenna configurations. Similar analysis is extended to the K-user MIMO interference channels with reconfigurable antennas and the sum LDoF is characterized for a class of antenna configurations.

Degrees of Freedom of the Two-User MIMO Broadcast Channel with Private and Common Messages Under Hybrid CSIT Models

We establish the degree of freedom (DoF) regions of the two-user multiple-input multiple-output (MIMO) broadcast channel with a general message set (BC-GM), that includes private and common messages, under fast fading. Nine different channel state knowledge assumptions—collectively known as hybrid channel state information at the transmitter (CSIT) models—are considered wherein the transmitter has either perfect/instantaneous, delayed, or no CSI from each of the two receivers. General antenna configurations are addressed wherein the three terminals have arbitrary numbers of antennas. The DoF regions are established for the five hybrid CSIT models in which either both channels are unknown at the transmitter or each of the two channels is known perfectly or with delay. In the four remaining cases in which exactly one of the two channels is unknown at the transmitter, the DoF regions under the restriction of linear encoding strategies—also known as the linear DoF (LDoF) regions—are established. As the key to the converse proofs of the LDoF region of the MIMO BC-GM under such hybrid CSIT assumptions, we show that, when only considering linear encoding strategies, the CSI from the receiver with more antennas does not help if there is no CSI available from the receiver with fewer antennas. This result is conjectured to be true even without the restriction on the encoding strategies to be linear. If true, the LDoF regions obtained for the four hybrid CSIT cases herein will also be the DoF regions for those cases. Many of the results of this paper when specialized to even the two-message problems are new. These include the LDoF regions, when one of the two channels is not known, of the MIMO BC-GM when specialized to the MIMO BC with private messages. They also include the DoF/LDoF regions for all the hybrid CSIT models obtained by specializing the corresponding regions for the MIMO BC-GM to the case with degraded messages.

Circling turning locomotion of a new multiple closed-chain-legs robot with hybrid-driven mechanism

A multi-legged robot based on a hybrid-driven mechanism is presented in this paper as an improvement of the legged robot based on crank-driven linkage mechanism. A hybrid-driven mechanism containing a full-rotational degree of freedom (DOF) and a linear translational DOF was obtained after a series of foot trajectory analyses on the Jansen mechanism. The stance phase trajectory of this hybrid-driven mechanism can maintain horizontality regardless of the length adjustment of the linear DOF. A turning gait of a hexapod robot based on this hybrid-driven mechanism was proposed, such that all of the legs had an identical crank angular speed, and the robot turned its orientation through different linear servo controls on the legs of the two sides. Simulation and experimental results showed that the hexapod robot could realize the turning gait when the legs of the two sides applied different length adjustments. The body center trajectories in all cases were approximate to a circle, and the smallest turning radius was close to the length of the robot. Moreover, the magnitude of the pitch and roll angles, and body center fluctuation in the simulations was all small, indicating that the hexapod robot based on the hybrid-driven mechanism was stable during the turning locomotion.

Linear Degrees of Freedom of the $X$-Channel With Delayed CSIT

We establish the degrees of freedom (DoF) of the two-user X-channel with delayed channel knowledge at transmitters [i.e., delayed channel state information at the transmitters (CSIT)], assuming linear coding strategies at the transmitters. We derive a new upper bound and characterize the linear DoF of this network to be 6/5. The converse builds upon our development of a general lemma that shows that, if two distributed transmitters employ linear strategies, the ratio of the dimensions of received linear subspaces at the two receivers cannot exceed 3/2, due to delayed CSIT. As a byproduct, we also apply this general lemma to the three-user interference channel with delayed CSIT, thereby deriving a new upper bound of 9/7 on its linear DoF. This is the first bound that captures the impact of delayed CSIT on the DoF of this network, under the assumption of linear encoding strategies.

Structures Analysis and Optimum Design of the Large Stroke Two-Axis Fast Tool Servo

A two degree of freedom large-stroke linear FTS device was designed in this paper, the device with flexible hinges as the guidance and support part, achieved the linear degrees of freedom in X and Z. In addition, structure design and optimizationanalysis of static characteristic and dynamic characteristicresponse surface analysis of FTS device were worked as well in this paper ,then the stiffness and strength characteristics of FTS device has been greatly improved, fully meet the design requirements, achieved the desired effect.

Bistable energy harvesting enhancement with an auxiliary linear oscillator

Recent work has indicated that linear vibrational energy harvesters with an appended degree-of-freedom (DOF) may be advantageous for introducing new dynamic forms to extend the operational bandwidth. Given the additional interest in bistable harvester designs, which exhibit a propitious snap through effect from one stable state to the other, it is a logical extension to explore the influence of an added DOF to a bistable system. However, bistable snap through is not a resonant phenomenon, which tempers the presumption that the dynamics induced by an additional DOF on bistable designs would inherently be beneficial as for linear systems. This paper presents two analytical formulations to assess the fundamental and superharmonic steady-state dynamics of an excited bistable energy harvester to which is attached an auxiliary linear oscillator. From an energy harvesting perspective, the model predicts that the additional linear DOF uniformly amplifies the bistable harvester response magnitude and generated power for excitation frequencies less than the attachment’s resonance while improved power density spans a bandwidth below this frequency. Analyses predict bandwidths having co-existent responses composed of a unique proportion of fundamental and superharmonic dynamics. Experiments validate key analytical predictions and observe the ability for the coupled system to develop an advantageous multi-harmonic interwell response when the initial conditions are insufficient for continuous high-energy orbit at the excitation frequency. Overall, the addition of an auxiliary linear oscillator to a bistable harvester is found to be an effective means of enhancing the energy harvesting performance and robustness.

Linear Degrees-of-Freedom for the $M\times N$ MIMO Interference Channels With Constant Channel Coefficients

This paper analyzes the linear degrees of freedom (LDoF) for K-user M ×N MIMO interference channels with constant channel coefficients. In this correspondence, we interpret the interference alignment problem as a multivariate polynomial system in terms of properness. The properness provides a LDoF upperbound for interference alignment. With this approach, we propose a method to obtain the upperbound for total LDoF achievable by linear interference alignment. The LDoF upperbound for properness condition results have two different cases which depend on the number of users, the number of transmit antennas, and the number of receive antennas. A key contribution of this paper is that it provides a closed-form LDoF upperbound for M ×N MIMO interference channels where the LDoF of each user may be different.

Vibratory energy exchange between a linear and a nonsmooth system in the presence of the gravity

The concept of the vibratory energy transfer between a linear master DOF and a nonsmooth nonlinear energy sink (NES) in the presence of gravity forces is studied. Different invariant manifolds of the system at different time scales are revealed and necessary conditions for leading the behavior of the system to strongly modulated response (SMR) are enlightened.

Research on the Influence of Unsprung Mass on Vehicle Handling Stability

A dynamical model of engine vehicle was built by using ADAMS/Car. Based on that, another dynamical model of four-independent-wheel-drive electric vehicle was built too. Two simulation experiments of steering wheel angle step input and steering wheel angle impulse input were done. Considering the vehicle mathematical model with two linear degrees of freedom, the transient response and frequency response characteristics were evaluated. Simulation results indicated that time-domain and frequency-domain characteristics of four-independent-wheel-drive electric vehicle were influenced because of its heavy unsprung mass, and that leaded to the deteriorative handling stability.

Reduced stiffness method for nonlinear analysis of structural frames

This paper addresses a numerical algorithm for nonlinear analysis of frames, using the unit displacement method, in generating a reduced stiffness matrix of the structure. This algorithm can properly be used in nonlinear static analysis or in the incremental response spectral method. Here, the instantaneous reduced stiffness matrix of the structure is calculated, considering its linear behavior at the latest state, by performing a set of numerical tests on the whole structure. Each numerical test consists of imposing prescribed displacement fields on the lateral displacement of stories and calculating the reactions of the structure. The solution procedure of each test is based on the division of degrees of freedom into three parts: (1) predefined lateral displacement of joints, (2) vertical displacement of joints, considered as linear degrees of freedom, and (3) rotation of joints, regarded as nonlinear degrees of freedom. The stiffness matrices are generated distinctly for all mentioned parts. Therefore, the linear stiffness matrix is inverted once at the beginning of the analysis. The suggested method is not limited to any special case or physical assumptions. This model has good accuracy in representing structural responses and modal properties, confirmed by different numerical examples. Regarding computational cost, the proposed algorithm is more efficient in comparison with the conventional method.

Vowel Production Manifold: Intrinsic Factor Analysis of Vowel Articulation

The manner in which the organization of vowels in a compact space reflects the relationship between their production and perception remains to be clarified in the field of speech science, although it is believed that vowels exist in a compact space with a regular structure rather than as an unstructured blob. In the articulatory domain, some traditional representations such as those based on the results of tongue position analysis and linear factor analysis are used. However, the former partially encodes information on vowel articulation, and the latter only reflects the linear degrees of freedom of vowel articulation. Since nonlinear degrees of freedom exist during the production of vowels, the traditional linear factor analysis is not suitable. In this paper, we proposed the use of Laplacian eigenmaps for analyzing the intrinsic factors affecting vowel articulation and obtain a compact manifold representation of vowels. On the manifold, vowels have distinct cluster positions depending on the similarities in their production and perception. On the basis of vowel articulation, we state that the first dimension of the manifold structure is related to the tongue height position and the second dimension to mouth opening. The third dimension is related to the articulation location of vowels along the vocal tract which is curved along the manifold. A similar topological manifold structure is explored in the vowel acoustic space. Quantitatively, on the basis of the conditional entropy criterion and vowel identification experiments, we confirmed that the analyzed compact manifold structure encodes more information on vowels than do traditional representations.

Approach to Automated Location Planning of Fixture Based on the Processing Procedure Requirements

A series of principles about fixture locating plan are proposed to automate the selection of locating datum and the layout of locating points. The constraint degrees of freedom(DOF) of workpiece datum can be classified into four types:linear translation DOF,linear rotation DOF,planar translation DOF and planar rotation DOF. The acquirement of constraint DOFs is realized by automatically extracting process requirements. Four kinds of constraint DOFs are represented in the format of vectors,and the locating capability of workpiece datum is denoted by the layout of locating points,by which the operation rules of constraint DOFs,such as merge rule,decomposition rule and coordinate transformation rule,are established. The evaluation method of datum locating ability and the judging method of datum conflicts are studied. The approach to the resolution of the datum conflicts and the datum locating problem is presented,and the rule of the layout of locating points is established.

Development of a Novel Algorithm for a Crack Detection, Localization, and Sizing in a Beam Based on Forced Response Measurements

Abstract The present work aims at the development of a method for the crack detection, localization and sizing in a beam based on the transverse force and response signals. The Timoshenko beam theory is applied for transverse vibrations of the beam model. The finite element method is used for the cracked beam forced vibration analysis. An open transverse surface crack is considered for the crack model, which contains standard five flexibility coefficients. The effect of the proportionate damping is also included. A harmonic force of known amplitude with sine-sweep frequency is used to dynamically excite the beam, up to few flexible modes, which could be provided with the help of an exciter. In practice, linear degrees of freedom (DOFs) can be measured quite accurately; however, rotational DOFs are difficult to measure accurately. All rotational DOFs, except at crack element, are eliminated by a dynamic condensation scheme; for elimination of rotational DOFs at the crack element, a new condensation scheme is implemented. The algorithm is iterative in nature and starts with a presumption that a crack is present in the beam. For an assumed crack location, flexibility coefficients are estimated with the help of forced responses. The Tikhonov regularization technique is applied in the estimation of bounded crack flexibility coefficients. These crack flexibility coefficients are used to obtain the crack size by minimizing an objective function. With the help of the estimated crack size and measured natural frequency, the crack location is updated. The procedure iterates till the crack size and location get stabilized up to the desired level of accuracy. The algorithm has a potential to detect no crack condition also. The crack flexibility and damping coefficients are estimated as a by-product. Numerical examples, with the simply supported and cantilevered beams, are given to justify the applicability and versatility of the algorithm in practice. With the numerically simulated forced responses, which have the noise contamination and the error in the natural frequency measurements, the estimated crack parameters (i.e., the crack location and size) are in good agreement.

A Refined Double-row Spherical Roller Bearing Model and its Application in Performance Assessment of Moving Race Shaft Misalignments

Largely due to their self-aligning and superior loading capabilities, spherical roller bearings have seen extensive application. Compared with the single-row deep-grooved-ball (DGB) bearing, the dynamics involved in the operation of double-row spherical roller bearings (SRBs) are much more complicated; double-row SRBs have at least twice as many degrees of freedom (DoFs) as DGBs. Also, the contact forces between each one of a pair of rollers and the inner race/outer race can be different, resulting in unbalanced axial forces on the moving race and causing axial displacement and angular movements of the moving race. Due to its complexity, modeling efforts carried out so far have not included the effects of the rotational DoFs of the moving race. Aiming at improving the state of the art, a comprehensive dynamic model of SRBs is developed in this investigation. This model takes into account all the DoFs of the moving race, including the angular movements about both the vertical and horizontal axes. Subsequently, the contact angle between each individual roller and the moving race is correlated with each linear and rotational DoF of the moving race. The model developed in this investigation can quantitatively analyze the effects of linear and rotational shaft misalignments. Therefore, it provides guidelines for optimizing system installation requirements/procedure, which will be valuable for high-precision machine systems. The simulation results demonstrate that the rotational DoFs of the moving race have major effects on the force/displacement responses and thus should be included in the model for a more accurate assessment of the system performance. Extensive case studies are carried out to assess the effects of the loading conditions and radial clearance, as well as shaft misalignment.

Nonlinear Dynamic Analysis of an Unsymmetrical Generator-Bearing System

Considering both nonlinear oil film force and unsymmetrical stiffness, this paper presents a mechanical model of a generator-bearing system. The complex mode synthesis method is used to reduce the linear degrees of freedom of the high order model in the rotating coordinates, and one-order modal differential equations are obtained which may not be solved directly by Newmark-β method. To solve this problem, a modified Newmark-β method is presented to investigate dynamic effects of the asymmetry of rotor stiffness, the viscosity of oil, the rotor unbalance and the ratio of length to diameter of bearings. Three-dimension diagrams and unfiltered vibration curves are used as tools to examine the dynamic behavior of the system, and some insights into the dynamic behavior are given. Numerical results show that instability of the system may be improved by modifying these parameters.

Propagation of the hip joint centre location error to the estimate of femur vs pelvis orientation using a constrained or an unconstrained approach

To estimate hip joint angles during selected motor tasks using stereophotogrammetric data, it is necessary to determine the hip joint centre position. The question is whether the errors affecting that determination propagate less to the angles estimates when a three degrees of freedom (DOFs) constraint (spherical hinge) is used between femur and pelvis, rather than when the two bones are assumed to be unconstrained (six DOFs). An analytical relationship between the hip joint centre location error and the joint angle error was obtained limited to the planar case. In the 3-D case, a similar relationship was obtained using a simulation approach based on experimental data. The joint angle patterns resulted in a larger distortion using a constrained approach, especially when wider rotations occur. The range of motion of the hip flexion–extension, obtained simulating different location errors and without taking into account soft tissue artefacts, varied approximately 7 deg using a constrained approach and up to 1 deg when calculated with an unconstrained approach. Thus, the unconstrained approach should be preferred even though its estimated three linear DOFs most unlikely carry meaningful information.

Ocular compensation due to labyrinthine input during natural motion.

With recent technical developments, it has become possible to study eye and head movements in all angular and linear degrees of freedom during natural activities such as standing and treadmill ambulation. Such studies have revealed that normal human gaze stabilization during ambulation is accomplished not only by ocular rotation in response to head rotation, but also by head translation coordinated with head rotation as appropriate to viewing distance. Typically, head translation in a given direction is coupled via an active mechanism with antiphase rotation in the opposite direction, accomplishing some gaze stabilization for near targets and supplementing the vestibulo-ocular reflex (VOR). Subunity angular VOR gain (eye velocity/head velocity) not only is observed during most natural activities, but also minimizes the disturbance to retinal image stability so that excellent visual acuity can be obtained. The generation of eye movements compensating for head motion during ambulation can be quantitatively modeled as an additive combination of semicircular canal responses, with otolith responses scaling by inverse viewing distance, so angular VOR gain correlates poorly with gaze stability. Compensatory eye movements during self-generated head rotations appear driven to a significant extent by nonvestibular mechanisms since they cannot be modeled as an additive combination of otolith and canal responses. People with unilateral vestibular deafferentation have normal gaze stability during natural activities such as standing, walking, and running, although gaze stability is impaired in bilateral deafferentation. Limitation of head motion during natural activities is a common strategy in those with reduced peripheral vestibular sensitivity.

Linear degrees of freedom in speech production: analysis of cineradio- and labio-film data and articulatory-acoustic modeling.

The following contribution addresses several issues concerning speech degrees of freedom in French oral vowels, stop, and fricative consonants based on an analysis of tongue and lip shapes extracted from cineradio- and labio-films. The midsagittal tongue shapes have been submitted to a linear decomposition where some of the loading factors were selected such as jaw and larynx position while four other components were derived from principal component analysis (PCA). For the lips, in addition to the more traditional protrusion and opening components, a supplementary component was extracted to explain the upward movement of both the upper and lower lips in [v] production. A linear articulatory model was developed; the six tongue degrees of freedom were used as the articulatory control parameters of the midsagittal tongue contours and explained 96% of the tongue data variance. These control parameters were also used to specify the frontal lip width dimension derived from the labio-film front views. Finally, this model was complemented by a conversion model going from the midsagittal to the area function, based on a fitting of the midsagittal distances and the formant frequencies for both vowels and consonants.

Three-dimensional manipulation of carbon nanotubes under a scanning electron microscope

Carbon nanotubes are manipulated in three dimensions inside a scanning electron microscope (SEM). A custom piezoelectric vacuum manipulator achieves positional resolutions comparable to scanning probe microscopes, with the ability to manipulate objects along one rotational and three linear degrees of freedom. This prototypical device can probe, select and handle nanometre-scale objects such as carbon nanotubes in order to explore and correlate their mechanical and electrical properties. Under real-time SEM inspection, carbon nanotubes are stressed while monitoring their conductivity, and nanotubes are attached to commercial atomic force microscope (AFM) tips such that the forces applied to the tubes can be measured from the cantilevers' deflections. The manipulator functions both as a research tool for investigating properties of carbon nanotubes and other nanoscale objects without surface restrictions, and as a rudimentary building device for larger nanotube assemblies. This capability to select and manipulate nanoscale components and to examine directly their suitability as construction materials during various phases of the construction process will play an important role in enabling the technology of assembling mechanical and electronic devices from prefabricated components.