Kinematic Function Research Articles

Characterization Based Design Under Dual State Vectors

This paper presents an automated design that is capable of generating large number of possible design concepts of hybrid combined mechanisms by given only the kinematic functions in requirement specifications. A hybrid mechanism is captured with considering its intrinsic multiple loop kinematic behavior being viewed as several kinematic state transformations. The input and output kinematic characteristic states of a subsystem or a basic mechanism unit are represented by qualitative dual state vectors related by characteristic matrix. Each element of the matrix defines a relative transformation and the operation rules of these transformations are defined. The subsystem characteristic matrix is the product of characteristic matrices of the serialized transformation units or addition of the paralleled. The dual state vectors of all available mechanism units are identified and the combination pattern decomposition rules for subsystem are established. Each set of such basic mechanism units and unit connections is the kinematic-to-structural representation of hybrid mechanism. By successive decomposition of logical hybrid connections, a thorough design process for hybrid mechanism is established. Then, the characteristic matrix of a subsystem can be successively decomposed into various sets of characteristic matrices of basic mechanism units. Due to this modularization of kinematic components and connection patterns, a hybrid system is described in functional hierarchy at two levels as the physical mechanism units and logical combination units which facilitate to map kinematic space to characteristic space till to dual state vector routing operations. This laid a ground work for hybrid mechanism design and examples are given to illustrate the proposed design principles.

Source inversion of the 1570 Ferrara earthquake and definitive diversion of the Po River (Italy)

AbstractAn 11‐parameter, kinematic‐function (KF) model was used to retrieve the approximate geometrical and kinematic characteristics of the fault source of the 1570 Mw 5.8 Ferrara earthquake in the Po Plain, including the double‐couple orientation (strike angle 127 ± 16°, dip 28 ± 7°, and rake 77 ± 16°). These results are compatible with either the outermost thrust fronts of the northern Apennines, which are buried beneath the Po Plain's alluvial deposits, or the blind crustal‐scale thrust. The 1570 event developed to the ENE of the two main shocks on 20 May 2012 (M 6.1) and 29 May 2012 (M 5.9). The three earthquakes had similar kinematics and are found 20–30 km from each other en echelon in the buried chain. Geomorphological and historical evidence exist which suggest the following: (i) the long‐lasting uplift of the buried Apenninic front shifted the central part of the course of the Po River approximately 20 km northward in historical times and (ii) the 1570 earthquake marked the definitive diversion of the final part of the Po River away from Ferrara and the closure of the Po delta 40 km south of its present position.

Free vibration analysis of two-dimensional functionally graded axisymmetric cylindrical shell on Winkler–Pasternak elastic foundation by First-order Shear Deformation Theory and using Navier-differential quadrature solution methods

This paper focuses on the dynamic behavior of moderately thick functionally graded cylindrical shell based on the First-order Shear Deformation Theory (FSDT). The FSDT is applied to investigate free vibration of 2D-FG cylindrical shell surrounded by Winkler–Pasternak elastic foundation. The material properties of functionally graded cylindrical shell are graded in two directional (radial and axial) and assumed to obey the power law distribution. The energy method is used to derive the potential, kinematic and virtual work energy functions. Then the Euler’s equation and Hamilton’s principle are employed to derive the stability and equations of motion, respectively. The GDQ method is examined by comparing its results with those available in the literature. The GDQ approach is used to obtain as natural frequencies and mode shapes as we want without any frequency missing. The main advantages of this method are known for its higher accuracy with small computational expensiveness in compare to Navier-type solution with twofold Fourier series. Fundamental frequencies and mode shapes are presented in this paper. The determined facets like boundary conditions, values of translational and rotational spring constants and the volume fraction indices on the natural frequencies and mode shapes are discoursed.

Effects of aerodynamic modeling on the optimal wing kinematics for hovering MAVs

The effects of aerodynamic model assumptions on the optimal wing-kinematics for hovering micro-air-vehicles are determined. Specific kinematic functions for the wing motion are specified and the parameters of these functions are considered as the design variables for the optimization problem. Four aerodynamic models having different levels of fidelity that capture various physical aspects of hovering aerodynamics are considered to assess the effects of these different aspects on the optimal wing kinematics. These physical aspects include the leading edge vortex, rotational lift, non-circulatory contributions, and flow unsteadiness. Conventional models for pitching wings are not adequate as they predict considerably high rotational lift and too little power requirements, which makes the optimizer, unrealistically, leans toward almost pure rotational motion with little flapping. In addition, quasi-steady modeling overestimates the generated lift and, as such, leads to a more optimal, but unrealistic, performance. Therefore efficient unsteady modeling is essential in design optimization of flapping-wing micro-air-vehicles.

An anatomic and kinematic analysis of a new total wrist arthroplasty design.

Background Total wrist arthroplasty (TWA) is a viable surgical treatment for disabling wrist arthritis. While current designs are a notable improvement from prior generations, radiographic loosening and failures remain a concern. Purpose The purpose of this investigation is to evaluate a new total wrist arthroplasty design kinematically. The kinematic function of a native, intact cadaveric wrist was compared with that of the same wrist following TWA. Method Six, fresh-frozen wrist cadaveric specimens were utilized. Each wrist was fixed to an experimental table and its range of motion, axis of rotation, and muscle moment arms were calculated. The following tendons were attached to the apparatus to drive motion: extensor carpi radialis longus (ECRL), extensor carpi radialis brevis (ECRB), extensor carpi ulnaris (ECU), flexor carpi radialis (FCR), flexor carpi ulnaris (FCU), and abductor pollicis longus (APL). The wrist was then manually moved along a guide by an experimenter through a series of motions including flexion-extension, radial-ulnar deviation, and circumduction. The experiment was then performed on the specimen following implantation of the TWA. Results Following the TWA procedure, there were statistically significant decreases in the ulnar deviation and the flexion/ulnar deviation component of dart throw ranges of motion. There were no statistically significant changes in flexion, extension, radial deviation, the extension/radial deviation component of the dart thrower motion, or the circumduction range of motion. Conclusions Kinematic analysis of the new TWA suggests that a stable, functional wrist is achievable with this design. Clinical Relevance While appreciating the limitations of a cadaveric study, this investigation indicates that the TWA design studied merits study in human populations.

Scapulohumeral Rhythm in Shoulders with Reverse Shoulder Arthroplasty

Little is known about kinematic function of the reverse total shoulder arthroplasty (RTSA). Scapulohumeral rhythm (SHR) is a common metric for assessing muscle function and shoulder joint motion. Understanding how RTSA affects shoulder function may help refine implant design, surgery, and rehabilitation strategies. The purpose of this study was to compare SHR in shoulders with RTSA to normal shoulders.

A computationally efficient method for incorporating spike waveform information into decoding algorithms.

Spike-based brain-computer interfaces (BCIs) have the potential to restore motor ability to people with paralysis and amputation, and have shown impressive performance in the lab. To transition BCI devices from the lab to the clinic, decoding must proceed automatically and in real time, which prohibits the use of algorithms that are computationally intensive or require manual tweaking. A common choice is to avoid spike sorting and treat the signal on each electrode as if it came from a single neuron, which is fast, easy, and therefore desirable for clinical use. But this approach ignores the kinematic information provided by individual neurons recorded on the same electrode. The contribution of this letter is a linear decoding model that extracts kinematic information from individual neurons without spike-sorting the electrode signals. The method relies on modeling sample averages of waveform features as functions of kinematics, which is automatic and requires minimal data storage and computation. In offline reconstruction of arm trajectories of a nonhuman primate performing reaching tasks, the proposed method performs as well as decoders based on expertly manually and automatically sorted spikes.

Scapulohumeral rhythm in shoulders with reverse shoulder arthroplasty

Little is known about kinematic function of reverse total shoulder arthroplasty (RTSA). Scapulohumeral rhythm (SHR) is a common metric for assessing muscle function and shoulder joint motion. The purpose of this study was to compare SHR in shoulders with RTSA to normal shoulders. Twenty-eight subjects, more than 12 months after unilateral RTSA, were recruited for an Institutional Review Board-approved study. Subjects performed arm abduction in the coronal plane with and without a 1.4-kg hand-held weight. Three-dimensional model-image registration techniques were used to measure orientation and position for the humerus and scapula from fluoroscopic images. Analysis of variance and Tukey tests were used to assess groupwise and pairwise differences. SHR in RTSA shoulders (1.3:1) was significantly lower than in normal shoulders (3:1). Below 30° abduction, RTSA and normal shoulders show a wide range of SHR (1.3:1 to 17:1). Above 30° abduction, SHR in RTSA shoulders was 1.3:1 for unweighted abduction and 1.3:1 for weighted abduction. Maximum RTSA shoulder abduction in weighted trials was lower than in unweighted trials. SHR variability in RTSA shoulders decreased with increasing arm elevation. RTSA shoulders show kinematics that are significantly different from normal shoulders. SHR in RTSA shoulders was significantly lower than in normal shoulders, indicating that RTSA shoulders use more scapulothoracic motion and less glenohumeral motion to elevate the arm. With these observations, it may be possible to improve rehabilitation protocols, with particular attention to the periscapular muscles, and implant design or placement to optimize functional outcomes in shoulders with RTSA.

The Navier‐Stokes equations with particle methods

AbstractWe consider the initial boundary value problem for the nonstationary Navier‐Stokes equations in a bounded three‐dimensional domain Ω with a sufficiently smooth boundary ∂Ω. These equations describe the motion of a viscous incompressible fluid contained in Ω for 0 < t < T. They represent a system of nonlinear partial differential equations concerning four unknown functions, i.e. the velocity vector v = (v1(t, x), v2(t, x), v3(t, x)) and the kinematic pressure function p = p(t, x) of the fluid at time t ∈ (0, T) in x ∈ Ω. The purpose of this paper is to construct a Leray‐Hopf type weak solution to the nonstationary Navier‐Stokes system, which exists globally in time. Our construction is based on a suitable approximation using particle methods for stationary fluid flow. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Useful properties of spinal circuits for learning and performing planar reaches

Objective. We developed a detailed model of the spinal circuitry plus musculoskeletal system (SC + MS) for the primate arm and investigated its role in sensorimotor control, learning and storing of movement repertoires. Approach. Recently developed models of spinal circuit connectivity, neurons and muscle force/energetics were integrated and in some cases refined to construct the most comprehensive model of the SC + MS to date. The SC + MS’s potential contributions to center-out reaching movement were assessed by employing an extremely simple model of the brain that issued only step commands. Main results. The SC + MS was able to generate physiological muscle dynamics underlying reaching across different directions, distances, speeds, and even in the midst of strong dynamic perturbations (i.e. viscous curl field). For each task, there were many different combinations of brain inputs that generated physiological performance. Natural patterns of recruitment and low metabolic cost emerged for about half of the learning trials when a purely kinematic cost function was used and for all of the trials when an estimate of metabolic energy consumption was added to the cost function. Solutions for different tasks could be interpolated to generate intermediate movement and the range over which interpolation was successful was consistent with experimental reports. Significance. This is the first demonstration that a realistic model of the SC + MS is capable of generating the required dynamics of center-out reaching. The interpolability observed is important for the feasibility of storing motor programs in memory rather than computing them from internal models of the musculoskeletal plant. Successful interpolation of command programs required them to have similar muscle recruitment patterns, which are thought by many to arise from hard-wired muscle synergies rather than learned as in our model system. These properties of the SC + MS along with its tendency to generate energetically efficient solutions might usefully be employed by motor cortex to generate voluntary behaviors such as reaching to targets.

Assessment of lower limbs kinematics during human–robot interaction using inertial measurement units

Introduction: The kinematic structure of wearable robots designed for lower limb rehabilitation usually replicates that of the human body (anthropomorphism), thus kinematic incompatibilities may arise from the mismatch between robotic and human joint axes of rotation. Conversely, non-anthropomorphic structures can be designed to be robust against misalignments, thus minimizing undesired interaction forces [1]. A non-anthropomorphic treadmill-based robot for hip and knee flexion/extension assistance, using compliant actuators [2] and deriving human joint kinematic patterns with forward kinematics, has been previously presented [3] and [4]. Inaccuracies in the mapping of rotations from the robot joint space to the human joint space may arise from: (1) human segments length estimation errors, which affect the human–robot parallel kinematic chain, (2) non-rigid human–robot connections and (3) uncertainty associated to the position of fastening points. The aim of this work is to validate the human joints kinematics estimated by the robot (RK) using that provided by inertial measurement units (IK) as reference. Methods:Ahealthy subject (male, 28 y.o.) walked on a treadmill at 0.55, 0.7 and 0.85 m/s wearing the robot. Four inertial measurement units (IMUs – Xsens, MTX, sampling frequency 50 Hz) were attached to the pelvis, thigh, and shank cuffs and to the foot on the right side (Fig. 1). The RK of hip and knee were estimated from the encoders measurements (sampling frequency 200 Hz) using the third-order polynomial approximation of the forward kinematic function derived in [3]. At the beginning of each trial, while the subject was standing (reference configuration), thigh and shank IMUs were mathematically aligned to the pelvis IMU. Hip and knee IK were estimated in terms of sagittal components of the relevant orientation vectors provided by the IMUs. Gait cycles were identified using the acceleration peaks at heel strike. Data from the encoders and IMUs were synchronized using an external trigger. The root mean square deviation (RMSD) between hip and knee RK and IK was computed for the three trials over 10 gait cycles. Results: Representative patterns of hip and knee angles in the sagittal plane (treadmill velocity: 0.55 m/s) are reported. RMSD values averaged over the three different gait speeds were 2.9±0.2◦ for the hip and 4.9±1.2◦ for the knee (mean±sd). In all the trials, maximum discrepancies were found at the peak values (RK peak extension angles were overestimated). Discussion: Non-anthropomorphic robots can offer several advantages in terms of wearability but they may introduce some inaccuracies in the estimation of human joints kinematics. However, results showed that hip and knee RK errors were within levels acceptable in the majority of clinical applications. Moreover, the systematic errors observed can be corrected through a proper calibration of the robot-to-human mapping. The estimate of lower limb kinematics from IMUs integrated in the robotic cuffs could facilitate the control of the robot.

The cost of moving optimally: kinematic path selection.

It is currently unclear whether the brain plans movement kinematics explicitly or whether movement paths arise implicitly through optimization of a cost function that takes into account control and/or dynamic variables. Several cost functions are proposed in the literature that are very different in nature (e.g., control effort, torque change, and jerk), yet each can predict common movement characteristics. We set out to disentangle predictions of the different variables using a combination of modeling and empirical studies. Subjects performed goal-directed arm movements in a force field (FF) in combination with visual perturbations of seen hand position. This FF was designed to have distinct optimal movements for muscle-input and dynamic costs while leaving kinematic cost unchanged. Visual perturbations in turn changed the kinematic cost but left the dynamic and muscle-input costs unchanged. An optimally controlled, physiologically realistic arm model was used to predict movements under the various cost variables. Experimental results were not consistent with a cost function containing any of the control and dynamic costs investigated. Movement patterns of all experimental conditions were adequately predicted by a kinematic cost function comprising both visually and somatosensory perceived jerk. The present study provides clear behavioral evidence that the brain solves kinematic and mechanical redundancy in separate steps: in a first step, movement kinematics are planned; and in a second, separate step, muscle activation patterns are generated.

Modeling the angular capability of the ball joints in a complex mechanism with two degrees of mobility

The paper puts forward a complex linkage mechanism with two degrees of mobility and three kinematic loops, which is used for the guiding (suspension and steering) system of the vehicles. The geometric parameters and the coordinates frames that define the mechanical system are presented, as well as the specific kinematic functions. For this complex mechanical system, the angular capability of the ball (spherical) joints is defined by two angles. The equations for these angles have been determined by matrix algebra tools, considering the transformation matrices between the bodies reference frames. The diagrams of the angular capability of the ball joints, which are represented in angular coordinates, describe the form, orientation and size of the sockets from the spherical casings. Wears, shocks, functional locks or the compromising of the joint strength can occur if scarce sockets are implemented. The risk points, in which the angular parameters have maximum values, have been determined, the simulation being performed for a real system (vehicle).

A stochastic filtering approach to recover strain images from quasi-static ultrasound elastography.

BackgroundModel-based reconstruction algorithms have shown potentials over conventional strain-based methods in quasi-static elastographic image by using realistic finite element (FE) or bio-mechanical model constraints. However, it is still difficult to properly handle the discrepancies between the model constraint and ultrasound data, and the measurement noise.MethodsIn this paper, we explore the usage of Kalman filtering algorithm for the estimation of strain imaging in quasi-static ultrasound elastography. The proposed strategy formulates the displacement distribution through biomechanical models, and the ultrasound-derived measurements through observation equations. Through this filtering strategy, the discrepancies are quantitatively modelled as one Gaussian white noise, and the measurement noise of ultrasound data is modelled as another independent Gaussian white noise. The optimal estimation of kinematic functions, i.e. the full displacement and velocity field, are computed through this Kalman filter. Then the strain images can be easily calculated from the estimated displacement field.ResultsThe accuracy and robustness of our proposed framework is first evaluated in synthetic data in controlled conditions, and the performance of this framework is then evaluated in the real data collected from elastography phantoms and patients with favourable results.ConclusionsThe potential of our algorithm is to provide the distribution of mechanically meaningful strain under a proper biomechanical model constraint. We address the model-data discrepancy and measurement noise by introducing process noise and measurement noise in our framework, and then the mechanically meaningful strain is estimated through the Kalman filter in the minimum mean square error (MMSE) sense.

Recurrent landsliding of a high bank at Dunaszekcső, Hungary: Geodetic deformation monitoring and finite element modeling

Five years of geodetic monitoring data at Dunaszekcső, Hungary, are processed to evaluate recurrent landsliding, which is a characteristic geomorphological process affecting the high banks of the Middle Danube valley in Hungary. The integrated geodetic observations provide accurate three dimensional coordinate time series, and these data are used to calculate the kinematic features of point movements and the rigid body behavior of point blocks. Additional datasets include borehole tiltmeter data and hydrological recordings of the Danube and soil water wells. These data, together with two dimensional final element analyses, are utilized to gain a better understanding of the physical, soil mechanical background and stability features of the high bank. Here we indicate that the main trigger of movements is changing groundwater levels, whose effect is an order of magnitude higher than that of river water level changes. Varying displacement rates of the sliding blocks are interpreted as having been caused by basal pore water pressure changes originating from shear zone volume changes, floods of the River Danube through later seepage and rain infiltration. Both data and modeling point to the complex nature of bank sliding at Dunaszekcső. Some features imply that the movements are rotational, some reveal slumping. By contrast, all available observational and modeling data point to the retrogressive development of the high bank at Dunaszekcső. Regarding mitigation, the detailed analysis of three basic parameters (the direction of displacement vectors, tilting, and the acceleration component of the kinematic function) is suggested because these parameters indicate the zone where the largest lateral displacements can be expected and point to the advent of the rapid landsliding phase that affects high banks along the River Danube.

Anterior Referencing versus Posterior Referencing in Total Knee Arthroplasty

Appropriate femoral component positioning and sizing is essential for proper kinematic function in total knee arthroplasty (TKA). Anterior or posterior referencing (AR or PR) are two major techniques for setting center of rotation and for balancing the sagittal plane of the arthroplasty. Both techniques have advantages and disadvantages. Minimally invasive surgical (MIS) TKA has added yet another aspect to intraoperative techniques and postoperative outcomes. A total of 100 consecutive patients undergoing unilateral MIS TKA were prospectively randomized to either AR or PR. Knee Society Scores, range of motion, SF-12, and strength testing by Cybex dynamometer were evaluated at standardized intervals postoperatively for 2 years. There were no statistically significant differences in surgical (incision length, surgical release, blood loss, surgical time, and length of stay) or clinical outcomes between two groups at all postoperative intervals (2 and 6 weeks, 3 and 6 months, and 1 and 2 years). Results demonstrate that both AR and PR are effective and can be used successfully during MIS TKA.

Evaluating lower-limb asymmetry in acl-patients: assesment of jumping performance and mechanical muscle function

Introduction: The ratio between the operated and nonoperated leg is typically used to distinguish between normal or abnormal test scores in knee patients (1). Traditionally, the asymmetry ratios are investigated by use of functional tests (i.e. one-leg jump for distance). However, mechanistic outcomes such as kinematic/kinetic data and isolated muscle force/power output may provide further insight into the origin of between-limb asymmetry. The study aim was to investigate differences in asymmetry ratios of unilateral jumpperformance bymeans of kinetic and kinematic analysis andmechanicalmuscle function in ACL-patients and healthy controls. Patients/materials and methods: This case-control study was performed in 23 ACL-reconstructed men (mean age: 27.2 ± 7.5 years and BMI: 25.4 ± 3.2) 18-30 month post-surgery and 25 healthy matched controls (mean age: 27.2 ± 5.4 years and BMI: 24.1 ± 1.8). Patients and controls performed (i) bilateral maximal counter movement jumps (CMJ) with each leg positioned on a separate force plate and (ii) maximal single-leg CMJs. Kinematic data were synchronously recorded by a 6 cameraViconMX system. Subsequently, center of mass jump height (JH), unilateral knee joint range of motion (ROM), unilateral peak (Mpeak) and mean sagittal knee moment (Mmean) were analyzed for the concentric phase, (iii) one-leg maximal jump for distance was performed [1], and (iv)maximal unilateral isometric knee extensor and flexor strength (MVC)weremeasuredusing stabilizeddynamometry [2]. Asymmetry ratios were calculated as operated/non-operated leg for ACLpatients, and non-dominant/dominant leg for controls. Good-tomoderate test-retest reliability has been reported for all measured variables [3]. Differences in asymmetry ratios were evaluated by student’s t-tests using a 0.05 level of significance. Results: No differences in age or BMI were observed between groups. CMJ:Asymmetry ratios for knee jointROMdiffered (p<0.01) between patients and controls in both types of CMJ (96.1% vs. 102.6% and 87.0% vs. 99.9% in bilateral and single-leg CMJs, respectively). Jump for distance: Patients demonstrated greater (p<0.01) asymmetry for jump length (92.9% vs. 98.6%). MVC: Asymmetry in hamstring MVC was greater (p<0.001) for patients than controls (77.4% vs. 101.3%). Discussion & conclusions: ACL patients showed reduced function of the operated leg 18-30 month post ACL-reconstruction for knee ROM, singleleg jump for distance and hamstring MVC. The most prominent reduction was observed for maximal hamstring muscle strength. This finding has significant clinical implications since the hamstring muscles are important protagonists to the ACL [4,5], with reduced hamstring MVC thus representing a potential risk factor for secondary ACL-rupture.

Application and theoretical analysis of C/SiC composites based on continuum damage mechanics

Based on the thermodynamic theory, an orthotropic damage constitutive model was developed to describe the nonlinear mechanical behavior of C/SiC composites. The different nonlinear kinematic and isotropic hardening functions were adopted to describe accurately the damage evolution processes. The damage variables were defined with the damaged modulus and the initial undamaged modulus on energy equivalence principle. The initial orthotropy and damage coupling were presented in the damage yield function. Tensile and in-plane shear loading and unloading tests were performed, and a good agreement between the model and the experimental results was achieved.

Reconfiguration Modules Based Displacement Group Propagation

This paper investigates a metamorphic mechanism that can be decomposed and expressed by group chain corresponding to the kinematic equivalence leading to equivalent kinematic function but with different configurations. The metamorphic process is implemented through metamorphic module combinations and corresponding reconfiguration operations. However, metamorphic module is a constitution of a group using intrinsic geometrical entities instead of frame-dependent motion matrices and considering the available kinematic pair structures, which has potential ability to degenerate as inherent components. Moreover, the kinematic sequencing can set up a model for metamorphic configuration characteristics and the topology variation can be operated by metamorphic module variation with the displacement group transformation and propagation. A metamorphic mechanism can be converted into various topological configurations with respect to kinematic metamorphosis of joints and links in terms of metamorphic modules based on set theoretic.

Automated Design of Mechanical System for Generating Alternate Mechanism Concepts

An automated design approach for combined mechanical system is presented in this paper. The mechanical system can be generated by combining mechanical units, in particularly, generate alternate mechanism concepts. Beginning with kinematic functions as the input and output of mechanism unit, which are presented as the input and output vectors. And then, equations are defined according to the input and output functional characteristic vectors. Meanwhile, the functional transition can also be established by motion relationship between the inputs and the outputs of combined system. And then, the combination models (series and parallel combined patterns) are provided from the different combination patterns. Additionally, the properties of the different combination are intensively researched and the decomposition rules. By manipulating the matrices and the vectors, a given task can be decomposed into sub-functions. An example is given to show the application of the concept.