Kinematic Approach Research Articles

Design and implementation of a 7-DOF cable-driven serial spray-painting robot with motion-decoupling mechanisms

This paper presents the design and implementation of a 7-DOF cable-driven serial spray-painting robot (CDSSR) featuring motion-decoupling mechanisms and introduces an improved non-singular inverse kinematics method for redundant serial robots. In the study, first, the motion-coupling characteristics of cable-driven joints and motion-decoupling methods based on translational and rotational compensation were examined. Next, the mechanical structure of the CDSSR was designed, including motion-decoupling mechanisms, cable-driven differential wrists, and tension-amplification mechanisms. In addition, an improved non-singular inverse kinematics approach incorporating dual-arm angles and configuration control parameters was developed. Finally, an experimentally scaled prototype of the proposed robot was constructed, and motion decoupling and spray trajectory planning experiments were conducted. The experimental and simulation results demonstrate the effectiveness of the non-singular inverse kinematics method in achieving efficient inverse kinematics solutions under global configuration control. Furthermore, the motion decoupling mechanisms designed for the serial robot successfully accomplished motion decoupling.

Limit analysis on roof failure mechanism of tunnels subjected to sequential excavations

Compared to traditional full-face excavation methods, sequential excavation methods (SEM), such as central diaphragm (CD) and sidewall drift (SD) methods, can significantly reduce rock disturbance and minimize the extent of roof failure in tunnel crowns. Therefore, they are particularly suitable for tunnel projects in weak rock formations and large cross-sectional underground chambers. This paper presents a kinematic approach to predict the roof failure mechanism of tunnels excavated using the CD method. The collapse blocks at the top are influenced by excavation steps and initial in-situ stresses, and the direction of their failure velocity field is typically non-vertical, posing challenges for limit analysis applications. To address this, a tilted velocity field for the collapse failure of the tunnel crown in the CD method is constructed based on the initial normal stress distribution along the tunnel’s top contour, obtaining an upper bound solution for tunnel collapse failure. The proposed method is compared with the full-face excavation method, demonstrating the superiority of the CD method over the full-section method. The rationality of the proposed tilted velocity field mechanism is verified through numerical validation using finite difference methods. Building upon the upper bound solution, safety assessment indicators for tunnels excavated using the CD method, namely allowable rock stress release and safety factor, are proposed. Furthermore, we extend this method to analyze the roof failure mechanism in tunnels constructed using the SD method and confirm its effectiveness through comparison with FDM analysis. Theoretical analysis and numerical validation both indicate that sequential excavation methods can significantly reduce the potential collapse range at the top and improve the safety of tunnel construction.

A pelvic kinematic approach for calculating hip angles for active hip disarticulation prosthesis control

BackgroundControl system design for a microprocessor-controlled hip–knee–ankle–foot (HKAF) prosthesis is a challenge since hip disarticulation amputees lack the entire leg and, therefore, only have pelvis movement as user-guided input. This research proposes a method for determining hip joint angles from pelvis movement in a control system for the next generation of powered prostheses.MethodThree-dimensional pelvic motion and stance time of 10 transfemoral (TF) prosthetic users were used to identify important features and to develop an algorithm to calculate hip angles from pelvis movement based on correlation and linear regression results. The algorithm was then applied to a separate (independent) TF group to validate algorithm performance.ResultsThe proposed algorithm calculated viable hip angles during walking by utilizing pelvic rotation, pelvic tilt, and stance time. Small angular differences were found between the algorithm results and motion capture data. The greatest difference was for hip maximum extension angle (2.5 ± 2.0°).ConclusionsSince differences between algorithm output and motion data were within participant standard deviations, the developed algorithm could be used to determine the desired hip angle from pelvis movements. This study will aid the future development of gait control systems for new active HKAF prostheses.

A study of kinematic viscosity approach with air as a gas medium for turbine flowmeter calibration

Calibrating a gas flowmeter requires a suitable working medium that represent its use in the real operating condition. However, factors like installation conditions, costs, and safety considerations may necessitate to utilize a different medium for calibration. The accuracy of measuring fluid flow by a flowmeter is greatly influenced by the kinematic viscosity property of the gas medium. In this particular study, a turbine flowmeter for compressed natural gas (CNG) application was calibrated using air as a substitute with an approach that simulated the kinematic viscosity property of CNG. Here, the pressure and temperature of the air were calculated to achieve the same kinematic viscosity value as CNG during the calibration process, which was accomplished by adjusting the setting of a regulating instrument in the calibration installation. Furthermore, argon (Ar) was also used for comparison with air, with a modification in working pressure to attain similar kinematic viscosity properties for both gases. The calculation results showed that the working pressure setting for the air used was 4.5 bars, while for argon was 3.38 bars to achieve similar kinematic viscosity. By utilizing air instead of CNG, a minimum and maximum volume flowrate difference of −0.0242 m3/h and 0.0016 m3/h, respectively, was observed, with an absolute average of 0.0086 m3/h or 0.8 %. This study reveals the effectiveness of the kinematic viscosity approach in calibrating a turbine flowmeter under working pressure of up to 4.5 barg. This process results in uncertainty measurement of under 1 % when calibrating gas flowmeters, using air as the medium.

Discretization-based kinematic approach for three-dimensional trench stability under slurry support in multilayered ground

Discretization-based kinematic approach for three-dimensional trench stability under slurry support in multilayered ground

Design and Kinematic Modeling of a Soft Continuum Telescopic Arm for the Self-Assembly Mechanism of a Modular Robot.

In recent years, the development of mining robots has grown significantly, offering improved efficiency and safety in hazardous environments. However, there is still room for improvement in adaptability, scalability, and overall performance. The ROBOMINERS project, funded by the European Union's Horizon 2020 Research and Innovation Program, aims to facilitate Europe's access to mineral resources applying disruptive robotic concepts. One such concept is resilience, which can be achieved providing modular mining robots with the ability to reconfigure during operation. To address this challenge, this article presents the development and kinematic modeling of a soft, telescopic, continuum arm integrated into a modular robot. The arm serves as a mechanical interface for coupling different robotic modules or tools following the principle of the car crane. With a fully 3D-printed design, the arm features two sections of variable length that are driven by an innovative actuation method based on soft racks. It provides a 6 degrees of freedom (DoF) motion. The arm kinematic models are obtained by backbone parameterization assuming constant curvature and independent bending between sections for forward kinematics and applying a machine learning-based approach for inverse kinematics. The models are validated through the evaluation of two trajectories, measuring the deviation in each DoF and rack extension. Furthermore, a demonstration of the arm's coupling procedure between two robotic modules and one possible configuration of the robotic system showcases its functionality.

TECTONIC STRESSES IN THE CHERSKY FAULT ZONE (BAIKAL RIFT SYSTEM

Based on the kinematic and structural-paragenetic approaches, there were performed the reconstructions of tectonic stresses in the Chersky fault zone. Rank analysis as applied to specialized mapping of fault zones was made for heterochronous rock complexes: Paleozoic, Upper Oligocene – Lower Pliocene and Upper Pliocene – Quaternary. There are distinguished three regional stress fields: Pre-Cenozoic compressive stress field with the NW-SE striking principal axis and two Cenozoic tensile stress fields with different axial orientations. The Cenozoic tensile stress field with a sub-meridionally striking minimum compression axis may be an earlier occurrence because it was found to exist in the Paleozoic and Oligocene – Early Pliocene rocks, and the tensile stress field, with the NW-SE axial orientation, may be later occurrence as reconstructed for all rock complexes including Quaternary pebbles. No evidence was found of tectonic shear stresses within the studied segment of the Chersky fault zone. Consideration is being given to probable reasons for the absence of residual shear deformations in the region and to the problems in the study of hierarchy of the upper crustal tectonic stresses.

Roof stability analysis of cylindrical tunnels in hard soil/soft rock with reduced tension strength

Three-dimensional roof stability analyses of cylindrical tunnel segments limited along the tunnel direction were performed based on the modified Mohr–Coulomb failure criterion with reduced tensile strength. A wedge-shaped region of the classical Mohr–Coulomb envelope, where unrealistic tensile and shear strengths are predicted, is truncated by a Mohr circle associated with the true tensile strength. This revised failure criterion with partial nonlinearity allows geomaterials deep into the roof to deform with large velocity gradients under the normality plastic flow rule, observed in field investigations. Using the kinematic approach of limit analysis, rigorous bounds for three quantitative stability measures–stability number, factor of safety, and supporting pressure–were calculated. The roof failure mechanism adopted is relatively elaborate, involving three-dimensional geometry intersecting with a cylindrical tunnel segment; thus, an efficient approach was presented for tunnels with long length constraints. With respect to extremely short tunnel lengths, a modified roof failure mechanism with distinct ridges was proposed. The factor of safety with accommodation of the nonlinear pressure dependency was estimated by a consistent procedure associated with a reduced elliptic failure criterion. The results show that roof stability distinctly depends on the magnitude of the true tensile strength, internal friction angle, and length constraint.

A multibody kinematic system approach for the design of shape-morphing mechanism-based metamaterials

Shape-morphing structures have the ability to adapt to various target shapes, offering significant advantages for many applications. However, predicting their behavior presents challenges. Here, we present a method to assess the shape-matching behavior of shape-morphing structures using a multibody systems approach wherein the structure is represented by a collection of nodes and their associated constraints. This representation preserves the kinematic properties of the original structure while allowing for a rigorous treatment of the shape-morphing behavior of the underlying metamaterial. We assessed the utility of the proposed method by applying it to a wide range of 2D/3D sample shape-morphing structures. A modular system of joints and links was also 3D printed for the experimental realization of the systems under study. Both our simulations and the experiments confirmed the ability of the presented technique to capture the true shape-morphing behavior of complex shape-morphing metamaterials.

Use of the 3D Equilibrium Equations in the Free-Edge Analyses for Laminated Structures with the Variable Kinematics Approach

This paper compares out-of-plane stresses evaluated with Hooke’s Law and the stress recovery technique, focusing on the free edges of composite plates and shells. The Carrera Unified Formulation and the finite element method are adopted to derive the governing equations. Lagrange polynomials are implemented in the equivalent single-layer, layer-wise, and variable kinematics approaches. The latter is used to refine structural models locally and reduce computational overheads. Laminated plates and shells subjected to uniaxial tension are considered. The out-of-plane stresses are compared with references from the existing literature for most cases. The results demonstrate that the stress recovery technique effectively calculates stresses and improves the accuracy of equivalent single-layer models. Furthermore, layer-wise models are needed for accurate results near the free-edge zone. Finally, variable kinematics theories are helpful in accurately detecting local phenomena along the structure’s thickness.

PPP-RTK with Rapid Convergence Based on SSR Corrections and Its Application in Transportation

Real-time Kinematic (RTK) positioning provides centimeter-level positioning accuracy within several seconds, but it has to rely on a nearby base station. Although Precise Point Positioning (PPP) supplies precise positions with one receiver, its convergence time takes several tens of minutes, which makes PPP not well suited for real-time kinematic applications where a rapid convergence is required. PPP-RTK integrates the benefits of PPP and RTK, which actually is PPP augmented by a ground GNSS network. The satellite orbit, clock offsets, signal biases, ionospheric and tropospheric corrections are determined based on this GNSS network, modeled as state space information and transmitted to PPP users. By applying these State Space Representation (SSR) corrections, a real-time kinematic PPP-RTK approach is developed and implemented, which can instantly resolve the ambiguities to integers and realize rapid convergence. In a static scenario, it realized an instant ambiguity resolution and a rapid convergence within 2 s in more than 90% of 120 hourly sessions. The PPP-RTK has been applied and evaluated in a kinematic scenario on the highway. The horizontal positioning errors are almost lower than 0.1 m except for the time of passing through bridges. After passing bridges, the PPP-RTK successfully resolved ambiguities within 2 s in 90.6% of the cases and achieved convergence in horizontal within 5 s in more than 90% of the cases. The PPP-RTK with a precision of 0.1 m and rapid convergence of several seconds benefits the precise navigation of automobile on the highway, which will support the development of autonomous driving in future.

Stability assessment of a non-circular tunnel face with tensile strength cut-off subject to seepage flows: A comparison analysis

This work aims to develop a numerical-analytical framework within the kinematic approach of limit analysis to assess the stability of non-circular tunnel faces under seepage conditions with tensile strength cut-off from a discretization-based perspective. Considering the overestimation of the tensile strength of the soil by the Mohr-Coulomb criterion, a modification based on the concept of tensile strength cut-off is recommended to reduce or eliminate the tensile strength. A modified 3D rotational discretization-based failure mechanism incorporating the tension cut-off is generated point-to-point starting from a real non-circular tunnel face to model the face failure, where the failure surface on the top intersects more rapidly due to the increasing rupture angle in the tensile regime. The seepage towards the non-circular tunnel face is numerically simulated, and then the numerical seepage field is extracted into the 3D discretization-based failure mechanism. Within the kinematic approach, the seepage effect is introduced from two aspects: pore pressure and seepage force. A hybrid optimization routine is employed to search for the maximum required face pressure. The developed framework is validated by comparisons with numerical fluid-mechanical simulations and previous studies. Afterward, parametric analyses are carried out on different seepage conditions, different face pressure distributions, different soil strengths, and different tension cut-off conditions. The developed framework can give insight into the combined effect of the tension cut-off and seepage on the stability of non-circular tunnel faces under various conditions.

How can saddle height changes the risk injuries of lumbar during the cycling: Kinematics and musculoskeletal modeling approach

How can saddle height changes the risk injuries of lumbar during the cycling: Kinematics and musculoskeletal modeling approach

Learning human inverse kinematics solutions for redundant robotic upper-limb rehabilitation

This paper proposes a real-time human inverse kinematics approach based on the Gaussian Process (GP) to address the open problem of finding appropriate inverse kinematic solutions for upper-limb rehabilitation using redundant robotic exoskeletons. The proposed approach is validated using recorded data from a Motion Capture (MoCap) system and is shown to achieve accurate and unique upper-limb natural solutions for different rehabilitation exercises. This approach is a computationally tractable alternative to existing solutions, which are not always feasible and unsuitable for real-time rehabilitation tests, as they are based on optimizing discomfort indices online or computationally demanding learning methods. A comparison with existing inverse kinematics solutions confirms the superior performance of the proposed approach. Additionally, a robust Model Predictive Control (MPC) with an Integral Sliding Mode (ISM) combination is proposed for safe trajectory tracking during rehabilitation exercises. Several real-time experiments were conducted on a 7-DoF exoskeleton robot with and without the presence of a healthy subject to verify the effectiveness of the proposed methods.

Enhancing Kinematic Calibration Accuracy for Parallel Manipulators Based on Truncated Total Least-Square Regularization

Abstract This article proposes a novel kinematic calibration approach to address the ill-conditioned identification matrix problem and enhance the accuracy of parallel manipulators (PMs). The kinematic calibration approach applies the truncated total least-square (T-TLS) regularization method to the inverse kinematic calibration of PMs and does not have the unit inconsistency issue and configuration selection issue. The performance of the T-TLS method in the inverse kinematic calibration of PMs that have the ill-conditioned identification matrix problem is compared to that of classical regularization methods, including the truncated singular value decomposition (TSVD) method and Tikhonov method, in simulations. Then, the kinematic calibration approach is applied to a 3-PSS/S spherical PM prototype in the real world. For the 3-PSS/S spherical PM prototype, the kinematic calibration approach can reduce the absolute angular errors of the end-effector from over 1.0 deg before calibration to less than 0.1 deg after calibration.

Kinematical Approach to the Drilling Mechanisms for n-Sided Polygonal Holes

Abstract The present analysis addresses the generation of regular polygonal paths with any number of sides, odd or even, by use of special rotors revolving with uniquely prescribed motions inside fixed polygonal holes of guidance, which may be coincident or similar to the paths to be traced. The whole rotation motion of the rotor is considered composed of a sequence of Cardan motions so that the active profile of contact is formed by a polycentric sequence of circular arcs. It is shown and proved that the guidance polygon and the target polygon may coincide in the hypothesis of an odd number n of sides, whereas the guidance profile must be larger than the one to be generated for n even, in which case two equal concentric polygons rotated of π/n between each other may be simultaneously generated by two particular points of the rotors. These devices are very useful to drill blind polygonal holes, providing the rotors of proper cutting tools and driving them by constant-speed motors through homokinetic joints.

Continental block motion in the Northern Andes from GPS measurements

SUMMARYNorthwestern South America is a plate boundary zone where the Nazca, Caribbean and South American plates interact to produce a wide area of active continental deformation from the Gulf of Guayaquil (latitude 3°S) to Venezuela. Previous studies have identified a ∼2000-km-long continental sliver, referred as the North Andean Sliver (NAS), squeezed between the Nazca, Caribbean and South American plates and escaping at ∼1 cm yr−1 northeastward with respect to South America. Subduction of the Nazca Plate beneath the NAS has produced a sequence of large and great earthquakes during the 20th century along the coast of Ecuador and Colombia. Large crustal earthquakes up to magnitude 7.7 have been documented along the proposed eastern boundary of the NAS. However, active tectonics data, historical and recent earthquakes all indicate active fault systems within the NAS, possibly resulting from the interaction of several tectonic blocks. Here, we derive an extensive horizontal velocity field using continuous and episodic GNSS data from 1994 to 2019.9, covering northern Peru, Ecuador, Colombia, Panama and Venezuela. We model the GNSS velocity field using a kinematic elastic block approach that simultaneously solves for rigid tectonic block rotations and interseismic coupling along the subduction interfaces and along major crustal faults. In contrast to previous results that considered a single rigid NAS, our dense GNSS velocity field demonstrates that the NAS undergoes significant internal deformation and cannot be modelled as single rigid block. We find that block kinematics in the northern Andes are well described by the rotation of 6 tectonic blocks, showing increasing eastward motion from south to north. The Eastern boundary of the sliver is defined by a right-lateral transpressive fault system accommodating 5.6–17 mm yr−1 of motion. Fragmentation of the NAS occurs through several fault systems with slip rates of 2–4 mm yr−1. Slow reverse motion is found across the sub-Andean domain in Ecuador and northern Peru at 2–4 mm yr−1, marking a transitional area between the NAS and stable South America. In contrast, such a transitional sub-Andean domain does not exist in Colombia and western Venezuela. At the northwestern corner of Colombia, fast (∼15 mm yr−1) eastward motion of the Panama block with respect to the NAS results in arc-continent collision. We propose that the Uramita fault and Eastern Panama Deformed Zone define the current Panama/NAS boundary, accommodating 6 and 15 mm yr−1 of relative motion, respectively. A fraction of the Panama motion appears to transfer northeastward throughout the San Jacinto fold belt and as far east as longitude ∼75°W. Along the Caribbean coast, our model confirms, slow active subduction at ∼4.5 mm yr−1 along the South Caribbean Deformed Belt offshore northern Colombia and a relatively uniform rate of ∼1–2 mm yr−1 offshore northern Venezuela. Along the Nazca/NAS subduction interface, interseismic coupling shows a first-order correlations between highly locked patches and large past earthquake ruptures. These patches are separated by narrow zones of low/partial coupling where aseismic transients are observed. Compared to previous studies, our interseismic coupling model highlights the presence of deep coupling down to 70 km in Ecuador.

Data-driven hyperelasticity, Part I: A canonical isotropic formulation for rubberlike materials

Data-driven hyperelasticity shows great promise for modeling the mechanical response of rubberlike materials. It enables an automated linkage between experimental data and mechanical response without a priori knowledge of specific analytical expression for the strain energy density function or the stress expression. In this study, we propose a new data-driven approach with three distinct kinematic approaches; (i) invariant-based formulation, (ii) modified invariant-based approach, and (iii) principal stretch-based formulation to model the hyperelastic response of rubberlike materials. Within this context, we replace the partial derivatives of the strain energy density functions with appropriate B-spline interpolations, using a set of control points to implement various multiaxial loading scenarios, such as uniaxial tension, pure shear, and equibiaxial tension deformations. To ensure a polyconvex and stable constitutive response, we enforce the polyconvexity requirement into the B-spline interpolation along with appropriate normalization conditions. In order to obtain the control points of the B-splines, we train the proposed data-driven approach with respect to the Treloar and Kawabata datasets. On the numerical side, the stress and moduli expressions are derived for the finite element implementation. The predictive capabilities of the proposed approach are demonstrated through representative boundary value problems.

Generalised Known Kinematics (GKK): an approach for kinematic observables in pair production events with decays involving invisible particles

Missing kinematic information of known invisible particles, such as neutrinos, limit several high-energy physics analysis. The undetected particle carries away momentum and energy information, preventing the total reconstruction of such an event. This paper presents a new method to handle this missing information, referred to as the Generalised Known Kinematics (GKK) approach. Its event-by-event probability density distributions that describe the physically allowed kinematics of an event. For GKK, we consider the available kinematic information and constraints given by the assumed final state. Summing these event-wise distributions over large data sets allows the determination of parameters that influence the event kinematics. Examples are particle masses obscured by the missing information on the invisible final-state particles. The method is demonstrated in simulation studies with τ+τ− events in e+e− collisions at the Υ (4S) resonance, presenting a new, promising approach for measuring the τ lepton mass.

Application of Leak 2D to Describe Preferential Water Flow in a Soil Containing Artificial Macropores

Leak 2D is a new two-dimensional dual permeability mathematical model for the simulation of the preferential flow in the vadose zone. In this model, water flow in the soil matrix domain is described by the two-dimensional h-based Richards’ equation. Water flow in the fracture domain is estimated using the kinematic wave approach. Richards’ equation is solved by a combination of the alternating direction implicit (A.D.I.) method and the Douglas and Jones predictor−corrector method. The kinematic wave equation is solved explicitly. In the present paper, Leak 2D is calibrated and validated with data obtained in a Hele–Shaw apparatus filled with sand. Preferential flow is achieved by inserting four artificial macropores of various sizes into the soil. Six irrigations of various intensities and durations were used for the calibration and validation process. The water content at various depths was recorded by five sensors that were inserted into the soil. A comparison of the simulated water content with the measured profiles shows that Leak 2D can sufficiently describe preferential flow into the unsaturated zone of the soil, even under extreme irrigation conditions.