Simple Kinematic Research Articles

Simple Inverse Kinematics Computation Considering Joint Motion Efficiency.

Inverse kinematics (IK) is an important and challenging problem in the operation of industrial manipulators. This study proposes a simple IK calculation scheme for an industrial serial manipulator. The proposed technique can calculate appropriate values of the joint variables to realize the desired end-effector position and orientation while considering the motion costs of each joint. Two scalar functions are defined for the joint variables: one is to evaluate the end-effector position and orientation, whereas the other is to evaluate the motion efficiency of the joints. By combining the two scalar functions, the IK calculation of the manipulator is formulated as a numerical optimization problem. Furthermore, a simple algorithm for solving the IK via the aforementioned optimization is constructed on the basis of the simultaneous perturbation stochastic approximation with a norm-limited update vector (NLSPSA). The proposed scheme considers not only the accuracy of the position and orientation of the end-effector but also the efficiency of the robot movement. Therefore, it yields a practical result of the inverse problem. Moreover, the proposed algorithm is simple and easy to implement owing to the high-calculation efficiency of NLSPSA. Finally, the effectiveness of the proposed method is verified through numerical examples using a redundant manipulator.

Kinematic Source Properties of the 2023 Mw 7.7 Türkiye Earthquake Inferred from Near-Fault Strong Ground Motions

Abstract The 2023 Mw 7.7 Türkiye earthquake provided densely observed near-fault ground-motion data, which enabled us to investigate their characteristics and generations. This study aimed to obtain an intuitive understanding of the characteristics of near-fault strong ground motions and their relationship with kinematic source properties using a simple source model. Synthetic ground motions were calculated using the discrete wave number method and compared with observed ground motions. The observed strong motions were used after a time correction based on the first P-wave arrival. Results showed that near-fault pulse-like velocities (0.02–0.6 Hz) were generally explained by the simple kinematic source model that assumed a continuous rupture propagation along the faults. Comparisons at individual sites indicate the various rupture properties of the fault segments. Near-fault ground motions along the Narli segment were explained by the fault plane along the surface trace and not by aftershock distribution. A supershear rupture propagation speed is necessary for a part of the Amanos segment. Rupture stops and restarts were implied near the stepover along the Amanos segment. Empirical site factors estimated by generalized inversion techniques did not show peaks around the frequency of observed large velocity pulses, indicating that the velocity pulses were mainly generated by the source. The model bias and uncertainties were also examined to supplement the simplified subsurface structure used in the simulation. Our results will help to associate the qualitative and quantitative aspects of the kinematic source process with near-fault strong ground motions.

Computer-aided design and optimization of a multi-level fruit catching system for fresh-market fruit harvesting

Tree fruit harvesting is a labor-intensive operation. Multi-level fruit catching and retrieval (MFCR) systems have been proposed for the mass harvesting of soft fruits using trunk shaking. However, overcoming excessive fruit damage as fruits fall through the canopy is very challenging and requires optimization of several aspects of an MFCR’s design. In this work, we present a novel computer-aided design approach for optimizing design parameters of MFCR systems. A simplified index that utilizes geometry and simple mechanics is developed to quantify the interference between an MFCR’s catching booms and tree branches. Also, an index is introduced that utilizes geometry and simplified collision kinematics to represent accumulated damage on fruits falling through the canopy. These two indices are used in a case study to determine the optimal solution – and its sensitivity – for the number of layers of an MFCR system that maximizes marketable fruit collection over twenty digitized pear trees. In conjunction with more elaborate machine-tree-fruit interaction models, the proposed methodology can be used to optimize the design of fresh-fruit mass harvesters that utilize multi-level catching and retrieval systems.

Koiter–Newton Reduced-Order Method Using Mixed Kinematics for Nonlinear Buckling Analysis

The Koiter–Newton method improves the computational efficiency of nonlinear buckling analysis; however, the construction of reduced-order models using fully nonlinear kinematics is still a tedious and time-consuming work. In this paper, the Koiter–Newton reduced-order method using mixed nonlinear kinematics is presented for the geometrically nonlinear buckling analysis of thin-walled structures. Strain energy variations up to the fourth order were achieved using mixed kinematics for the improved Koiter theory. Corotational kinematics, which is inconvenient for high-order variations, was applied to calculate the first- and second-order variations for the internal force and tangent stiffness, respectively, whereas the third- and fourth-order strain energy variations were facilitated by explicit algebraic formulations using updated von Kármán kinematics. A reduced-order model with 1+m degrees of freedom was established, of which m perturbation loads were considered to make the method applicable for buckling problems. The geometrically nonlinear response was traced using a predictor–corrector strategy by combining the nonlinear prediction solved by the reduced-order model and the correction using Newton iterations. Numerical examples of structures with various buckling behaviors demonstrate that the performance of the proposed method is not obviously affected by using simplified kinematics, and sometimes it even exhibits a superior capability for path-following analysis.

Adaptive hierarchical origami-based metastructures

Shape-morphing capabilities are crucial for enabling multifunctionality in both biological and artificial systems. Various strategies for shape morphing have been proposed for applications in metamaterials and robotics. However, few of these approaches have achieved the ability to seamlessly transform into a multitude of volumetric shapes post-fabrication using a relatively simple actuation and control mechanism. Taking inspiration from thick origami and hierarchies in nature, we present a hierarchical construction method based on polyhedrons to create an extensive library of compact origami metastructures. We show that a single hierarchical origami structure can autonomously adapt to over 103 versatile architectural configurations, achieved with the utilization of fewer than 3 actuation degrees of freedom and employing simple transition kinematics. We uncover the fundamental principles governing theses shape transformation through theoretical models. Furthermore, we also demonstrate the wide-ranging potential applications of these transformable hierarchical structures. These include their uses as untethered and autonomous robotic transformers capable of various gait-shifting and multidirectional locomotion, as well as rapidly self-deployable and self-reconfigurable architecture, exemplifying its scalability up to the meter scale. Lastly, we introduce the concept of multitask reconfigurable and deployable space robots and habitats, showcasing the adaptability and versatility of these metastructures.

Assessment of stabilizing feedback control of walking: A tutorial

Walking without falling requires stabilization of the trajectory of the body center of mass relative to the base of support. Model studies suggest that this requires active, feedback control, i.e., the nervous system must process sensory information on the state of the body to generate descending motor commands to the muscles to stabilize walking, especially in the mediolateral direction. Stabilization of bipedal gait is challenging and can be impaired in older and diseased individuals. In this tutorial, we illustrate how gait analysis can be used to assess the stabilizing feedback control of gait. We present methods ranging from those that require limited input data (e.g. position data of markers placed on the feet and pelvis only) to those that require full-body kinematics and electromyography. Analyses range from simple kinematics analyses to inverse dynamics. These methods assess stabilizing feedback control of human walking at three levels: 1) the level of center of mass movement and horizontal ground reaction forces, 2) the level of center of mass movement and foot placement and 3) the level of center of mass movement and the joint moments or muscle activity. We show how these can be calculated and provide a GitHub repository (https://github.com/VU-HMS/Tutorial-stabilizing-walking) which contains open access Matlab and Python code to calculate these. Finally, we discuss what information on feedback control can be learned from each of these.

A finite element implementation of phase-field approach of fracture for nonlinear solid shells including inelastic material behavior

The parametrization of shell structures using the so-called solid shell concept has been widely exploited in the last decades. This trend is mainly attributed to the relatively simple kinematic treatment of solid shells in the corresponding finite element formulation in conjunction with the use of unmodified three-dimensional material laws, among other aspects. In the present investigation, we provide a comprehensive finite element implementation of solid shells incorporating: (i) the use of Enhanced Assumed Strain (EAS) and the Assumed Natural Strain (ANS) methods to prevent locking issues, (ii) the phase-field approach for triggering fracture events, and (iii) some representative inelastic material models. The current modular implementation has been integrated into the FE package ABAQUS via the user-defined routine UEL. Several representative examples demonstrate the applicability of the present formulation.

Composite continuum robots: Accurate modeling and model reduction

Models of continuum robots often trade off accuracy and speed. The constant curvature assumption model can perform fast calculations but with poor accuracy. Static models can obtain good calculation accuracy but with slower computation speed. In this paper, a precise and efficient method for establishing a non-constant curvature kinematic model for composite continuum robots is proposed. First, an algorithm based on the Beam Constraint Model is proposed to establish the static model of the continuum robot. The situation in which friction changes gradually in continuum robots is considered in the static model. Then, the Kepler elliptic curve is used to simplify the static model to build a non-constant curvature kinematic model of the continuum robot. Then, complex inverse kinematics solutions are transformed into explicit sets of equations by mathematical transformation. Finally, simulations and experiments are designed to demonstrate the algorithm proposed in this paper. The simulation results show that the proposed algorithm is 1572 times faster than the Levenberg–Marquardt algorithm. The experimental results show that the average error of the static model is 0.065 mm, accounting for 0.13% of its length. The maximum error is 0.309 mm, accounting for 0.618% of its length. The positioning accuracy of the non-constant curvature model proposed in this paper is 2.02 times that of the constant curvature model. The results show that the simplified kinematic model algorithm based on the static model has high accuracy and computational efficiency. This research is crucial for the practical application of continuum robots in engineering.

Seismic response of tripod suction bucket foundation for offshore wind turbine considering multidirectional earthquake loads

Tripod suction buckets offer several advantages as offshore wind turbine (OWT) foundations, including cost-effective installation, high stability, and resistance to overturning. In seismically active regions, OWTs experience horizontal and vertical directions seismic excitations. This study employed an advanced three-dimensional nonlinear finite element analysis to investigate the influence of vertical seismic motions on the dynamic behavior of tripod bucket foundations installed in nonhomogeneous clay deposits. By adopting a simple kinematic hardening model to capture the foundation-soil nonlinear dynamic interaction, parametric analyses were conducted to study the effect of vertical seismic motions, considering several earthquake types and undrained shear strengths of the clay deposit. The results show that the influence of the vertical seismic motion on the dynamic response and deformation of the nacelle depends on the dominant frequency of the vertical seismic motion and the overturning resistance capacity of the OWT in different horizontal directions. The deformation mechanisms of an OWT vary with the strengths of the clay deposits. Based on these analyses, this study offers insights into the influence of vertical seismic motions on the dynamic response of tripod suction bucket foundations.

Estimating the mechanical cost of transport in human walking with a simple kinematic data-driven mechanical model.

This work utilizes a simplified, streamlined approach to study the mechanical cost of transport in human walking. Utilizing the kinematic motion data of the center of mass, velocities and accelerations are determined using kinematic analysis; the applied force is then obtained using inverse dynamics. We calculate the mechanical cost of transport per step from both synthetic and measured data, using a very simple mechanical model of walking. The approach studied can serve as an informative gait characteristic to monitor rehabilitation in human walking.

Inverse Differential Quadrature Based Model for Static Behaviour of Variable Stiffness Curved Composite Beams

Recent advancements in fibre placement technologies have expanded the potential applications of variable stiffness curved composite beams in industries such as aerospace, automotive, and naval engineering. Accurate solution techniques for examining these beams, especially those composed of advanced composite materials, are indispensable. In view of this demand, this study proposes a new high-order computational tool that combines the higher-order accuracy of the emerging inverse differential quadrature method (iDQM) and the simple kinematics of the Timoshenko beam theory for efficient and accurate prediction of the static behaviour of both constant stiffness and variable stiffness curved beam structures. This novel application of iDQM to curved beam analysis is leveraged upon its excellent potential to mitigate differentiation-induced errors by using the so-called indirect approximation strategy. Simple procedures for implementing different orders of iDQM models are presented to analyse curved beam problems, and are independently benchmarked against closed-form Navier's solutions, as well as numerical solutions obtained through the differential quadrature method (DQM) and finite element method (FEM), demonstrating excellent spectral accuracy. Furthermore, the iDQM scheme offers outstanding potential in recovering transverse shear stress, achieving superior accuracy over lower-order FEM in approximating higher-order derivatives. Remarkably, iDQM predictions for variable stiffness curved beams exhibit satisfactory agreement with the Strong Unified Formulation, achieving over 98% computational efficiency. Finally, convergence analysis of iDQM solutions reveal up to three orders of improved accuracy and faster convergence rates compared to the DQM, constituting a new benchmark for curved beam analysis.

The multi-sightline compact D-D neutron spectrometers based on CLYC7-scintillator for beam ion anisotropy study in LHD

Abstract Three compact neutron emission spectrometers (CNESs) based on the novel inorganic scintillator Cs2LiYCl6:Ce with 99% 7Li-enrichment (CLYC7) were newly installed in different lines of sight in the Large Helical Device (LHD) to study the anisotropy of the velocity distribution of the beam ions. Neutron energy spectra measurements using multi-sightline CNESs were performed under neutral-beam (NB)-heated deuterium plasma. A significant Doppler shift of the deuterium-deuterium (D-D) neutron energy induced by different NB heating and different lines of sight was observed. The measured peak neutron energies were nearly consistent with those calculated by the simple two-body kinematics of the D-D reaction using the tangency radii of CNESs and NBs. These results demonstrated the capabilities of the CNESs for neutron energy spectra measurements and the study of fast-ion physics in magnetic confinement fusion research.

A discrete model for layered growth

We present a discrete model that captures the fundamental properties of layered deposition in a minimal setting. The model is based on simplified kinematics and allows for the onset of incompatible deformations between discrete layers of a growing stack. Thanks to the discrete nature of the model, we obtain an averaged formulation of mechanical equilibrium for the growing stack, leading to closed-form solutions that are both analytically simple and physically transparent. In particular, we are able to explain the origin of residual stress by the accumulation of incompatible deformations between adjacent layers. The model can also be regarded as an elementary approximation of additive manufacturing. Within this context, we are able to formulate the technologically relevant inverse problem that provides the deposition protocol required to produce a desired state of internal stress in an additively-manufactured stack. Another important aspect analyzed in the work is the role played by an ideal “glue” between the layers, whose presence is fundamental to prevent their sliding and whose mechanical behavior can quantitatively influence the final stress distribution in the stack. The simplicity of the model makes it possible to highlight how the controls exerted during deposition will have qualitative or quantitative effects on the final stress state of the stack.

Contribution to the formability improvement in sheet metal stamping by a novel technique to control press kinetics

The thickness variation during sheet deep drawing process has an impact on the quality of the final product and can lead to local material fractures. To minimize this phenomenon caused by varying degrees of stretching in different areas of the sheet, various methods can be employed. This research paper introduces a novel technique for metal sheet deep drawing, specifically designed for parts with complex geometric shapes that exhibit significant variations in deformation levels across different areas. The objective of this method is to enhance the quality of the deep drawing process by reducing thickness variations in the final part. In this proposed approach, the vertical movement of the punch is accomplished through two vertical rotational movements. This increases the flexibility of the deformation process, ensuring that the active tools elements occupy the most advantageous positions determined by the material flow in the die. As a result, the material's deformability is improved, allowing for a higher degree of deformation. Additionally, this new method offers a relatively simple design and kinematics solutions for the press and eliminates the need for lengthy assembly-disassembly times.

Controlled power distribution mechanisms in the transmission of an integral tractor

The key features of the integral tractor concept are considered. The roles of controlled inter-axle and inter-wheel power distribution mechanisms are analyzed. Variants of the transmission structure are proposed. An example of simplified kinematic diagrams of interaxle and interwheel power distribution mechanisms is considered. Approaches to determining the external parameters of such mechanisms, their control technology, and the technological base for their design and manufacture are proposed.

Basculing in elite show jumping horses: a motion analysis study of trunk and neck movement

Abstract The movement of the trunk and neck plays a crucial role in training and assessing the technical performance in show jumping horses. The term ‘bascule’ describes a rounded and harmonious jumping movement characterised by an arched or bulged back and a lower, stretched neck position. However, there is a lack of consensus in the literature regarding the specific kinematic features that define basculing. The question remains whether the impression of a rounded back is the result of spine flexion into an upward curved position or a combination of thorax elongation and a downward movement of the neck. Additionally, the timing of these movement components remains unclear. To address these questions, we conducted kinematic analyses on six ridden show jumpers with varying levels of competition experience. Using a simplified kinematic model, we analysed the trajectories of the trunk length, trunk height, neck length, and trunk-neck angle throughout different phases of a jump over a single 130 cm vertical fence during a training session. Furthermore, we explored potential differences in basculing execution based on the horses’ competition levels. Our findings indicate that the horses’ body posture while jumping over the fence does not exhibit true flexion of the thoracolumbar spine, resulting in an upward arched shape of the spine. Instead, during the take-off phase, the trunk shows elongation, suggesting a reduced curvature of the spine in this region, accompanied by a downward movement of the neck. However, we consistently observed a shortening of the neck segment, indicating flexion of the cervical spine. Correlation analyses suggest that these changes are associated with the horses’ level of competition, with more pronounced basculing observed in horses with higher competition levels.

Design guidelines for the morphing of stiff lattice materials

Materials and structures with shape morphing capabilities are attractive in aerospace, maritime vehicles and robotics: such systems offer lighter weight, better distributed stresses, simpler kinematics, smaller numbers of actuators and higher reliability. Current morphing materials are either very compliant to achieve large shape changes (metamaterials, compliant mechanisms, hydrogels), or very stiff but with infinitesimal shape changes that require large actuation forces (metallic or composite sandwich panels with piezoelectric actuation). Morphing efficiency and structural stiffness are therefore mutually exclusive properties in current engineering morphing materials, which limit the range of their application. Here we propose a design for a stiff morphing beam made of “meta-elements” with unusual combinations of elastic properties, and which can be actuated from a simple push/pull at the base. To capture the performance of the beam we propose and use three metrics: The “morphing amplitude”, the “morphing compliance” and “structural stiffness”. We develop nonlinear finite elements to explore a wide range of designs, and to show some inevitable tradeoffs of stiffness and morphing. To aid the design of the structure we propose ternary diagrams to select optimum combinations of properties for the meta-elements. Finally, we fabricated and tested three prototypes of stiff morphing beams to validate the approach.

Transport Barriers in Geophysical Flows: A Review

In the Lagrangian approach, the transport processes in the ocean and atmosphere are studied by tracking water or air parcels, each of which may carry different tracers. In the ocean, they are salt, nutrients, heat, and particulate matter, such as plankters, oil, radionuclides, and microplastics. In the atmosphere, the tracers are water vapor, ozone, and various chemicals. The observation and simulation reveal highly complex patterns of advection of tracers in turbulent-like geophysical flows. Transport barriers are material surfaces across which the transport is minimal. They can be classified into elliptic, parabolic, and hyperbolic barriers. Different diagnostics in detecting transport barriers and the analysis of their role in the dynamics of oceanic and atmospheric flows are reviewed. We discuss the mathematical tools, borrowed from dynamical systems theory, for detecting transport barriers in simple kinematic and dynamic models of vortical and jet-like flows. We show how the ideas and methods, developed for simple model flows, can be successfully applied for studying the role of barriers in oceanic and atmospheric flows. Special attention is placed on the significance of transport barriers in important practical issues: anthropogenic and natural pollution, advection of plankton, cross-shelf exchange, and propagation of upwelling fronts in coastal zones.

Genetic Fuzzy Inference System-Based Three-Dimensional Resolution Algorithm for Collision Avoidance of Fixed-Wing UAVs

Fixed-wing Unmanned Aerial Vehicles (UAVs) cannot fly at speeds lower than critical stall speeds. As a result, hovering during a potential collision scenario, like with rotary-wing UAVs, is impossible. Moreover, hovering is not an optimal solution for Collision Avoidance (CA), as it increases mission time and is innately fuel-inefficient. This work proposes a decentralized Fuzzy Inference System (FIS)-based resolution algorithm that modulates the point-to-point mission path while ensuring the continuous motion of UAVs during CA. A simplified kinematic guidance model with coordinated turn conditions is considered to control the UAVs. The model employs a proportional-derivative control of commanded airspeed, bank angle, and flight path angle. The commands are derived from the desired path, characterized by airspeed, heading, and altitude. The desired path is, in turn, obtained using look-ahead points generated for the target point. The FIS aims to mimic human behavior during collision scenarios, generating modulation parameters for the desired path to achieve CA. Notably, it is also scalable, which makes it easy to adjust the algorithm parameters, as per the required missions, and factors specific to a given UAV. A genetic algorithm was used to optimize FIS parameters so that the distance traveled during the mission was minimized despite path modulation. The proposed algorithm was optimized using a pairwise conflict scenario. The effectiveness of the algorithm was evaluated through a Monte Carlo simulation of random conflict scenarios involving multiple UAVs operating in a confined space.

Design and Validation of a Nonparasitic 2R1T Parallel Hand-Held Prostate Biopsy Robot With Remote Center of Motion

AbstractAn increasing number of grounded robots are being used in prostate interventions to improve clinical outcomes, but their large size and high-cost limit their popularity. Thus, we present a hand-held 3-degree-of-freedom (DoF) parallel robot with remote center of motion (RCM) for minimally invasive prostate biopsy applications, combining the flexibility of hand-held devices with the precision of robotic assistance. First, the kinematic structure of robotic assistance is introduced according to its design requirements. Then, the kinematic analysis of robotic assistance is carried out by using a simplified kinematic model. The kinematic parameters are designed according to the desired workspace. A prototype has been developed and validated in animal experiments. Twenty beagles of different sizes were selected for the robot-assisted and controlled experiments, resulting in target errors of 3.30 ± 1.63 mm and 5.40 ± 1.76 mm, respectively. The error of robot-assisted experiments was significantly better than in controlled experiments. Preliminary animal tests have demonstrated that the hand-held robot can improve the accuracy of free-hand biopsy punctures.