Kinematic Method Research Articles

Shape-controllable inverse kinematics of hyper-redundant robots based on the improved FABRIK method

AbstractHyper-redundant robots have good prospects for applications in confined space due to their high flexibility and slim body size. However, the super-redundant structure brings great challenges for its inverse kinematics with shape constraints. Unfortunately, traditional Jacobian pseudo-inverse-based inverse kinematics method and forward and backward reaching inverse kinematics (FABRIK) method are difficult to constrain the arm shape and realize trajectory tracking in confined spaces. To solve this problem, we propose a shape-controllable FABRIK method to satisfy the given path and shape constraints. Firstly, the kinematic model of the hyper-redundant robot is established, and the canonical FABRIK method is introduced. Based on the preliminary works, the single-layer improved FABRIK method is developed to solve the position and pointing inverse kinematics considering path environment and joint angle constraints instead of two-layer geometric iterations. For tracking the desired end roll angles, the polygonal virtual arm is designed. The real arm roll angle is achieved by controlling its winding on the virtual arm. In this way, the shape can be controlled. Finally, we compare the proposed method with other three approaches by simulations. Results show that the proposed method is more efficient and the arm shape is controllable.

A method for the kinematic analysis of a novel wave compensation bed for ships based on the 8PSS-UP parallel platform

In addressing the need to reduce internal vessel vibrations and alleviate crew motion sickness during maritime voyages, this paper introduces a novel wave compensation resting bed and presents a kinematic analysis method tailored for marine environments. Diverging from conventional designs, this shipboard bed features a fixed platform hosting the drive unit, controlling the upper platform's movement via a slider's displacement, and incorporating a bottom Anti-Torsion (UP) frame. Employing the closed-loop vector method, the paper initially undertakes inverse kinematics of the shipboard bed, yielding solutions for slider displacement, velocity, and acceleration. Subsequently, the forward kinematics are resolved using the Newton-Gauss iterative method, with validation through ADAMS and MATLAB simulations. The velocity matrix analysis is then utilized to assess platform singularity, gauging the shipboard bed design's viability. Lastly, a wave model and a vessel heave-surge model in random waves are established to explore shipboard bed motion in unpredictable sea conditions. This study provides insights for the innovative design of shipboard resting beds and establishes a theoretical foundation for future wave compensation control in similar structures.

GPS-SBAS-Based Orbit Determination for Low Earth Orbiting Satellites

A space-based augmentation system (SBAS) provides real-time GNSS correction signals via geostationary satellites for near-ground GNSS users. To use the SBAS correction for low Earth orbit (LEO) satellites, the correction, especially the ionosphere correction, must be adjusted for the LEO altitude. We apply modified SBAS data to LEO satellite onboard navigator to improve the positioning accuracy of a LEO satellite for possible real-time use. The onboard navigator requires high positioning reliability, and code pseudoranges, rather than phase pseudoranges, are used for the primary measurements. The Galileo NeQuick G model is used to determine the real-time conversion factor of the SBAS ionosphere correction for a LEO satellite. The GPS L1 data from GRACE satellite are combined with the SBAS data from the ground receiver. The onboard navigator combines the precise satellite dynamic model with an extended Kalman filter to improve positioning accuracy and stability. The kinematic positioning method, which uses the weighted least square method without the dynamic model, is also performed for comparison. The SBAS correction reduces the positioning error in both the kinematic positioning and the dynamic positioning. The positioning error reduction of the GPS and WAAS case over the GPS-only case is 25.2% for the kinematic method and 30.6% for the dynamic method. In the case of the dynamic method with the SBAS corrections, the positioning error remains smaller than that of the GPS-only dynamic method even after the satellite has left the SBAS service area.

Revisiting the face stability of circular tunnels driven in strength nonlinearity soils

The face stability of shield-driven tunnels in soil materials with distinct strength nonlinearity is re-evaluated, based on the kinematic limit analysis theorem. The nonlinear Power-Law failure criterion is piecewise approximated by a multi-tangent technique to improve the conventional single straight-line substitution. A new multi-cone rotational mechanism formed by n curvilinear cones is proposed to accommodate the nonlinearity of the strength envelope considering the associative flow rule. The analytical solution of the critical support pressure on tunnel faces is derived from the energy equilibrium equation. Calculation results show that the multi-tangent method can improve the calculated values by up to 20% compared to the generalized tangent method. According to the back-calculated stress vectors, it is interestingly found that the stress level is not the critical factor influencing the tunnel face stability, while the shear strength parameters are the direct factor. Although the upper-bound analysis is a kinematic method without involving stress analysis, the parametric form of the strength criterion gives a chance to infer the possible stress distribution on the rupture surface and explain the variational trend of the result based on the distribution of back-calculated stress vectors.

Kinematic Modeling and Optimization of a Clustered Tensegrity Mobile Robot

Abstract Clustered tensegrity mechanisms have elicited extensive attention in recent research due to their easy control system and high stiffness-to-mass ratio. However, modeling and analyzing these mechanisms are still challenging due to the clustering of cables and redundant structural parameters. This article proposes an energy-based kinematic modeling method for a modular clustered tensegrity mobile robot. The design of the clustered tensegrity robot is inspired by the biomechanics of worms, allowing it to achieve two locomotion modes resembling earthworm-like and inchworm-like movements using two motors. Moreover, the clustered and modular structure enables the robot to increase the number of modules as needed without increasing the number of actuators. This feature enhances the robot's terrain adaptability without adding complexity to the control system. The article establishes kinematic models using the energy method and clarifies the motion law of nodes on the sliding cables of the robot, considering multiple structural parameters for both locomotion modes. Based on these models, the article reveals the mapping relationships among various structural parameters (i.e., cable-hole gap, cable-hole friction, stiffness and original length of elastic cables, and ground–robot friction) and locomotion performance (i.e., morphology, displacement, and velocity) of the robot. Furthermore, structural parameter optimization is performed to enhance the kinematic performance of the robot in both locomotion modes simultaneously. To validate the proposed kinematic modeling method, a prototype with two modules is developed, and experiments are conducted to assess the robot's locomotion performance. These experiments demonstrate the effectiveness and rationality of the proposed method.

Kinematics of the Local Spiral Structure Revealed by Young Stars in Gaia DR3

Using young open clusters and O–B2-type stars in Gaia Data Release 3, we investigate the kinematics of the local spiral structure. In general, the young sources in the outer spiral arms may present larger peculiar motions than those in the inner spiral arms. The young open clusters appear to have smaller peculiar motions than the O–B2-type stars, and the sources in both the Perseus and Local Arms may show an inward motion toward the Galactic center and rotate slower than Galactic rotation. Meanwhile, the sources in the Carina Arm may move in the opposite direction from the Sun to the Galactic center and rotate marginally faster than Galactic rotation. In addition, using young open clusters and O–B2-type stars, we have improved the distance estimations of kinematic methods for several regions near the Sun.

An analytical approach based on Dixon resultant for the inverse kinematics of 6R robot manipulators with offset wrists

6-revolute (6R) robot manipulators with offset wrists are widely applied in industrial scenarios. However, the autonomous and highly-precise manipulations of these robots are restricted for online industrial uses due to the lack of effective inverse kinematic methods. The inverse kinematic problem for 6R robot manipulators with offset wrists is addressed with a novel kinematic modelling and elimination approach in this study. To begin, kinematic models with non-redundant equations for joint variables are established An improved Dixon elimination approach is then introduced for inverse kinematic calculation to reduce the high computational cost and get rid of the singularity issues. The core is to efficiently extract the linear terms from variable sequences, such that the number of terms can be reduced in the polynomial equations. By further examining the characteristics of offset wrists, the fourth and fifth joint variables are eliminated from kinematic formulas, without increasing the polynomial degrees. The formulas are demonstrated to produce a polynomial with a single joint variable and a minimum degree using the elimination approach. Finally, experiments are carried out to verify the computing performance of the inverse kinematic problem. The main focus of this study is to develop a systematic and automatic procedure for solving the inverse kinematic problem for 6R robot manipulators with offset wrists and producing highly precise and efficient solutions by means of a novel modelling and elimination method.

Simultaneous calibration of hand-eye and kinematics for industrial robot using line-structured light sensor

For visually guided industrial robots, it is necessary to calibrate the robot's hand-eye relationship to accurately guide the robot's operations with the measurement data of the visual coordinate system. In most cases, the calibration process of hand-eye error does not consider the impact of kinematic errors, which accumulates the error in the calibration process and reduces the calibration accuracy. To enhance the calibration accuracy of industrial robots, a simultaneous calibration method of robot hand-eye relationship and kinematics using a line-structured light sensor is proposed. A simultaneous calibration model is established by using the differential kinematics principle. Afterward, the line-structured light sensor and two standard balls with known center distances are used in the calibration and accuracy verification experiments. After calibration and compensation with the proposed method, the average distance error of the robot declined from 3.967 mm to 1.001 mm. The proposed simultaneous calibration method for hand-eye relationship and kinematics dramatically improves the robot's positioning accuracy.

Kinematic calibration method with high measurement efficiency and robust identification for hybrid machine tools

Geometric error is the main factor affecting the machining accuracy of hybrid machine tools. Kinematic calibration is an effective way to improve the geometric accuracy of hybrid machine tools. The necessity to measure both position and orientation at each pose, as well as the instability of identification in case of incomplete measurements, severely affects the application of traditional calibration methods. In this study, a kinematic calibration method with high measurement efficiency and robust identification is proposed to improve the kinematic accuracy of a five-axis hybrid machine tool. First, the configuration is introduced, and an error model is derived. Further, by investigating the mechanism error characteristics, a measurement scheme that only requires tool centre point position error measurement and one alignment operation is proposed. Subsequently, by analysing the effects of unmeasured degrees of freedom (DOFs) on other DOFs, an improved nonlinear least squares method based on virtual measurement values is proposed to achieve stable parameter identification in case of incomplete measurement, without introducing additional parameters. Finally, the proposed calibration method is verified through simulations and experiments. The proposed method can efficiently accomplish the kinematic calibration of the hybrid machine tool. The accuracy of the hybrid machine tool is significantly improved after calibration, satisfying actual aerospace machining requirements.

Pseudodynamic Estimation of 3D Active Earth Pressures with a Nonlinear Strength Criterion

This paper presents an analytical framework for predicting three-dimensional (3D) seismic active earth pressures for soils governed by a nonlinear strength criterion. The kinematic limit analysis method that incorporates a pseudodynamic approach is used to carry out the analysis. A generalized tangential technique is adopted to realize transition of the nonlinear criterion into the commonly used linear form. A 3D failure mechanism of rigid rotation is employed. Because the use of the modified pseudodynamic approach leads to a variation of seismic forces along the depth, the work rate due to earthquake effects is calculated by using a horizontal layer–wise summation method. By virtue of the balance equation of work and energy, the thrust of active earth pressures is determined, and the final solutions are expressed as dimensionless active earth pressure coefficients. A comparison between the solutions obtained in this paper and those of the existing studies shows the effectiveness of the developed method. A parametric analysis is carried out to investigate the influences of several parameters. The findings of this work can help understand the service behavior of retaining structures subjected to seismic loadings, which could provide references for designs.

The Importance of the Kinematic Evaluation Methods of the Upper Limbs in Women with Breast Cancer Mastectomy: A Literature Review.

The kinematic assessment of the upper limbs in breast cancer (BC) survivors is one of the most common procedures to determine the recovery process after BC surgery. However, the methodology used is heterogeneous, finding various evaluation methods, which makes it difficult to compare results between studies. The objective of this review was to identify the technical features of the kinematic evaluation methods used in patients with mastectomy for BC. A literature review was conducted to search in electronic databases, such as PubMed, ScienceDirect, Clinical Key, Google Scholar, and Scopus. A total of 641 articles were obtained. After screening the title and the summary of the investigations, 20 manuscripts were kept for a deeper analysis. Different methodologies were found for the analysis of the kinematics of the upper limbs. Eight (40%) articles used the optoelectronic system, nine (45%) used the electromagnetic system, and three (15%) used other optoelectronic systems to assess shoulder kinematics. Each investigation studied different variables such as the type of surgery, the evaluation time, the age of the patients, the rehabilitation protocol, and so on. This makes the comparison among studies difficult, and the recovery process of the patients cannot be easily determined. In conclusion, the interpretation of the movement of the upper limbs should be easy to understand for oncologists, physiotherapists, clinicians, and researchers.

Numerical Analysis of GNSS Signal Outage Effect on EOPs Solutions Using Tightly Coupled GNSS/IMU Integration: A Simulated Case Study in Sweden.

The absence of a reliable Global Navigation Satellite System (GNSS) signal leads to degraded position robustness in standalone receivers. To address this issue, integrating GNSS with inertial measurement units (IMUs) can improve positioning accuracy. This article analyzes the performance of tightly coupled GNSS/IMU integration, specifically the forward Kalman filter and smoothing algorithm, using both single and network GNSS stations and the post-processed kinematic (PPK) method. Additionally, the impact of simulated GNSS signal outage on exterior orientation parameters (EOPs) solutions is investigated. Results demonstrate that the smoothing algorithm enhances positioning uncertainty (RMSE) for north, east, and heading by approximately 17-43% (e.g., it improves north RMSE from 51 mm to a range of 42 mm, representing a 17% improvement). Orientation uncertainty is reduced by about 60% for roll, pitch, and heading. Moreover, the algorithm mitigates the effects of GNSS signal outage, improving position uncertainty by up to 95% and orientation uncertainty by up to 60% using the smoothing algorithm instead of the forward Kalman filter for signal outages up to 180 s.

Inverse kinematics and multi-objective configuration optimization of the SSRMS manipulator

The Space Station Remote Manipulator System (SSRMS) type redundant manipulator with higher flexibility and foldability is widely used in the space environment. Inverse kinematics and multi-objective configuration optimization are analyzed in this paper. An arm angle parameterized inverse kinematics method using the approximate solution and error compensation scheme is proposed, which has the advantages of not requiring a selection of initial estimates of joint variables, being insensitive to Jacobian matrix singularities, having no pose error, and finding multiple solutions. In addition, Multiple Objective Particle Swarm Optimization (MOPSO) scheme is adopted to optimize the arm angle trajectory in null space, and the optimization index is set as joint torque and manipulability. Unlike traditional trajectory planning methods, we synthesize null space and configuration control to provide a novel perspective for trajectory planning. Finally, the experiments prove that the inverse kinematics algorithm is efficient and reliable, and the effectiveness of the configuration optimization method is verified by the numerical simulation of single objective and multi-objective optimization.

Synthesis on cardioid crank rocker mechanism with approximate uniform motion

The cardioid crank is a planetary mechanism that generates a cardioid line. It is a crank with varying length and speed that moves along the cardioid line. The cardioid crank is used to replace the crank of the crank rocker mechanism, and its rocker mechanism with approximate uniform motion is obtained. The kinematic analysis method of the cardioid crank rocker mechanism is studied in this paper. The calculating method for the limit position and oscillating angle and the time ratio of the guide bar are given. Finally, the approximate uniform motion conditions of the rocker are obtained. The synthesis method of the approximate uniform motion mechanism is put forward in accordance with the time ratio or rocker oscillate angle, the minimum length of the guide bar is calculated, and the influence of center distance on the kinematic performance of the mechanism is discussed.

MANEUVERABILITY OF THE 15-METER BUS

Buses play a significant role in the public transport system and, in particular, in the transpor-tation of passengers in intercity traffic. This is the most common way of moving people over short and medium distances both in cities and in most rural areas. The bus industry as a part of the general automotive industry has its own characteristic feature: despite the fact that the total production of buses is only a few percent of the total output of automotive equipment, their production is carried out at a much larger number of enterprises than cars and even trucks, and very often in limited quantities. The idea of using extra-large buses seems ap-propriate, because there are a number of city routes on which the use of 12-meter buses will lead to their over-load, and the use of 18-meter articulated buses can lead to their underloading, or to increase the intervals of traffic. When developing any bus, including an extra-large capacity bus, the mass and geometric limitations laid down in the regulatory documents must be taken into account. At the same time, a 15-meter three-axle city bus without special devices cannot meet the requirements of GOST due to its increased length. Therefore, it is still relevant today to improve the fitting of such buses into the transport network of large cities. This problem can be solved by controlling not only the front but also the rear wheels of the bus. The paper shows that the control of an extra-large capacity bus can be carried out not only by a kinematic method – by turning the steered wheels of the bus, but also in a combined method – by controlling the steered wheels of the bus and its driving wheels by creating different torques on the wheels of this axis or by creating braking moments on the third axis, which can significantly simplify the bus control system. At the same time, the dependence of the difference in the torques on the wheels of the driving axle of the bus, the braking moments on the wheels of the third axle and total moments on the second (driving) and third axles of the bus was obtained, which is equivalent to the angle of rotation of the steered wheels of the bus. For different control methods, it has been established that the bus according to the kinematic control method (turning the steered wheels of the bus – the control system) does not meet the requirements of UNECE Regulation No. 36.03 regarding maneuverability. With the combined method of bus control for the magnitude of the difference in moments on the wheels of the second and third axles within Delta-M=2550-3000 Nm, these requirements are met, and the preferred design is the control system, which uses the braking of the wheels of the third axle. However, this method of turning can only be proposed to improve maneuverability at low speeds (up to 10 m/s). When the speed increases above 10 m/s, the wheel con-trol system of the third axle should be blocked.

ГРАФОАНАЛІТИЧНЕ ПРОФІЛЮВАННЯ СПРЯЖЕНИХ КРИВОЛІНІЙНИХ ПОВЕРХОНЬ РІЖУЧОГО ІНСТРУМЕНТУ

In the research, graphic-analytical methods for profiling the cutting tool for processing the helical surface of the drill groove were developed. The basis of these studies was the definition of the characteristics of conjugated surfaces, as the locus of the bases of the normal, which are directed from the points of the surface of revolution to a given helical surface. The methods were based on the position of the differential geometry about the common normal at the points of tangent conjugacy of the surface. Graphic-analytical profiling is a fairly wide and developed branch of science, based on the one hand on the theoretical and practical achievements of applied geometry, which makes it possible to use it, and on the other hand, it is a powerful analytical tool. Formation is an approximate representation of any set of objects, phenomena of the external world through geometric diversity and relationships between them. Conjugation of curvilinear surfaces of the cutting tool for processing parts in weapons and military equipment is one of the most important topics. The article proposes to optimize the process by creating universal tools, which may include the creation of a kinematic method that will be used to design products with specified parameters. The use of graphic-analytical formation of curved surfaces as a design tool in the "manual" mode, in which all graphic formations of conjugate curved surfaces, their interconnection and interdependence will be laid. Of great importance in the design of mating curvilinear surfaces of a cutting tool is the exact reproduction of their shape as the basis for reliable and long-term operation of future real products in weapons and military equipment. This article aims to take a certain step in this direction regarding the creation of mating curved surfaces for the design of cutting tools, processing of products in weapons and military equipment. Keywords: Graph-analytical formation, kinematic method, surface conjugation, kinematic pairs, parameters, shaping, curved surfaces, drill groove.

ЗАСТОСУВАННЯ ДІАГРАМИ КІНЕМАТИЧНОГО ГВИНТА ПРИ ФОРМУВАННІ КРИВОЛІНІЙНИХ ПОВЕРХОНЬ В ОЗБРОЄННІ ТА ВІЙСЬКОВІЙ ТЕХНІЦІ

The article deals with the formation of surfaces by the movement of auxiliary surfaces (intermediaries), based on a parametric kinematic screw. In modern existing mechanisms operating at high speeds, dynamic loads exceed static loads many times over. To improve accuracy, it is necessary that the process of processing a part with a cutting tool is carried out taking into account the coefficient of uneven rotation in the manufacture of products. The technology of processing complex surfaces by the most productive method of running is closely related to the profiling of conjugated curved surfaces formed by the movement of intermediaries. The mating curved surfaces of kinematic pairs, with different parameters, in turn, require the development of effective kinematic methods of formation and ensuring high accuracy in the processing of products used in mechanisms and processed on automatic lines, allowing to expand the scope of the most advanced methods of processing complex products.. Proposed  1 the kinematic screw has proven itself well for the formation of mating ruled surfaces, so the urgent task arose to investigate the possibility of using a kinematic screw for mating curved surfaces. The study was developed on the basis of the proven theorem of Academician A.N. Podkorytov, about instantaneous envelope axoids, which allows you to form mating curved surfaces, using a parametric kinematic screw, which takes into account the kinematics of metal-cutting machines. When solving the set task, the design time is reduced and the accuracy of manufacturing parts in the mechanisms of weapons and military equipment is increased. Keywords: kinematic method, geometric model, cutting tool, mating surfaces, curved surface, parametric kinematic screw, auxiliary surface (intermediaries), instantaneous axoid envelopes.

AUTOMATED DEVICE PARTS TRANSPORTATION SYSTEM IN THE CONDITIONS OF MEDIUM-SERIES PRODUCTION

The article analyzes previous research and publications on the development and application of various types of automated transport carts used in serial production, from which a conclusion is drawn about the need to develop an automated transport cart that can be used in instrument manufacturing and which will increase the productivity of the transport system.
 After conducting the analysis, the main element of the automated transportation system was developed, which is an automated transport cart mounted on mecanum wheels, which ensure its all-directional movement, without changing the orientation in space or its change regardless of the direction of movement, with two on-board manipulators that have removable gripping devices, and an individual removable storage device. Changeable elements increase the flexibility of the automated cart, because this feature allows the cart to be adapted to a large number of various technological processes. With the help of the CAD system, a three-dimensional model of the schematic design of the automated transport cart was developed, which takes into account all its important elements, as well as a detailed model of the mecanum wheels, designed specifically for the design of the cart.
 Using the parameters of the developed automated transport cart, the kinematics of the cart were calculated and formulas for solving the forward and inverse kinematics problem were determined, as well as the algorithms of the cart operation were developed, which describe each cycle performed by the cart at each workplace. Based on formulas for solving kinematics problems, formulas and methods for leveling spatial errors that occur during movement from one point to another are defined, as well as functions for optimizing the process of moving an automated transport cart are defined, and how optimization affects performance is determined.

Prototype design education for cinematic learning mechanisms:aplications to the mechanisms to conrod crank with runner

The present investigation is related to the design, construction and manufacture of a didactic prototype of a rod-crank mechanism with a slider that allows to visualize and understand fundamental principles of its operation as well as its kinematics. Relating the traditional method of kinematics called Velocity Polygon with CAD design, additive manufacturing and automatic control. The objective of this project is to generate a controllable didactic prototype that allows us to visualize and understand fundamental concepts of the mechanism's operation as well as real-time information on the kinematics of its joints (nodes). Through the database generated by a instrumentation created in LabVIEW, movement simulation of the cad design and the velocity polygon graphic method, it was found that the speed of the sliding node coincides in the three methods, thus achieving a device that allows us to offer a more practical approach, in the development of technical skills, resolution of mechanism problems in undergraduate students in mechatronics, mechanics and Industrial

Kinematics modeling method of continuum space manipulator based on virtual discrete-jointed manipulator models

Continuum space manipulators (CSMs) have key application prospects in the maintenance of spacecrafts in narrow environments and space debris removal. Similar to conventional articulated space manipulators (ASMs), CSMs encounter a number of kinematic, dynamic, and control problems caused by the dynamic coupling between the continuum manipulator and its microsatellite platform. However, the continuum manipulator has no obvious kinematic joints. In addition, its motion is generated by the continuum deformation of its elastic body; thus, the virtual manipulator (VM) model of ASM in the free-floating state becomes inappropriate for CSMs. In this study, we propose a kinematic equivalent method for a free-floating CSM, which is equivalent to a virtual discrete-jointed manipulator (VDJM) connected to a virtual ground. First, the constraint relationship is used to establish the virtual vector manipulator (VVM) model for the CSM such that its center of mass in the free-floating mode remains unchanged. Furthermore, on the basis of the VVM model and D-H parameters of the CSM, virtual discrete joints are introduced, and a VDJM model for the CSM is proposed. Compared with the VVM model, the developed VDJM model can more intuitively express the motion characteristics of the CSM. Finally, we demonstrate the application potential of the developed VDJM model in the inverse kinematics solution, workspace, and dynamic coupling of CSMs.