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Study of stiffness characteristics plays a key role in application of parallel robots in precision manufacturing. In this study, stiffness index improvement is utilised as the objective function to obtain optimal configurations and dimensions for parallel robots. The optimisation goal is to maximise the stiffness index throughout workspace of the robots. First, stiffness of the robots is obtained by the strain energy of main components of the robots and Castigliano's theorem. For a more realistic simulation, compliance of moving platform of the robots is considered. Then a non-dominated sorting genetic algorithm (NSGA-II) is utilised to solve the optimisation problem. A comprehensive case study of stiffness analysis of three conventional SPS (spherical– prismatic–spherical) Stewart platforms to examine such a platform's optimised design is performed. The relationship between the objective and decision spaces is investigated. A similar approach can be utilised to study optimised design for other parallel robots. Findings of this study provide a general stepwise and conceptual approach to the stiffness analysis of parallel robots that depends on design parameters and configuration of the robots. In case of Stewart platforms, 3SPS configuration was found to be optimised in terms of stiffness performance in their workspace. [ABSTRACT FROM AUTHOR]

The authors of the article developed a mathematical model of Stewart platform management. The angles of rotation of the servo shafts were obtained when setting various laws of motion of the mobile platform, in matrix mode. The hardware part of the prototype of the basic module of a scalable robotics system for modeling composite surfaces for dynamic tests was developed. The results of calculations of the maximum permissible load on the shafts of servos are presented. The CubeIDE settings for programming the STM32 microcontroller are given. The results of software development for the control of this prototype were obtained, namely, a library for controlling 6 servo drives under driver control was written. The problems that may arise during the above-described developments by future developers are considered, solutions to these problems are obtained. Detailed design features of this prototype are described, the control code of the servo drive is given; steps for further development of the final robotic system are considered

The application of offshore wind power gangways ensures the normal operation of offshore wind turbines and provides reliable support for optimizing the boarding process, improving the operation and maintenance efficiency, and reducing the cost of wind power projects. This paper provides an overview of the development history and technological progress of gangways, and analyzes the main equipment in this field and its performance at home and abroad, as well as discussing the key technologies of offshore wind turbine gangways in such aspects as motion sensing and data analysis, compensation control and execution, structural design and reliability, and composite material application. It is pointed out that the parallel platform is the mainstream offshore gangway actuator; wave compensation is the core of equipment performance and the source of competitiveness; and advanced wave compensation technology depends on the development of sensor technology, artificial intelligence technology and other multidisciplinary development. This paper makes a comprehensive analysis for researchers and practitioners in the field of offshore wind power gangways, providing valuable references for subsequent technology exploration.

AbstractIn this article, a transient road signals simulation strategy in a Stewart platform is presented. Real world road signals are transient signals and thus the accurate simulation of its frequency, amplitude and damping components is key for further simulation of comfort. This simulation strategy combines a kinematic model and a transient signal reconstruction strategy using an autoregressive method. First, the developed experimental kinematic model on a Stewart platform is presented. Then, the procedure to simulate real-world transient road signals in the driving simulator is explained. Finally, the developed strategy has been validated under real road signals combined in the 6 degrees-of-freedom to prove the accuracy between the real world experimental measured signal and the simulated signal in the hexapod. The final goal of the presented transient road signals simulation strategy is to perform further vehicle dynamics and ride and comfort studies in the simulation phase using electric Stewart platforms. [ABSTRACT FROM AUTHOR]

The present work aims to develop an object tracking controller for the Stewart platform using a computer vision-assisted machine learning-based approach. This research is divided into two modules. The first module focuses on the design of a motion controller for the Physik Instrumente (PI)-based Stewart platform. In contrast, the second module deals with the development of a machine-learning-based spatial object tracking algorithm by collecting information from the Zed 2 stereo vision system. Presently, simple feed-forward neural networks (NN) are used to predict the orientation of the top table of the platform. While training, the x, y, and z coordinates of the three-dimensional (3D) object, extracted from images, are used as the input to the NN. In contrast, the orientation information of the platform (that is, rotation about the x, y, and z-axes) is considered as the output from the network. The orientation information obtained from the network is fed to the inverse kinematics-based motion controller (module 1) to move the platform while tracking the object. After training, the optimised NN is used to track the continuously moving 3D object. The experimental results show that the developed NN-based controller has successfully tracked the moving spatial object with reasonably good accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we propose a complex structure of Stewart platform, in 3-RSS configuration, for high precision elevator tasks. After defining the dynamic model based on the Lagrange method, we present the simulation studies concerning the system movement ability. Thereafter, based on the theoretical analysis and considerations, we design and construct a real-life object. The obtained verification tests of the system confirm its applicability in industrial automation and robotics system. [ABSTRACT FROM AUTHOR]

This study describes the design of a parallel spatial manipulator with four degrees of freedom actuated with shape memory alloy (SMA) wire to validate the use of SMA in complicated mechatronics systems. The manipulator has a closed kinematic structure, which includes a fixed base and a moving square platform (end effector). The four arms of the manipulator are SMA wires fastened between the fixed base and the end effector. SMA wire-based actuators replace bulky conventional revolute actuators. This work spotlights the development of an actuator model, dimensional analysis, and design of cascade control strategies of various PID and sliding mode controller in their integral and fractional order configurations. Experimental evaluation of the actuator is performed through trajectory tracking to quantify the different controller configurations. The experimental results indicate that the parallel manipulator associated with SMA wire actuators is the best alternative to conventional motion stages for highly precise micro-positioning and tracking applications in the fields of 3D printing, intricate surgical operations, the medical and pharmaceutical industries, and flight and gaming simulators. [ABSTRACT FROM AUTHOR]

Copyright of FME Transactions is the property of University of Belgrade, Faculty of Mechanical Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Physiotherapy is a treatment that may be required permanently by many patients. As a result, a robot that can execute physiotherapy exercises for the legs like a professional therapist with adequate performance and acceptable safety may be efficient and widely used. In this study, a robust control system for a Stewart platform with six degrees of freedom is provided. First, the Newton-Euler approach is used in conjunction with a methodology and some simplification tools to achieve explicit dynamics formulation for the Stewart platform. For the primary application of this research, which is to follow the specified trajectory of ankle rehabilitation, computed torque control law (CTCL) and polynomial chaos expansion (PCE) were used to examine and consider any uncertainty in geometric and physical parameters. In fact, this strategy integrated the uncertainties with CTCL using PCE. The suggested PCE-based CTCL eliminates the system's nonlinearity by applying feedback linearization to evaluate generalized driving forces; hence, the nondeterministic multi-body system follows the desired direction. Uncertainties in the patient's foot as well as the main diameter parameters of the moment of inertia of the upper platform of the Stewart robot with various uniform, beta, and normal distributions, have been analyzed. The PCE technique's results were compared to the Monte Carlo method's outcomes, and the strengths and weaknesses of each method were investigated. In brief, the PCE method operated far better than the Monte Carlo (MC) method in speed, accuracy, and numerical volume. [ABSTRACT FROM AUTHOR]

Parallel manipulators, a distinctive subset of closed-loop multi-body systems, are in high demand due to their precision-centric applications. This research introduces a unified approach to tackle both inverse and forward dynamic analyses of parallel manipulators, rooted in joint-based principles. The methodology dissects a given parallel manipulator into symmetric open-loop subsystems and a mobile body within either a planar or spatial context, depending on the manipulator's nature. Conventional practices, involving the introduction of joint cuts at relevant locations, are employed to partition the system into multiple open-loop subsystems. Subsequently, the joint coordinate-based approach, typically applied to open-loop systems such as industrial manipulators, is utilized to derive solutions. In particular, this approach focuses on forward dynamics by introducing the generalized inertia constraint matrix for parallel manipulators (GICM-P), a concept built upon the authors' prior work, originally addressing the GICM for general closed-loop systems. Notably, GICM-P aligns conceptually with the operational space inertia matrix (OSIM) designed for closed-loop systems elsewhere. However, unlike OSIM, which requires mapping joint-space inertia to operational-space inertia, GICM-P leverages acceleration-level constraints between subsystems and the moving platform through straightforward matrix operations. GICM-P offers a deeper understanding of the physics of the problem compared to OSIM, primarily due to its ability to explicitly express subsystem-level interactions via various block matrices – an aspect not previously documented. The paper provides explicit numerical values for GICM-P in the context of a spatial six degrees of freedom (6-DOF) Stewart platform and a planar 3-DOF parallel manipulator along with interpretations. [ABSTRACT FROM AUTHOR]

Accurate calibration of a Stewart platform is important for their precise and efficient operation. However, the calibration of these platforms using forward kinematics is a challenge for researchers because forward kinematics normally generates multiple feasible and unfeasible solutions for any pose of the moving platform. The complex kinematic relations among the six actuator paths connecting the fixed base to the moving platform further compound the difficulty in establishing a straightforward and efficient calibration method. The authors developed a new forward kinematics-based calibration method using Denavit-Hartenberg (DH) convention and used the Stewart platform "Tiger 66.1" developed in their lab for experimenting with the photogrammetry-based calibration strategies described in this paper. This system became operational upon completion of construction, marking its inaugural use. The authors used their calibration model for estimating the errors in the system and adopted three compensation options or strategies as per least-square method to improve the accuracy of the system. These strategies leveraged a high-resolution digital camera and off-the-shelf software to capture the poses of the moving platform's center. This process is non-invasive and does not need any additional equipment to be attached to the hexapod or any alteration of the hexapod hardware. This photogrammetry-based calibration process involves multiple high-resolution images from different angles to measure the position and orientation of the platform center in the three-dimensional space. The target poses and actual poses are then compared, and the error compensations are estimated using the least-square methods to calculate the predicted poses. Results from each of the three compensation approaches demonstrated noticeable enhancements in platform pose accuracies, suggesting room for further improvements. Given that "Tiger 66.1" is based on the general Stewart platform structure, the proposed calibration method holds promise for extension to machines operating on similar principles where non-invasive calibration is desirable. This study contributes to advancing the field of Stewart platform calibration, paving the way for more precise and efficient applications in various domains. [ABSTRACT FROM AUTHOR]

Small‐radius curved bridges are mostly used for overpass ramps, that are spatially irregular and usually have very complex seismic behavior. It is not easy to reproduce such behavior because of the need for large‐scale shaking tables. The hybrid test is one of the most effective approaches for solving this problem by considering the structural elements of interest as physically tested substructure while the rest is numerically simulated. In this paper, a hybrid test system was first developed based on the OpenFresco framework, where one of the piers was considered as the tested substructure, and the rest was simulated by OpenSees. A novel spatial loading device (SLD), configured as the Stewart pattern, was then developed to achieve the boundary conditions between substructures. The control schemes to perform the force‐displacement mixed control, conduct the geometric transformation while considering the load point offset, and achieve an external displacement control were proposed and validated through several rounds of hybrid testing. The experimental results indicate that the experimental system including loading control subsystem and hybrid control subsystem can realize the loading command accurately. [ABSTRACT FROM AUTHOR]

In this research project, a closed-chain robotic active ankle orthosis with six degrees of freedom is designed, constructed, numerically valued, instrumented, and experimentally validated. The mechanical arrangement to implement the orthosis corresponds to a six-legged Stewart platform. An adaptive gain control strategy with state constraints based on a state-dependent gains control (that behaves as a diverging function as the states approach the state restrictions) operates the device's motion. The convergence to an invariant positive set centered at the origin of the tracking error space is validated using the stability analysis based on the second method of Lyapunov, with the implementation of a state barrier Lyapunov-like function. The ultimate boundedness of the tracking error is proven with an endorsed gains adjustment method leading to a reachable minimum size of the ultimate bound. Hence, the impact of the state constraints and the formal reason for applying the controller on the suggested orthosis are all established. The orthosis is also controlled using a conventional state feedback strategy to assess the tracking error for an external disturbance and contrast its performance with the proposed control approach. The technology is tested on a few carefully chosen volunteers, successfully limiting the range of motion within a pre-defined region based on the scope of movement reported by patients with ankle illnesses discovered in the literature. Based on a unique mechatronic device, the created system offers a fresh approach to treating this class of impairments. • A new state-restricted controller solves the motion sequence for a Stewart platform-based ankle rehabilitation system. • A novel barrier Lyapunov function leads to the development of state-dependent gains for the state feedback controller. • A self-developed Stewart platform served to test the proposed controller in numerical and experimental evaluations. • The tracking error dynamics is proven to be ISS for modeling uncertainties and external perturbations. [ABSTRACT FROM AUTHOR]

Micro-acceleration generation during ultra-low-frequency micro-vibration calibration is a sensitive issue. There are issues of traditional pendulum tables being unable to change the pendulum radius and direction to produce micro-accelerations of different magnitudes, and the line shakers having a low signal-to-noise ratio when the vibration amplitude is the same as that of the pendulum tables. Therefore, a novel ultra-low-frequency micro-vibration calibration method is proposed to solve the above issues based on virtual pendulum motion trajectories of the Stewart platform. The micro-accelerations of 10-5 to 10-3 m/s2 can be generated by the trajectories with the radius of up to 12 m, the displacement amplitudes of up to 11.636 mm and the frequencies between 0.01 and 0.1 Hz. In the virtual pendulum motion, the maximum acceleration can be 2481 times greater than the acceleration of linear motion at the same frequency and displacement amplitude. In a comparison experiment with the current rotating platform, the maximum relative deviation of sensitivity amplitude calibration for pendulum motion around the x- and y-axis based on the Stewart platform are 0.411% and 0.295% respectively. The above results demonstrate the validity and reliability of this kind of method. [ABSTRACT FROM AUTHOR]

Copyright of Light Industry Machinery is the property of Light Industry Machinery Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Space-based gravitational wave detection missions use multiple satellites to form a very large scale Michelson laser interferometer in space. This requires extremely high precision displacement measurements at the picometer level between test masses even millions of kilometers apart. Drag-free control is a key technology to ensure the ultra-static and ultra-stable space experiment platform for space-based gravitational wave detection. This paper proposes an innovative ground simulation scheme for drag-free control principle based on the Stewart platform. The kinematics and dynamics modeling of the Stewart platform used in the experiment is presented. A drag-free ground simulation experimental equipment is designed and built. A two-degree-of-freedom (2-DOF) drag-free controller is designed based on the H ∞ loop shaping algorithm which outperforms a PID controller in Simulink simulation. A semi-physical simulation experiment is conducted to verify the controller designed using rapid control prototyping technology. The experimental results show that the control performance reaches the limit accuracy of the hardware device, thus verifying the effectiveness of the drag-free control algorithm. • Introduce a novel ground simulation scheme for drag-free control using the Stewart platform. • Design a drag-free controller based on H ∞ loop shaping. • Validate our approach through a two-degree-of-freedom semi-physical simulation experiment. [ABSTRACT FROM AUTHOR]

This article develops a charge couple device (CCD)-based dual-stage system consisting of cubic Stewart platform and tip-tilt mirror to stabilize the line-of-sight (LOS) for space optical payloads. Due to the conventional offloading strategy needing the accurate characteristic of the CCD and additional position sensor in terms of precision and bandwidth, a novel model-following offloading strategy is presented to achieve the offloading for the dual-stage system. The essence of the proposed strategy is that the following position signal can be estimated through combining the controller output with the model-based estimation of the tip-tilt mirror to be offloaded into the Stewart platform. Besides, an error-based observation control technique is introduced to relax the limitations imposed by the low sampling rate of the CCD on closed-loop performance for the tip-tilt mirror loop. This technique reduces reliance on the precise control model and optimizes the tracking performance by the design of an appropriate Q-filter. The simulations and experiments of the dual-stage image stabilization system demonstrate the validity of the presented approach.

The digital twin is considered a new and promising concept whose added value is seen mainly in end applications. However, the benefit of considering the digital twin application since the early development of the system seems not to be stressed enough. The ability to choose system components, methods, and tools can have a symbiotic effect during system integration. This work describes a development process of a Stewart platform digital twin based on its multibody simulation model created in Matlab/Simulink. Although the multibody simulation model is useful in the design phase, after adjustments and verification, it can also be reused as a virtual entity of the digital twin. This integration is enabled by the methods, tools, and system architecture selected for the purpose of including a digital twin. This is considered to be the main contribution of this paper to emerging methodologies for the development of mechatronic systems and its digital twins. However, practical integration comes with challenges that are related to the model fidelity and synchronisation of the virtual and physical entities and are important to overcome in order to employ the system in the real applications.

Optical payloads are widely used in many fields, such as aerospace, drones, autonomous vehicles, or other highly precise instrumentation. Vibration is one of the causes that greatly affect the quality of data of highly precise optical payloads. Recently, many researcher focuses on isolating the vibration for the precise equipment, those study just only mention the overcoming of vibration in one or two directions, but in reality, an object will exist vibration in six directions in space. Therefore, it is necessary to find a new mechanism that can isolate vibration in six axes in space. The parallel mechanism is considered a viable system because of its strengths in accuracy, rigidity, and stability. In this research, the author proposes a novel 6-DOF passive vibration isolator based on the Steward platform with S-shaped legs. We have developed a 6-DOF passive vibration isolator using the S-shaped non-linear stiffness and damping characteristics. In this study, the model parameters of a vibration isolator device with legs using an S-shaped will be proposed. Based on geometrical parameters and vibration sources and some loads assuming the structure's durability problem will be calculated and evaluated the efficiency of the isolator at different frequencies. With the specially designed S-shaped it can be deformity like a spring, and with the change of structural and material parameters, we can adjust the system's stiffness and damping capacity. Due to the high static stiffness and low dynamic stiffness of each leg, and thus it is designable to isolate very well vibration isolation performance in all six directions. This research is organized as firstly the kinematics and 3D model are introduced. Secondly, the stiffness matrix of the novel 6-DOF passive vibration isolators is presented. Statics analysis of the 6-DOF passive vibration isolators revealed that the S-shaped structure provides sufficient load-carrying capacity and isolation due to its very good static nonlinear stiffness. The dynamic stiffness of the isolator in this study in each direction is very low but does not reduce the load-carrying capacity of the structure. By changing the structure and material parameters (which is very simple in a purely passive manner), we can completely adjust both the dynamic and static stiffness of the mechanism. The last series of numerical simulation results on displacement and a statics response in random excitation is carried out to show the effectiveness of the proposed 6-DOF passive vibration isolator, as well as the influence of structural parameters on vibration attenuation performance. The simulation results with the different exciting are shown to demonstrate the efficiency of the 6-DOF passive vibration isolators. Considering its simulation results A proposed new 6-DOF isolator will be applied in various engineering practices with multi-degree of freedom vibration isolation such as for precise optical payloa [ABSTRACT FROM AUTHOR]

This work presents the development of a state-input affine differential neural network that approximates a class of nonlinear systems with uncertain dynamics and perturbations. The feasibility of using differential neural networks is based on the approximation capabilities of artificial neural networks, assuring that the approximation error of the right-hand side of the system with uncertain dynamics is bounded. The dynamics of the free parameters of the differential neural network is obtained using the Lyapunov's second stability method, which provides the convergence of the identification error to an invariant set around the origin. The approximation capabilities of the proposed identifier are compared with a classical differential neural network, aiming to identify the dynamics of a Stewart platform, which is used as testing example. The results show that the cumulative norm of identification's error is smaller using the state-input affine differential neural network, which demonstrates better identification outcomes with the proposed modified identifier. An additional advantage of the state-input affine differential neural network is that it has a quasi-linear structure that could help formulate a controller for several systems, which is a further research interest. • Learning laws for State-input affine differential neural network (SIADNN) identifier. • Design based on the second stability method of Lyapunov. • The novel DNN identifier has more applications than the traditional DNN identifier. • Evaluation of performing the non-parametric identification of a Stewart platform. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Harbin Institute of Technology. Social Sciences Edition / Haerbin Gongye Daxue Xuebao. Shehui Kexue Ban is the property of Harbin Institute of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

At the present stage, with the current demands for the accuracy of motion control processes for a moving object on a specified or programmable trajectory, it is necessary to synthesize the optimal structure and parameters of the stabilization system (controller) of the object, taking into account both real controlled and uncontrolled stochastic disturbing factors. Also, in the process of synthesizing the optimal controller structure, it is necessary to assess and consider multidimensional dynamic models, including those of the object itself, its basic components, controlled and uncontrolled disturbing factors that affect the object in its actual motion. Objective. The aim of the research, the results of which are presented in this article, is to obtain and assess the accuracy of the Stewart platform dynamic model using a justified algorithm for the multidimensional moving object dynamics identification. Method. The article employs a frequency-domain identification method for multidimensional stochastic stabilization systems of moving objects with arbitrary dynamics. The proposed algorithm for multidimensional moving object dynamics model identification is constructed using operations of polynomial and fractional-rational matrices addition, multiplication, Wiener factorization, Wiener separation, and determination of dispersion integrals. Results. As a result of the conducted research, the problem of identifying the dynamic model of a multidimensional moving object is formalized, illustrated by the example of a test stand based on the Stewart platform. The outcomes encompass the identification of the dynamic model of the Stewart platform, its transfer function, and the transfer function of the shaping filter. The verification of the identification results confirms the sufficient accuracy of the obtained models. Conclusions. The justified identification algorithm allows determining the order and parameters of the linearized system of ordinary differential equations for a multidimensional object and the matrix of spectral densities of disturbances acting on it under operating conditions approximating the real functioning mode of the object prototype. The analysis of the identification results of the dynamic models of the Stewart platform indicates that the primary influence on the displacement of the center of mass of the moving platform is the variation in control inputs. However, neglecting the impact of disturbances reduces the accuracy of platform positioning. Therefore, for the synthesis of the control system, methods should be applied that enable determining the structure and parameters of a multidimensional controller, considering such influences. [ABSTRACT FROM AUTHOR]

In this paper, we focus on enhancing the performance of the controller utilized in the Stewart platform by investigating the dynamics of the platform. Dynamic modeling is crucial for control and simulation, yet challenging for parallel robots like the Stewart platform due to closed-loop kinematics. We explore classical methods to solve its inverse dynamical model, but conventional approaches face difficulties, often resulting in simplified and inaccurate models. To overcome this limitation, we propose a novel approach by replacing the classical feedforward inverse dynamic block with a reinforcement learning (RL) agent, which, to our knowledge, has not been tried yet in the context of the Stewart platform control. Our proposed methodology utilizes a hybrid control topology that combines RL with existing classical control topologies and inverse kinematic modeling. We leverage three deep reinforcement learning (DRL) algorithms and two model-based RL algorithms to achieve improved control performance, highlighting the versatility of the proposed approach. By incorporating the learned feedforward control topology into the existing PID controller, we demonstrate enhancements in the overall control performance of the Stewart platform. Notably, our approach eliminates the need for explicit derivation and solving of the inverse dynamic model, overcoming the drawbacks associated with inaccurate and simplified models. Through several simulations and experiments, we validate the effectiveness of our reinforcement learning-based control approach for the dynamic modeling of the Stewart platform. The results highlight the potential of RL techniques in overcoming the challenges associated with dynamic modeling in parallel robot systems, promising improved control performance. This enhances accuracy and reduces the development time of control algorithms in realworld applications. Nonetheless, it requires a simulation step before practical implementations. [ABSTRACT FROM AUTHOR]

Introduction: We study optimization methods for poses and movements of chained Stewart platforms (SPs) that we call an “Assembler” Robot. These chained SPs are parallel mechanisms that are stronger, stiffer, and more precise, on average, than their serial counterparts at the cost of a smaller range of motion. By linking these units in a series, their individual limitations are overcome while maintaining truss-like rigidity. This opens up potential uses in various applications, especially in complex space missions in conjunction with other robots. Methods: To enhance the efficiency and longevity of the Assembler Robot, we developed algorithms and optimization models. The main goal of these methodologies is to efficiently decide on favorable positions and movements that reduce force loads on the robot, consequently minimizing wear. Results: The optimized maneuvers of the interior plates of the Assembler result in more evenly distributed load forces through the legs of each constituent SP. This optimization allows for a larger workspace and a greater overall payload capacity. Our computations primarily focus on assemblers with four chained SPs. Discussion: Although our study primarily revolves around assemblers with four chained SPs, our methods are versatile and can be applied to an arbitrary number of SPs. Furthermore, these methodologies can be extended to general overactuated truss-like robot architectures. The Assembler, designed to function collaboratively with several other robots, holds promise for a variety of space missions. [ABSTRACT FROM AUTHOR]

We introduce the notion of the Lie derivative in the context of dual quaternions that represent rigid motions and twists. First we define the wrench in terms of dual quaternions. Then we show how the Lie derivative helps understand how actuators affect an end effector in parallel robots, and make it explicit in the two cases case of Stewart Platforms, and cable-driven parallel robots. We also show how to use Lie derivatives with the Newton-Raphson Method to solve the forward kinematic problem for over constrained parallel actuators. Finally, we derive the equations of motion of the end effector in dual quaternion form, which include the effect of inertia from the actuators. [ABSTRACT FROM AUTHOR]

This paper presents a control system algorithm for a five-axis parallel mechanism system (PMS) CNC milling machine based on a 6-DOF Stewart platform parallel manipulator with a universal-prismatic-spherical (UPS) configuration. The control system reads the G-Code commands as standard CNC machine language, then extract data points and interpolates them to generate the robot trajectory patterns as motion references. Then, the control system uses the modified inverse kinematic equation to determine the length of each link to move the end effector to track the trajectory patterns from the previous G-code extraction process. The inverse kinematic equation is modified especially for the five-axis PMS CNC milling machine by including machine-offset and tools-offset parameters so it will be easier for the control system to implement the kinematic equation. As expected, the system simulation results successfully followed the G-Code program moving commands. The average error of the length control system is 0,1 mm, while the average error of the length change rate control system is 1,8 mm/s. The maximum error is 26.9 mm was caused by the system's inability to follow the motion profile in transient. It can be concluded that 6-DOF Stewart platform parallel structures,which provide better performance than serial structures, can be implemented as a new concept for the motion mechanism of five-axis CNC milling machines. The five-axis PMS CNC milling machine also promises better performance than conventional five-axis gantry structures CNC.

The article considers the control system of a parallel structure mechatronic device for space application such as a hexapod (Stewart platform). The solution of the inverse problem of kinematics is described and the necessity of solving the direct problem of kinematics by numerical methods is substantiated. During the research, it was revealed that the main source of positioning errors of the hexapod without the main feedback is its linear drives, which have systematic errors in the mechanical part of the linear transmission, gearbox, in the location of the motor windings; temperature errors due to changes in the dimensions of parts due to heating or cooling; errors caused by elastic deformations under load. To improve the static accuracy of the hexapod, a number of both design and software solutions are proposed: mechanical transmission preload, individual calibration of each drive, compensation for thermal expansion, etc. To improve the dynamic accuracy, it is proposed to use the method of controlling linear drives in the servo mode along with ensuring the trajectory of the platform with the limitation of the speed of its movement and derivatives of the speed. The use of these methods makes it possible to significantly improve the accuracy of the operation of the mechanisms of a parallel structure and, thereby, to approach the achievement of the limiting qualitative properties of onboard optical-electronic and information systems of spacecraft and stations.

Background: The vestibular end organs (semicircular canals, saccule and utricle) monitor head orientation and motion. Vestibular stimulation by means of controlled translations, rotations or tilts of the head represents a routine manoeuvre to test the vestibular apparatus in a laboratory or clinical setting. In diagnostics, it is used to assess oculomotor postural or perceptual responses, whose abnormalities can reveal subclinical vestibular dysfunctions due to pathology, aging or drugs.Objective: The assessment of the vestibular function requires the alignment of the motion stimuli as close as possible with reference axes of the head, for instance the cardinal axes naso-occipital, interaural, cranio-caudal. This is often achieved by using a head restraint, such as a helmet or strap holding the head tightly in a predefined posture that guarantees the alignment described above. However, such restraints may be quite uncomfortable, especially for elderly or claustrophobic patients. Moreover, it might be desirable to test the vestibular function under the more natural conditions in which the head is free to move, as when subjects are tracking a visual target or they are standing erect on the moving platform. Here, we document algorithms that allow delivering motion stimuli aligned with head-fixed axes under head-free conditions.Methods: We implemented and validated these algorithms using a MOOG-6DOF motion platform in two different conditions. 1) The participant kept the head in a resting, fully unrestrained posture, while inter-aural, naso-occipital or cranio-caudal translations were applied. 2) The participant moved the head continuously while a naso-occipital translation was applied. Head and platform motion were monitored in real-time using Vicon.Results: The results for both conditions showed excellent agreement between the theoretical spatio-temporal profile of the motion stimuli and the corresponding profile of actual motion as measured in real-time.Conclusion: We propose our approach as a safe, non-intrusive method to test the vestibular system under the natural head-free conditions required by the experiential perspective of the patients.

This paper presents the process of designing a highly repeatable calibration station for the NaviFast 6D measuring arm. This is a new solution, characterized by repeatability at the level of 1 μm for access from one direction, the ability to change the setting of the base and effector of the arm, fully automatic measurement, and relatively low construction cost. In this solution, human error has been eliminated as much as possible. The stand consists of two Stewart platforms equipped with double-acting pneumatic actuators on which the calibration arm is placed. The stand is able to provide 4096 different positions – a sufficient number for calibrating the arms. In addition, the paper presents the methodology of designing stations for various types of measuring arms and the methodology of selecting parameters for the appropriate working space of a measuring arm. • The design of stand for calibration the NaviFast6D measuring arms. • The method of measuring the repeatability of the test stand. • Simulation and experimental studies of the repeatability of the test stand. [ABSTRACT FROM AUTHOR]

The windy environment is the main cause affecting the efficiency of offshore wind turbine installation. In order to improve the stability and efficiency of single-blade installation of offshore wind turbines under high wind speed conditions, the Stewart platform is used as an auxiliary tool to help dock the wind turbine blade in this paper. In order to verify the effectiveness of the Stewart platform for blade docking, a blade docking simulation system consisting of the Stewart platform, wind turbine blade, and wind load calculation module was built based on Simulink/Simscape Multibody. At the same time, the PID algorithm is used to control the Stewart platform so that the blade can effectively track the desired trajectory during the docking process to ensure the successful docking of the blade. Through the simulation of the docking process for blades with a length of 61.5 meters, this paper successfully demonstrates a docking system that might facilitate future docking processes. It also shows that the Stewart platform can effectively reduce the vibration and the movement range of the blade root and improve the stability and efficiency of blade docking. [ABSTRACT FROM AUTHOR]

This paper presents how forces are perceived in a racing simulator based on a Stewart Platform. By retrieving calculated forces in a racing game by its physics engine and comparing them to real-life measurements during the platforms motions it is possible to evaluate the platforms immersiveness. Virtual values extracted from the game engine are deemed satisfactory to their real life counterparts and serve as a baseline. In order to evaluate forces created by the simulator, a lap around a virtual test track is recorded and played back while an accelerometer and gyroscope record its movements. Overall, accelerations recorded in the direction of X and Y axis along with angular speed of rotation around the aforementioned those axis. To accurately comparing every derived force, the recorded virtual lap is divided into sections representing the five most common manoeuvres during racing. These comparisons serve as an evaluation method to measure the immersiveness of the simulator. [ABSTRACT FROM AUTHOR]

Introduction: We study optimization methods for poses and movements of chained Stewart platforms (SPs) that we call an “Assembler” Robot. These chained SPs are parallel mechanisms that are stronger, stiffer, and more precise, on average, than their serial counterparts at the cost of a smaller range of motion. By linking these units in a series, their individual limitations are overcome while maintaining truss-like rigidity. This opens up potential uses in various applications, especially in complex space missions in conjunction with other robots.Methods: To enhance the efficiency and longevity of the Assembler Robot, we developed algorithms and optimization models. The main goal of these methodologies is to efficiently decide on favorable positions and movements that reduce force loads on the robot, consequently minimizing wear.Results: The optimized maneuvers of the interior plates of the Assembler result in more evenly distributed load forces through the legs of each constituent SP. This optimization allows for a larger workspace and a greater overall payload capacity. Our computations primarily focus on assemblers with four chained SPs.Discussion: Although our study primarily revolves around assemblers with four chained SPs, our methods are versatile and can be applied to an arbitrary number of SPs. Furthermore, these methodologies can be extended to general over-actuated truss-like robot architectures. The Assembler, designed to function collaboratively with several other robots, holds promise for a variety of space missions.

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Singular positions may be identified in planning the motion of a robotic platform (for example, the Stewart platform). The presence of singular positions in the working region is determined by means of the controllability index, which compares singular values of the singular expansion of the Jacobi matrix. The controllability of the platform is analyzed in terms of the mean controllability index and the percentage of points in the working region that exceed the critical value of the index. Computational experiments are conducted for platform designs differing in the position of the hinges relative to the mobile platform and the immobile base. The influence of the hinge position on the platform's controllability is described. [ABSTRACT FROM AUTHOR]

The hybrid vibration isolation, which takes advantages of both the passive and active approaches, has been an important solution for space missions. The objective of this paper is to design a vibration isolation platform for payloads on spacecrafts with the robust, wide bandwidth, and multi-degree-of-freedom (MDOF). The proposed solution is based on a parallel mechanism with six voice-coil motors (VCMs) as the actuators. The linear active disturbance resistance control (LADRC) algorithm is used for the active control. Numerical simulation results show that the vibration isolation platform performs effectively over a wide bandwidth, and the resonance introduced by the passive isolation is eliminated. The system robustness to the uncertainties of the structure is also verified by simulation.

This paper presents the automatic approach procedure of a flying vehicle, attached to an ABB 7600 robot, and a mobile platform, attached to a Stewart platform. Due to a nonlinear dynamic behavior, it is necessary to implement complex control, stabilization and guidance schemes. The proposed solution for this system includes the development of an algorithm based on a backstepping control method, the controller design methodology being based on Lyapunov's stability theory. The proposed command law requires that the states are known, but it is also necessary to introduce a series of state estimators. Tracking a mobile platform is critical in surveillance, reconnaissance and tracking missions, with the control methodology defining a clear distinction between translational and rotational dynamics. The proposed algorithm is developed by separating two types of states involving an inverse kinematics, known as algebraic kinematics, in which the dynamic movements of the two pieces of equipment are used. The dynamics of the ABB 7600 robot involves a movement with seven degrees of freedom, while the Stewart platform can be used with a movement of six degrees of freedom. The proposed algorithm is implemented in both Matlab software and experimental testing. This paper provides results in terms of generating dynamics for both devices that can be used for simulating different scenarios of aerospace missions.