Stewart-Gough Platform Research Articles

An automatic test complex for unmanned aerial vehicle engines

One of the most important components of an aircraft ground testing infrastructure is hardware and software test benches with complete or partial imitation of the aircraft in complex, on-board electronic equipment and controls. The development and debugging of such complexes is a complicated problem. The solution for this problem is presented in in the form of the automatic test complex for unmanned aerial vehicle engines and propulsion devices mounted on the Gough–Stewart platform manipulator. The complex is based on the modular measuring platform and also includes a set of various sensitive elements for forces, vibration, speed, torque, video and sound registration. The article also describes the procedure for one of the functional assessment stages of the U AV engine test complex, notably, the assessment of the tensometric measurement accuracy. Further development of the complex associated with the software implementation of atmosphere, wind turbulence models and modules for preliminary formation of test scenarios-UAV flight paths.

Path generation and optimization for DBB measurement with continuous data capture

In this paper we present a systematic approach to generating a path for continuous Double Ball Bar(DBB) measurement. The generated path is feasible, free of collision, jerk-optimized and sensitive to the perturbation in kinematic parameters. The approach could be automated and be applied not only to parallel kinematic machines(PKM) but also to serial mechanism. We will discuss about the properties of continuous DBB measurement and conclude that the condition number of identification Jacobian is a proper index to describe the sensitivity of a continuous path to the perturbation in kinematic parameters. The sensitivity of the generated path will be experimentally validated on a Stewart-Gough platform with comparison to two otherwise designed paths. Measurement shows that the generated path is also suitable for time-demanding tasks.

Evaluation of Topological Properties of Parallel Manipulators Based on the Topological Characteristic Indexes

SUMMARYThe topological structure of a parallel manipulator (PM) determines its intrinsic topological properties (TPs). The TPs further determine essential kinematic and dynamic properties of the mechanism. TPs can be expressed through topological characteristics indexes (TCI). Therefore, defining a set of TCIs is an important issue to evaluate the TPs of PMs. This article addresses the evaluation of topological properties (ETP) of PMs based on TCI. A general and effective ETP method for PMs is proposed. Firstly, 12 TCIs are proposed, including 8 quantitative TCIs, that is, position and orientation characteristics sets (POC), dimension of the POC set, degrees of freedom (DOF), number of independent displacement equations, types and number of an Assur kinematic chain (AKC), coupling degrees of the AKCs, degrees of redundancy and the number of overs; as well as 4 qualitative TCIs, that is, selection of actuated joints, identification of inactive joints, DOF type and Input–Output motion decoupling. Secondly, the ETP method is illustrated by evaluating some well-known PMs including the Delta, Tricept, Exechon, Z3, H4 and the Gough–Stewart platform manipulators, as well as 28 other typical PMs. Via the ETP analysis of these mechanisms also some valuable design knowledge is derived and guidelines for the design of PMs are established. Finally, a 5-DOF decoupled hybrid spraying robot is developed by applying the design knowledge and the design guidelines derived from the ETP analysis.

Математическая модель динамики периферийного стыковочного механизма с накоплением кинетической энергии сближения космических аппаратов

The new peripheral docking mechanism is part of a docking unit designed in compli-ance with the International Docking System Standard (IDSS). The mechanism kinematics is based on the Gough-Stewart platform. Spring mechanisms are used for transformation of spacecraft approach kinetic energy. However, traditional damping is replaced by energy ac-cumulation. Therefore, the design includes new devices. The dynamic math model of the dock-ing mechanism described in this paper takes into account its main features – kinematics, inertia properties and generation of internal active forces by separate devices. Along with spacecraft motion equations and algorithms of docking unit contact interaction analysis, this model is part of a docking math model used for the analysis of kinematics and dynamics processes from the first contact to the end of retraction. Key words: spacecraft, docking mechanism, dynamics equations.

Alignment-and-metrological facility for fine adjustment of antenna linear and angular position during spacecraft assembly

The paper discusses issues involved in fine adjustment of the linear and angular position of antenna system reflectors on a spacecraft (SC) during its assembly using an alignment-and-metrology facility that has been developed, which consists of a 6-DOF pointing device and a laser coordinate measurement tracker. Achieving the specified linear and angular positions of antenna system elements in the SC datum reference frame, reducing human effort and time needed to perform this processing operation is an important task when building a spacecraft. To address this problem, a procedure was developed and tried out during an actual SC assembly consisting in the joint use of the 6-DOF pointing device Hexapod PM-mkm-P and the high-precision laser tracker Leica AT 403 for measuring the coordinates. An algorithm was developed for hardware/software interfacing between elements of the alignment-and-metrology facility, which provides iterative linear and angular positioning of the antenna reflectors in a closed loop with a feedback. The paper discusses sources of errors and the way to minimize their effect on the operation of various types of pointing using continuous monitoring by means of an external measuring system. The developed alignment-and-metrology facility provided high-precision spatial positioning of antenna elements in the SC coordinate system, which made it possible to rule out any errors by operator/installation worker during alignment and significantly reduce the time needed to perform the said operation. Key words: spacecraft, antenna alignment, 6-DOF hexapod-type platform with parallel kinematics, Gough-Stewart platform, laser coordinate measuring system.

Evolution and Current Applications of Robot-Assisted Fracture Reduction: A Comprehensive Review.

Robots in orthopedic surgery have been developed rapidly for decades and bring significant benefits to the patients and healthcare providers. However, robotics in fracture reduction remains at the infant stage. As essential components of the current robotic system, external fixators were used in fracture reduction, including the unilateral and Ilizarov-like ring fixators. With emerging of the industrial robots and mechanical arms, their sterilized variants were developed as the serial robots, including the traction device and robotic arm, for fracture reduction. Besides, parallel robots (e.g., Gough-Stewart platform) were devised for lower extremity traction and fracture reduction. After combining the advantages of the serial and parallel mechanisms, hybrid robots can fulfill specific clinical requirements (e.g., the joint fracture, including multiple major fragments). Furthermore, with the aid of intra-operative navigation systems, fracture reduction can be performed under real-time guidance. The paper presents a comprehensive overview of the advancement of the robots in fracture reductionand evaluates research challenges and future perspectives, including ergonomic and economic issues, operation time, artificial realities and intelligence, and telesurgery.

Realization, Programming and Controlling of the Stewart-Gough platform

Realization, Programming and Controlling of the Stewart-Gough platform

Dynamic analysis of a six-degree of freedom wave energy converter based on the concept of the Stewart-Gough platform

A novel wave energy converter (WEC) design, based on the concept of the Stewart-Gough platform (SGP) is being investigated. The main objectives of this study are to present the proposed WEC based on the SGP (WEC-SGP) and to establish the necessary equations to describe the motion of the SGP to be used as a WEC. A kinematic analysis is developed to evaluate the leg lengths required to track the planned trajectory determined by the elevation of the free surface of the sea. Furthermore, the WEC-SGP dynamical analysis as formulated by the Newton-Euler approach is solved to find the required leg forces to support the effect of the hydrodynamic forces and the force moments acting on the upper floating component. Linear wave theory is used to analyze the WEC-SGP and some of the kinematic aspects of linear waves are used as input information for the kinematic and dynamic analysis. The instantaneous and mean power provided by the WEC-PSG are calculated for regular wave conditions. The results show that the proposed WEC-SGP configuration might increase the conversion of the wave energy, since all degrees of freedom in its motion are being used, as compared with the traditional heaving point absorber WEC.

A new method for the study of parabolic impact of foam-core sandwich panels

Lightweight sandwich panels with composite facesheets and foam core have high impact energy absorption capability and are widely employed in multifunctional applications such as aircraft and marine structures. The dynamic behaviour of sandwich panels is typically studied for impact loading at normal angle of incidence but the structures are more frequently loaded at some oblique angle or with a complex tri-dimensional trajectory in real engineering situations. The damage area and damage modes for these trajectories are significantly different and it is not sufficient to study only normal impacts. There are well established experimental protocols for normal or oblique impact tests using devices like the drop tower, but impacts with complex trajectory are difficult to characterise experimentally. In this paper, a Gough-Stewart platform with six degrees of freedom has been modified to develop an original tri-dimensional impact device called Hexapod. The trajectory is defined to an impactor attached to the seventh jack of the Hexapod to study the response of sandwich plates to impact loading with complex trajectories. The applicability of the newly developed device is demonstrated by studying parabolic impact with different trajectories on sandwich plates with Kevlar facesheets and Rohacell foam core. The time history of vertical and horizontal components of force is measured using tri-axial load cell and strain history is obtained from Digital Image Correlation of a high speed camera images. The results of the parabolic impact show the importance of shear behaviour of the foam in the progression of damage in the sandwich panels. Additionally, the response of the sandwich panels to parabolic impact was simulated numerically using explicit finite element code LS-DYNA. The results of the FE model are compared with experimental data in terms of the force history and strain contours.

Optimization based trajectory planning for real-time 6DoF robotic patient motion compensation systems.

PurposeRobotic stabilization of a therapeutic radiation beam with respect to a dynamically moving tumor target can be accomplished either by moving the radiation source, the patient, or both. As the treatment beam is on during this process, the primary goal is to minimize exposure of normal tissue to radiation as much as possible when moving the target back to the desired position. Due to the complex mechanical structure of 6 degree-of-freedom (6DoF) robots, it is not intuitive as to what 6 dimensional (6D) correction trajectory is optimal in achieving such a goal. With proportional-integrative-derivative (PID) and other controls, the potential exists that the controller may generate a trajectory that is highly curved, slow, or suboptimal in that it leads to unnecessary exposure of healthy tissue to radiation. This work investigates a novel feedback planning method that takes into account a robot’s mechanical joint structure, patient safety tolerances, and other system constraints, and performs real-time optimization to search the entire 6D trajectory space in each time cycle so it can respond with an optimal 6D correction trajectory.MethodsComputer simulations were created for two 6DoF robotic patient support systems: a Stewart-Gough platform for moving a patient’s head in frameless maskless stereotactic radiosurgery, and a linear accelerator treatment table for moving a patient in prostate cancer radiation therapy. Motion planning was formulated as an optimization problem and solved at real-time speeds using the L-BFGS algorithm. Three planning methods were investigated, moving the platform as fast as possible (platform-D), moving the target along a straight-line (target-S), and moving the target based on the fastest descent of position error (target-D). Both synthetic motion and prior recorded human motion were used as input data and output results were analyzed.ResultsFor randomly generated 6D step-like and sinusoidal synthetic input motion, target-D planning demonstrated the smallest net trajectory error in all cases. On average, optimal planning was found to have a 45% smaller target trajectory error than platform-D control, and a 44% smaller target trajectory error than target-S planning. For patient head motion compensation, only target-D planning was able to maintain a ≤0.5mm and ≤0.5deg clinical tolerance objective for 100% of the treatment time. For prostate motion, both target-S planning and target-D planning outperformed platform-D control.ConclusionsA general 6D target trajectory optimization framework for robotic patient motion compensation systems was investigated. The method was found to be flexible as it allows control over various performance requirements such as mechanical limits, velocities, acceleration, or other system control objectives.

Аналіз характеристики точності відтворення еталонної траєкторії платформою Гауфа-Стюарта з системою управління для різних видів завдань

Аналіз характеристики точності відтворення еталонної траєкторії платформою Гауфа-Стюарта з системою управління для різних видів завдань

Complete kinematic analysis of the Stewart-Gough platform by unit quaternions

In this paper, a complete analysis of Stewart–Gough platform kinematics by unit quaternions is proposed. Even when unit quaternions have been implemented in different applications (including a kinematic analysis of the Stewart platform mechanism), the research regarding the application of this approach is limited only to the analysis of some issues related to the kinematic properties of this parallel mechanism. For this reason, a complete analysis of the Stewart–Gough platform is shown. The derivation of the inverse and forward kinematics of the Stewart platform using unit quaternions shows that they are suitable to represent the orientation of the upper platform due to their simplicity, equivalence, and compact representation as compared to rotation matrices. Then, the leg velocities are derived to compute these values under different conditions.

Kinematics of the Gough-Stewart Platform by Means of the Newton-homotopy Method

In this work the forward kinematic problem of the general Gough-Stewart is easily formulated and solved combining the homotopy continuation method and the Newton-Raphson method. Unlike most contributions approaching the topic, in this work the Gough-Stewart platform is considered as a parallel manipulator of general geometry, e.g., it is composed of two three-dimensional platforms. The closure kinematic constraints required to approach the forward displacement analysis are formulated based on linear combinations of three unit vectors attached to the moving platform and one vector relating the position of the moving platform as observed from the base. For the robot manipulator of general geometry a non-linear system of twelve non-linear equations are generated and solved by means of the Newton-homotopy continuation method. Numerical examples are provided with the purpose to illustrate the proposed method.

Optimal Kinematic Design of a 6-UCU Kind Gough-Stewart Platform with a Guaranteed Given Accuracy

The 6-UCU (U-universal joint; C-cylinder joint) kind Gough-Stewart platform is extensively employed in motion simulators due to its high accuracy, large payload, and high-speed capability. However, because of the manufacturing and assembling errors, the real geometry may be different from the nominal one. In the design process of the high-accuracy Gough-Stewart platform, one needs to consider these errors. The purpose of this paper is to propose an optimal design method for the 6-UCU kind Gough-Stewart platform with a guaranteed given accuracy. Accuracy analysis of the 6-UCU kind Gough-Stewart platform is presented by considering the limb length errors and joint position errors. An optimal design method is proposed by using a multi-objective evolutionary algorithm, the non-dominated sorting genetic algorithm II (NSGA-II). A set of Pareto-optimal parameters was found by applying the proposed optimal design method. An engineering design case was studied to verify the effectiveness of the proposed method.

Miniaturized multiaxial force/torque sensor with a rollable hexapod structure

Abstract Miniaturized force/torque sensors are relevant components for robotic interaction with humans and unknown environments. This paper presents a disruptive manufacturing process for multiaxial force/torque sensors based on a Stewart-Gough platform. The deformation element consists of a hexapod geometry with six sensing elements with a total diameter of 9 mm. The sensor manufacturing process is divided into three steps: 1. Milling a planar arrangement of sensing elements out of a 2 mm steel (1 .4301) plate, 2. applying twelve strain gauges in half-bridge configuration and 3. rolling the elements into a hexapod structure. The dimensions of the sensing elements are scalable to adjust the size and nominal measurement range of the sensor. The first prototype has a measuring range of 4 N and 66 mNm. The characterization of the sensor shows a maximal linearity and hysteresis error of 1.16% and a cross-sensitivity smaller than 2.76% .

An analytical approach for positioning error and mode shape analysis of n – legged parallel manipulator

ABSTRACTPrecise part positioning on a parallel manipulator is a challenging task for industries where positioning errors can restrict achieving the required quality of the part. However, in the literature, the positioning errors of the parallel manipulator are not explored extensively. In this paper, the main focus was to find out positioning errors of the parallel manipulator caused while machining. Lagrange formulation is used as part of the proposed analytical model to calculate the positioning errors of the platform under external forces. Moreover, the proposed generalised algorithm gives the positioning error of ‘n’ legged manipulator for any initial orientation of the platform, along with, eigenvalues and corresponding eigenvectors of the manipulator. The results are validated with software-based finite element analysis and by solving a numerical study from the literature. This approach can also be used for optimisation of design variables for minimum positioning error of the Gough–Stewart Platform.

A Novel Three-Loop Parallel Robot With Full Mobility: Kinematics, Singularity, Workspace, and Dexterity Analysis

A novel parallel robot, dubbed the SDelta, is the subject of this paper. SDelta is a simpler alternative to both the well-known Stewart–Gough platform (SGP) and current three-limb, full-mobility parallel robots, as it contains fewer components and all its motors are located on the base. This reduces the inertial load on the system, making it a good candidate for high-speed operations. SDelta features a symmetric structure; its forward-displacement analysis leads to a system of three quadratic equations in three unknowns, which admits up to eight solutions, or half the number of those admitted by the SGP. The kinematic analysis, undertaken with a geometrical method based on screw theory, leads to two Jacobian matrices, whose singularity conditions are investigated. Instead of using the determinant of a 6 × 6 matrix, we derive one simple expression that characterizes the singularity condition. This approach is also applicable to a large number of parallel robots whose six actuation wrench axes intersect pairwise, such as all three-limb parallel robots whose limbs include, each, a passive spherical joint. The workspace is analyzed via a geometric method, while the dexterity analysis is conducted via discretization. Both show that the given robot has the potential to offer both large workspace and good dexterity with a proper choice of design variables.

Adaptive sliding-mode controller based on the “Super-Twist” state observer for control of the Stewart platform

To provide a highly efficient control of nonlinear systems in the presence of nonmodeled dynamics and external perturbations, a new control law with feedback based on the sliding modes with an observer of the “Super-Twist” kind was proposed. For acceptable use of the continuous observer signal in the controller, presented were adaptive laws for adjustment of the control system parameters. Using the methods of Lyapunov function, system stability (convergence to a zone) was proved. This technique was proposed as an example of control and stabilization of the position of a parallel manipulator (Gough–Stewart platform). The presented mechanism with six degrees of freedom is used to control the secondary mirror of the “Large Millimeter Telescope Alfonso Serrano” situated in the state of Puebla, Mexico.

ADAMS-MATLAB co-simulation for kinematics, dynamics, and control of the Stewart–Gough platform

The mechanical structure known as Stewart–Gough platform is the most representative parallel robot with a wide variety of applications in many areas. Despite the intensive study on the kinematics, dynamics, and control of the Stewart–Gough platform, many details about these topics are still a challenging problem. In this work, the use of automatic dynamic analysis of multibody systems software for the kinematic and dynamic analysis of the Stewart–Gough platform is proposed. Moreover, a co-simulation automatic dynamic analysis of multibody systems (ADAMS)-MATLAB is developed for motion control of the Stewart–Gough platform end-effector. This computational approach allows the numerical solution for the kinematics, dynamics, and motion control of the Stewart–Gough platform and a considerable reduction on the analytical and programming effort. The obtained results in the three topics (kinematics, dynamics, and control) are validated by comparing them with analytical results reported in the literature. This kind of computational approach allows for the creation of virtual prototypes and saves time and resources in the development of Stewart–Gough platform-based robots applications.

Kinematic effects of number of legs in 6-DOF UPS parallel mechanisms

SUMMARYIn this paper, we study the kinematic effects of number of legs in 6-DOF UPS parallel manipulators. A group of 3-, 4-, and 6-legged mechanisms are evaluated in terms of the kinematic performance indices, workspace, singular configurations, and forward kinematic solutions. Results show that the optimum number of legs varies due to priorities in kinematic measures in different applications. The non-symmetric Wide-Open mechanism enjoys the largest workspace, while the well-known Gough–Stewart (3–3) platform retains the highest dexterity. Especially, the redundantly actuated 4-legged mechanism has several important advantages over its non-redundant counterparts and different architectures of Gough–Stewart platform. It has dramatically less singular configurations, a higher manipulability, and at the same time less sensitivity. It is also shown that the forward kinematic problem has 40, 16, and 1 solution(s), respectively for the 6-, 3-, and the 4-legged mechanisms. Superior capabilities of the 4-legged mechanism make it a perfect candidate to be used in more challenging 6-DOF applications in assembly, manufacturing, biomedical, and space technologies.