Gough-Stewart Parallel Manipulator Research Articles

Study the effect of changing Cables’ pattern on the workspace of a six DOF floating parallel marine robot (FPMR)

In this study, a Floating Parallel Marine Robot (FPMR) is studied while it is subjected to external forces generated by the sea waves. Two FPMR cable-bundles’ configurations are used. The 6–6 Stewart-Gough parallel manipulator configuration is compared with a new cable-bundles’ configuration called 6–3-3 FPMR. The effect of changing cable-bundles’ configuration is explored to enhance the workspace and the dynamic behavior of the FPMR. This study is performed using six DOFs FPMR having twelve cables i.e. 6 bundles. Over the FPMR workspace, the dynamic response and platform stiffness are investigated. The workspace and the dynamic analysis of FPMR are enhanced using the new 6–3-3 cable-bundles’ configuration.

The Stewart Hand: A Highly Dexterous, Six-Degrees-of-Freedom Manipulator Based on the Stewart-Gough Platform

In this work, the design, modeling, dimensional synthesis, and experimental characterization of a dexterous robotic hand based on the Stewart-Gough parallel manipulator are presented. The mechanism consists of three parallel linkage fingers with six prismatic actuators that control manipulation. An additional actuator maintains stable grasping forces. A computational model to predict the hand's workspace is then utilized to determine the optimal design parameters that maximize the workspace size and manipulability. A physical prototype based on the optimized parameters is built and experimentally characterized to assess its performance (Figure 1).

Load Parameter Identification for Parallel Robot Manipulator Based on Extended Kalman Filter

Load is the main external disturbance of a parallel robot manipulator. This disturbance will cause dynamic coupling among different degrees of freedom and make heaps of model-based control methods difficult to apply. In order to compensate this disturbance, it is crucial to obtain an accurate dynamic model of load. However, in practice, the load is always uncertain and its dynamic parameters are arduous to know a priori. To cope with this problem, this paper proposes a novel and simple approach to identify the dynamic parameters of load. Firstly, the dynamic model of the parallel robot manipulator with uncertain load is established and the dynamic coupling caused by load is also analyzed. Then, according to the dynamic model, the excitation signal is designed and a weak nonlinear dynamic model is derived. Furthermore, the identification model is presented and the identification algorithm based on the extended Kalman filter is designed. Lastly, numerical simulation results, obtained using a six-degree-of-freedom Gough–Stewart parallel manipulator, demonstrate the good estimation performance of the proposed method.

A calibration procedure for reconfigurable Gough-Stewart manipulators

This paper introduces a calibration procedure for the identification of the geometrical parameters of a reconfigurable Gough-Stewart parallel manipulator. By using the proposed method, the geometry of a general Gough-Stewart platform can be evaluated through the measurement of the distance between couples of points on the base and mobile platform, repeated for a given set of different poses of the manipulator. The mathematical modelling of the problem is described and a numeric algorithm for an efficient solution to the problem is proposed. Furthermore, an application of the proposed method is discussed with a numerical example, and the behaviour of the calibration procedure is analysed as a function of the number of acquisitions and the number of poses.

Trajectory-tracking of 6-RSS Stewart-Gough manipulator by feedback-linearization control using a novel inverse dynamic model based on the force distribution algorithm

ABSTRACT 6-RSS Stewart-Gough parallel manipulator contains six crank-rod limbs connecting the base and moving platforms to each other, forming a 6DOF manipulator. In this paper, we introduce a novel decoupled inverse dynamic model for this manipulator based on the Force Distribution Algorithm. The performance of the proposed model was evaluated in tracking a complex trajectory (of multiple segments with simultaneous translational and rotational motions) using feedback-linearization control in the joint space and compared with that of the Lagrangian inverse dynamic model. Results showed that this model leads to a better performance in feedback-linearization control, especially when the reference trajectory is quantized, and with less calculation burden in comparison with the Lagrangian model. The control system employing both models showed robustness against payload uncertainty on the moving platform (150% of the moving platform’s mass). The performance assessment and the robustness approval were performed in simulation using a Simscape model specifically built for this purpose in the Simulink environment.

A Gough–Stewart parallel manipulator with configurable platform and multiple end-effectors

This work describes a novel robot manipulator with configurable platform. Three internal degrees-of-freedom are added for controlling the relative orientation of the terminal links supporting multiple end-effectors of a Gough–Stewart-type parallel manipulator. The instantaneous forward and inverse kinematic analyses of the robot are derived using the theory of screws. Furthermore, the exploitation of this approach for deriving the acceleration analyses of a parallel manipulator with configurable platform is novel in this research field. As an intermediate step the forward and inverse displacement analyses are also investigated. A numerical example is compared with the outcome of a commercial software demonstrating the approach correctness.

Dynamic decoupling analysis and experiment based on a class of modified Gough-Stewart parallel manipulators with line orthogonality

In this paper, a class of modified Gough-Stewart parallel manipulators (MGSPMs) with line orthogonality is presented in order to fulfill the dynamic decoupling along the Z-axis. Relations between kinematic orthogonality, static orthogonality, and dynamic orthogonality are analytically formulated using double hyperboloids. Based on the derived formulas, it is proven that a class of MGSPMs with line orthogonality does exist, which expands the dynamic orthogonality from a point to a line. The evaluating factors are defined to carry out thorough cross coupling investigations. With the aid of numerical examples, a class of MGSPMs with line dynamic orthogonality is shown to exhibit large workspace with low coupling and high precision. A physical prototype is established and the experimental results confirm the high precision and approximately decoupled characteristics. The presented MGSPMs with line dynamic orthogonality possess better mechanical feasibility than conventional GSPMs. Moreover, two major constraints, namely that all six struts must have the same stiffness and a compliant center - which are difficult to satisfy - are removed or relaxed, thus greatly expanding the range of possible applications.

Kinematics Simulation of Gough-Stewart Parallel Manipulator by Using Simulink Package in Matlab Software

The Gough Stewart Robotic manipulator is a parallel manipulator with six-degree of freedom, which has six equations of Kinematics (Inverse and forward), with six variables (Lengths, Position, and Orientation). In this work derived the inverse equations, which used to compute the lengths of the linkages and its changes depended on the position and orientation of the platform's center, then derived the forward equations to calculate the position and orientation of the moving platform in terms of the lengths. This theoretical model of the kinematics analysis of the Gough Stewart has been built into the Simulink package in Matlab to obtain the lengths, position, and orientation for the manipulator at any time of motion. The input parameters (Position and Orientation) in inverse blocks compared with the output parameters (Position and Orientation) in the forward blocks, which show good results.

Workspace analysis of a Gough-Stewart type cable marine platform subjected to harmonic water waves

A floating cable marine platform is put forward using the 3–3 Stewart-Gough parallel manipulator as an inspiring structure. The marine platform has three degrees of freedom and is composed of a cylindrical floating structure and six mooring cables anchored to the seabed. In order to provide necessary motion compensation to impinging harmonic water wave loads, necessary mooring tensions are applied to the cables to prevent them from becoming slack under the external load. The platform is analyzed in the framework of rigid-body dynamics and water wave loading is estimated by integral methods. Workspace is identified for the cable marine platform, minimum static submerged depths are calculated, and kinematic variables are investigated for various platform positions within the marine platform workspace.

Compatible reachable workspaces of symmetrical Stewart–Gough parallel manipulators

The reachable workspace of a 6-DOF parallel manipulator developed using most existing methods is not a compatible workspace, as some of its subspaces might not be reachable through a continuous motion starting from the initial assembly configuration. This paper uses simple geometric properties and some characteristics of workspace boundaries to develop a compatible reachable workspace for a symmetrical Stewart–Gough manipulator. Equations that generate the entire workspace boundary can be easily determined by solving direct kinematics at five specific points, and the compatible workspace of a symmetrical manipulator can be developed within 10min using a personal computer.

Optimal Design of Acceleration Sensor Based on Generalized Gough-Stewart Parallel Manipulator Lying on Pair of Circular Hyperboloids

A parallel manipulator is a better solution to be used as the contracture sensitive element for a six-dimensional acceleration sensor, and its isotropy directly affects the measuring accuracy and control performance. A traditional Gough-Stewart parallel manipulator is impossible to achieve complete isotropy because the payload is restricted rigorously and does not exist in physics. Therefore, it is proposed to solve this problem by using a generalized Gough-Stewart parallel manipulator(GGSPM). The concept and description of a pair of circular hyperboloids are introduced to define and generate a generalized Gough-Stewart parallel manipulator with the minimal and independent parameters, and the close-formed and analytical formulations of acceleration isotropy are derived. The results prove that the acceleration isotropy for a GGSPM can be achieved and mechanically feasible. The proposed routine has geometric meaning and can be used to generate and classify generalized Gough-Stewart parallel manipulators, which is a novel method to design the configuration of a parallel manipulator based six-dimensional acceleration sensor.

Six-DOF parallel manipulators with maximal singularity-free joint space or workspace

SUMMARYSingularity-free workspace is a very important criterion for the design of manipulators, especially for parallel manipulators which are well known for their limited workspace and complex singularities. This paper studies geometric parameters and dexterity measures that affect the size of a singularity-free joint space and proposes methods for the development of 6-DOF Stewart–Gough parallel manipulators that have better singularity-free joint space. With a local dexterity measure as the objective function, a systematic method is employed to search for the design with a maximal singularity-free joint space. The related workspaces are also investigated. It is shown that the workspace is not proportional to the size of the joint space and that manipulators with a larger singularity-free workspace usually have relatively poor dexterity.

Orientation-singularity analysis and orientationability evaluation of a special class of the Stewart–Gough parallel manipulators

SUMMARYThis paper addresses the orientation-singularity analysis and the orientationability evaluation of a special class of the Stewart–Gough parallel manipulators in which the moving and base platforms are two similar semi-symmetrical hexagons. Based on the half-angle transformation, an analytical polynomial of degree 13 that represents the orientation-singularity locus of this special class of parallel manipulators at a given position is derived. Graphical representations of the orientation-singularity locus of this class of manipulators are illustrated with examples to demonstrate the results. Based on the description of the orientation-singularity and nonsingular orientation region of this class of parallel manipulators, a performance index, referred to as orientationability, which describes the orientation capability of this class of manipulators at a given position, is introduced. A discretization algorithm is proposed for computing the orientationability of the special class of parallel manipulators at a given position in the workspace. Moreover, the effects of the design parameters and position parameters on the orientationability are also investigated in detail. Based on the orientationability performance index, another performance index, referred to as practical orientationability, representing the practical orientation capability of the manipulators at a given position, is introduced. In this performance index, singularities, the limitations of active and passive joints and link interferences are all taken into consideration. Furthermore, the practical orientationability of the special class of parallel manipulators studied here is also analyzed over several plane sections of the position-workspace in detail.

Orientationability analyses of a special class of the Stewart–Gough parallel manipulators using the unit quaternion representation

This paper addresses the orientation-singularity and orientationability analyses of a special class of the Stewart–Gough parallel manipulators whose moving and base platforms are two similar semi-symmetrical hexagons. Employing a unit quaternion to represent the orientation of the moving platform, an analytical expression representing the singularity locus of this class of parallel manipulators in a six-dimensional Cartesian space is obtained. It shows that for a given orientation, the position-singularity locus is a cubic polynomial expression in the moving platform position parameters, and for a given position, the orientation-singularity locus is an analytical expression but not a polynomial directly with respect to the mobile platform orientation parameters. Further inspection shows that for the special class of parallel manipulators, there must exist a nonsingular orientation void in the orientation space around the orientation origin for each position in the position-workspace. Therefore, a new performance index referred to as orientationability is introduced to describe the orientation capability of the special class of manipulators at a given position. A discretization algorithm is proposed for the computation of the orientationability of the special class of manipulators. Moreover, effects of the design parameters and position parameters on the orientationability are investigated in details. Based on the orientationability performance index, another novel performance index referred to as practical orientationability is presented which represents the practical orientation capability of the manipulator at a given position. The practical orientationability not only can satisfy all the kinematic demands and constraints of such class of manipulators, but also can guarantee that the manipulator is nonsingular.

Optimal design of a class of generalized symmetric Gough–Stewart parallel manipulators with dynamic isotropy and singularity-free workspace

SUMMARYIn this paper, the definition of generalized symmetric Gough–Stewart parallel manipulators is presented. The concept of dynamic isotropy is proposed and the singular values of the bandwidth matrix are introduced to evaluate dynamic isotropy and solved analytically. Considering the payload's mass-geometry characteristics, the formulations for completely dynamic isotropy are derived in close form. It is proven that a generalized symmetric Gough–Stewart parallel manipulator is easer to achieve dynamic isotropy and applicable in engineering applications. An optimization procedure based on particle swarm optimization is proposed to obtain better dexterity and large singularity-free workspace, which guarantees the optimal solution and gives mechanically feasible realization.

Singularity kinematics principle and position-singularity analyses of the 6-3 Stewart-Gough parallel manipulators

This paper presents a new principle and method of kinematics to analyze the singularity of Stewart-Gough parallel manipulators and addresses the property identification of the position-singularity loci of the 6-3 Stewart-Gough manipulators for special orientations. Based on the kinematic relationship of a rigid body, a necessary and sufficient condition that three velocities of three non-collinear points in a moving rigid body can determine a screw motion is addressed and some typical singular configurations of the 6-3 Stewart-Gough parallel manipulators are also addressed in detail. With the above-mentioned condition, a symbolic analytical polynomial expression of degree three in the moving platform position parameters, representing the position-singularity locus of the 6-3 Stewart-Gough manipulators for special orientations, is derived; and the property identification of the position-singularity loci of the 6-3 Stewart-Gough manipulator for these special orientations is investigated at length. It is shown that position-singularity loci of the 6-3 Stewart-Gough parallel manipulator for these special orientations will be a plane and a hyperbolic paraboloid, even three intersecting planes.

Dynamic isotropic design of a class of Gough–Stewart parallel manipulators lying on a circular hyperboloid of one sheet

Abstract This paper proposes an optimal design method based on dynamic isotropy conditions of a generalized natural frequency matrix in task space for a standard Gough–Stewart parallel manipulator (GSPM). Firstly, the dynamic isotropy conditions are discussed and presented. Next, it is proved that standard GSPMs lie on a circular hyperboloid of one sheet. Further, we present a method to use a circular hyperboloid to construct 3-3-, 6-3- and 6-6-type standard GSPMs. Moreover, such novel definition is used to examine various dynamic isotropy conditions as functions of the coefficients of a hyperboloid. An optimal design method is also proposed accordingly. Finally, a numerical example is given to illustrate the design procedures. The results are very close to the complete dynamic isotropy.

Dynamics of the 6-6 Stewart parallel manipulator

Recursive matrix relations in kinematics and dynamics of the 6-6 Stewart-Gough parallel manipulator having six mobile prismatic actuators are established in this paper. Controlled by six forces, the manipulator prototype is a spatial six-degrees-of-freedom mechanical system with six parallel legs connecting to the moving platform. Knowing the position and the general motion of the platform, we develop first the inverse kinematics problem and determine the position, velocity and acceleration of each manipulator's link. Further, the inverse dynamics problem is solved using an approach based on the principle of virtual work, but it has been verified the results in the framework of the Lagrange equations with their multipliers. Finally, compact matrix relations and graphs of simulation for the input velocities and accelerations, the input forces and powers are obtained.

Orientation workspace analysis of a special class of the Stewart–Gough parallel manipulators

SUMMARYThe workspace of a robotic manipulator is a very important issue and design criteria in the context of optimum design of robots, especially for parallel manipulators. Though, considerable research has been paid to the investigations of the three-dimensional (3D) constant orientation workspace or position workspace of parallel manipulators, very few works exist on the topic of the 3D orientation workspace, especially the nonsingular orientation workspace and practical orientation workspace. This paper addresses the orientation workspace analysis of a special class of the Stewart–Gough parallel manipulators in which the moving and base platforms are two similar semisymmetrical hexagons. Based on the half-angle transformation, a polynomial expression of 13 degree that represents the orientation singularity locus of this special class of the Stewart–Gough parallel manipulators at a fixed position is derived and graphical representations of the orientation singularity locus of this special class of the Stewart–Gough manipulators are illustrated with examples to demonstrate the result. Exploiting this half-angle transformation and the inverse kinematics solution of this special class of the Stewart–Gough parallel manipulators, a discretization method is proposed for computing the orientation workspace of this special class of the Stewart–Gough parallel manipulators taking limitations of active and passive joints and the link interference all into consideration. Based on this algorithm, this paper also presents a new discretization method for computing the nonsingular orientation workspace of this class of the manipulators, which not only can satisfy all the kinematics demand of this class of the manipulators but also can guarantee the manipulator is nonsingular in the whole orientation workspace, and the practical orientation workspace of this class of the manipulators, which not only can guarantee the manipulator is nonsingular and will never encounter any kinematic interference but also can satisfy the demand of the orientation workspace with a regular shape in practical application, respectively. Examples of a 6/6-SPS Stewart–Gough parallel manipulator of this special class are given to demonstrate these theoretical results.

Research on the orientation-singularity and orientation-workspace of a class of Stewart—Gough parallel manipulators

This article addresses the orientation-singularity analysis and orientation-workspace computation of a class of Stewart—Gough manipulators in which the moving and base platforms are two similar semisymmetrical hexagons. Based on the half-angle transformation, a polynomial expression of 13 degrees that represents the orientation-singularity locus of this class of Stewart—Gough manipulators at a fixed position is derived, and graphical representations of the orientation-singularity locus of this class of Stewart—Gough manipulators are illustrated with examples to demonstrate the result. Using this half-angle transformation, a discretization method is proposed for computing the orientation-workspace of this class of Stewart—Gough manipulators taking limitations of active and passive joints and the link interference into consideration. In addition, this article also presents a new discretization method for the computation of the non-singular orientation-workspace of this class of Stewart—Gough manipulators, where singularities, limitations of active and passive joints, and the link interference are all taken under consideration. The non-singular orientation-workspace can not only satisfy the kinematics demand of this class of Stewart—Gough parallel manipulators, but also can guarantee that the manipulator is non-singular in the whole orientation-workspace. Examples of a 6/6-SPS Stewart—Gough manipulator of this class are given to demonstrate the results.