Stewart-Gough Manipulator Research Articles

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.

Analytical determination of shape singularities for three types of parallel manipulators

Singularity analysis is an important issue in mechanism design, as kinetostatic properties of a manipulator will undergo a sudden and dramatic change close to singular configurations. Architecture singularity is a type of singularity caused by a special architecture of a manipulator. In this work, a new approach is developed to find efficiently architectural singularity due to special platform shapes, or shape singularity for short. The new method is based on analytical formulation combined with detection of singularity with selected configurations. By this way, intensive calculation and equation solving are avoided and the shape singularity can be detected more efficiently. With the developed method, shape singularities are determined for three parallel manipulators, including 3-DOF planar and spatial parallel mechanisms, and the 6-DOF Stewart–Gough manipulator.

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.

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.

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.

Structure and property of the singularity loci of the 3/6-Stewart-Gough platform for general orientations

This paper focuses on the structure and property of the singularity loci of the 3/6-Stewart-Gough platform for general orientations. Based on the singularity kinematics principle, a planar singularity-equivalent-mechanism is proposed, by which the complicated singularity analysis of that parallel mechanism is transformed into a simpler position analysis of the planar mechanism. All the possible positions of the planar mechanism form the singularity loci of the 3/6-Stewart-Gough manipulator. The result shows that the singularity equation become quite simple moreover the structure and property of the singularity loci are also identified and explained. For the most general orientations of the typical 3/6-Stewart-Gough platform, the singularity locus equation is a special irresolvable polynomial expression of degree three, which in infinite parallel principal sections includes a parabola, four pairs of intersecting straight lines and infinity of hyperbolas. This result is beneficial to analysis of the similar issue of other Stewart-Gough manipulators.

Analysis of Active Joint Failure in Parallel Robot Manipulators

In this study, the effect of active joint failure on the mobility, velocity, and static force of parallel robot manipulators is investigated. Two catastrophic active joint failure types are considered: joint jam and actuator force loss. To investigate the effect of failure on mobility, the Gru¨bler’s mobility equation is modified to take into account the kinematic constraints imposed by various branches in the manipulator. In the case of joint jam, the manipulator loses the ability to move and apply force in a specific portion of its task space; while in the case of actuator force loss, the manipulator gains an unconstrained motion in a specific portion of the task space in which an externally applied force cannot be resisted by the actuator forces. The effect of joint jam and actuator force loss on the velocity and on the force capabilities of parallel manipulators is investigated by examining the change in the Jacobian matrix, its inverse, and transposes. It is shown that the reduced velocity and force capabilities after joint jam and loss of actuator force could be determined using the null space vectors of the transpose of the Jacobian matrix and its inverse. Computer simulation is conducted to demonstrate the application of the developed methodology in determining the post-failure trajectory of a 3-3 six-degree-of-freedom Stewart-Gough manipulator, when encountering active joint jam and actuator force loss.

Solving the Inverse Dynamics of a Stewart-Gough Manipulator by the Principle of Virtual Work

This paper presents a systematic methodology for solving the inverse dynamics of a Stewart-Gough manipulator. Based on the principle of virtual work and the concept of link Jacobian matrices, a methodology for deriving the dynamical equations of motion is developed. It is shown that the dynamics of the manipulator can be reduced to solving a system of six linear equations in six unknowns. A computational algorithm for solving the inverse dynamics of the manipulator is developed and several trajectories of the moving platform are simulated. [S1050-0472(00)00401-3]

A New Algorithm Based on Two Extra-Sensors for Real-Time Computation of the Actual Configuration of the Generalized Stewart-Gough Manipulator

It is well known that the direct position analysis of fully-parallel manipulators provides more than one solution, i.e., more than one configuration of the mechanism is possible for a given set of the actuated variables of motion. Extra information is, thus, necessary to find the actual configuration of the manipulator. This paper presents a new algorithm for the real-time computation of the actual configuration of the generalized Stewart-Gough manipulator, also known as 6-6 fully-parallel manipulator with general geometry. The proposed algorithm makes use of two extra rotary sensors in addition to five out of the six sensors normally implemented in the servosystems of the manipulator. A one-to-one correspondence between the sensor measurements and the manipulator configuration is provided. With respect to other algorithms recently presented in the literature, the proposed method greatly reduces the computational burden. Finally a case study shows the effectiveness of the proposed procedure. [S1050-0472(00)01703-7]