Workspace Of Parallel Manipulator Research Articles

Sensor-Based Identification of Singularities in Parallel Manipulators

Singularities are configurations where the number of degrees of freedom of a robot changes instantaneously. In parallel manipulators, a singularity could reduce the mobility of the end-effector or produce uncontrolled motions of the mobile platform. Thus, a singularity is a critical problem for mechanical design and model-based control. This paper presents a general sensor-based method to identify singularities in the workspace of parallel manipulators with low computational cost. The proposed experimental method identifies a singularity by measuring sudden changes in the end-effector movements and huge increments in the forces applied by the actuators. This paper uses an inertial measurement unit and a 3D tracking system for measuring the end-effector movements, and current sensors for the forces exerted by the actuators. The proposed sensor-based identification of singularities is adjusted and implemented in three different robots to validate its effectiveness and feasibility for identifying singularities. The case studies are two prototypes for educational purposes—a five-bar mechanism and an L-CaPaMan parallel robot—and a four-degree-of-freedom robot for rehabilitation purposes. The tests showcase its potential as a practical solution for singularity identification in educational and industrial robots.

Design and implementation of a novel modal space active force control concept for spatial multi-DOF parallel robotic manipulators actuated by electrical actuators

Robotic spine brace based on parallel-actuated robotic system is a new device for treatment and sensing of scoliosis, however, the strong dynamic coupling and anisotropy problem of parallel manipulators result in accuracy loss of rehabilitation force control, including big error in direction and value of force. A novel active force control strategy named modal space force control is proposed to solve these problems.Considering the electrical driven system and contact environment, the mathematical model of spatial parallel manipulator is built. The strong dynamic coupling problem in force field is described via experiments as well as the anisotropy problem of work space of parallel manipulators. The effects of dynamic coupling on control design and performances are discussed, and the influences of anisotropy on accuracy are also addressed. With mass/inertia matrix and stiffness matrix of parallel manipulators, a modal matrix can be calculated by using eigenvalue decomposition. Making use of the orthogonality of modal matrix with mass matrix of parallel manipulators, the strong coupled dynamic equations expressed in work space or joint space of parallel manipulator may be transformed into decoupled equations formulated in modal space. According to this property, each force control channel is independent of others in the modal space, thus we proposed modal space force control concept which means the force controller is designed in modal space. A modal space active force control is designed and implemented with only a simple PID controller employed as exampled control method to show the differences, uniqueness, and benefits of modal space force control. Simulation and experimental results show that the proposed modal space force control concept can effectively overcome the effects of the strong dynamic coupling and anisotropy problem in the physical space, and modal space force control is thus a very useful control framework, which is better than the current joint space control and work space control.

Workspace Analysis and Optimization of 3-RRR Planar Parallel Manipulator

Predicting shape and finding out exact area of the workspace of 3-DOF planar parallel manipulator having three rotary joints has been a research topic for long time. Optimal design based on such calculations provides a conclusive design methodology. In this work, geometrical method is used o get the exact shape of the workspace and expression of area for the shape obtained. The 3-DOF parallel manipulator is treated as a combination of three independent serial manipulators and its workspace as the common intersection area of these three serial manipulators. The three workspaces are then translated by length equal to radius of the end effecter and the common intersection area is obtained as the workspace of the parallel manipulator under study. The area is determined using the mathematical expression for the shape obtained. Based on direct search algorithm, a methodology is developed to optimize the area. Thus, following, this methodology, an user with specification of area of the workspace can be provided with an optimized parallel manipulator taking into account the inventory of link lengths and the cost of the links.

Maximal singularity-free orientation workspace over a position region of Gough–Stewart platform

Maximizing the singularity-free workspace of parallel manipulators is highly desirable in a context of robot design. So far, no work has been found to address the maximal singularity-free orientation workspace over a position region. In practice, this type of workspace is interesting because a mechanism often works in a range of positions. This work focuses on the Gough–Stewart platform. An optimal position at which the mechanism holds the maximal singularity-free orientation workspace is determined. This optimal position lies on the line which is perpendicular to the base and passes the centroid of the base. Considering the symmetry, a parallelepiped with centre at the determined optimal position could be an interesting working position region for the Gough–Stewart platform. Two algorithms are presented to compute the maximal singularity-free orientation workspace over such an interesting position region. An example is provided for demonstration.

The Workspace Analysis of an Improved 6-DOF Parallel Handcontroller

In order to improve the response effectiveness, extend the workspace of parallel manipulator and make it more conveniently to be used in realistic tasks, this paper has introduced an improved mechanism based on the traditional 6-PUS, which applied the rails leaning outside and the linear motor as its driving system. This has optimized the initial parameters of the improved mechanism, and analyzed its workspace in the software Matlab using the method of cylindrical coordinate search. The result has a guiding significance in optimization of traditional parallel manipulators and the manufacturing of the new prototype.

Analysis and Evaluation of Non-Singularity Workspace of Parallel Manipulator

This paper studied the novel 3-PRRR manipulator, the non-singularity workspace was deduced, satisfying various constrains, containing the angle scales of driving pairs, the travelling limits of driven pairs and the singular position conditions. Stepwise refinement method was employed and acceleration approaching method were put forward to improve the performance evaluation solving speed.

Motion capability analysis of a quadruped robot as a parallel manipulator

This paper presents the forward and inverse displacement analysis of a quadruped robot MANA as a parallel manipulator in quadruple stance phase, which is used to obtain the workspace and control the motion of the body. The robot MANA designed on the basis of the structure of quadruped mammal is able to not only walk and turn in the uneven terrain, but also accomplish various manipulating tasks as a parallel manipulator in quadruple stance phase. The latter will be the focus of this paper, however. For this purpose, the leg kinematics is primarily analyzed, which lays the foundation on the gait planning in terms of locomotion and body kinematics analysis as a parallel manipulator. When all four feet of the robot contact on the ground, by assuming there is no slipping at the feet, each contacting point is treated as a passive spherical joint and the kinematic model of parallel manipulator is established. The method for choosing six non-redundant actuated joints for the parallel manipulator from all twelve optional joints is elaborated. The inverse and forward displacement analysis of the parallel manipulator is carried out using the method of coordinate transformation. Finally, based on the inverse and forward kinematic model, two issues on obtaining the reachable workspace of parallel manipulator and planning the motion of the body are implemented and verified by ADAMS simulation.

Enhancing the useful workspace of a reconfigurable parallel manipulator by grasp point optimization

Reconfigurable parallel manipulators combine the properties of parallel manipulators with high flexibility. However, the workspace of parallel manipulators is, compared to serial manipulators, relatively small and hence the optimization of the useful workspace is an important design factor. Different efficient algorithms for calculating the workspace for parallel manipulators have been developed, but they need to be adapted to reconfigurable systems with additional parameters. These variables for those systems are the parameters of the reconfiguration, e.g. the grasping points. This paper presents a method to obtain the grasping point combinations of a parallel reconfigurable manipulator that leads to a useful workspace containing the largest geometric object. The largest geometric object inside the useful workspace describes its regularity and represents a useful evaluation criterion. The method is introduced for a general reconfigurable parallel manipulator and then studied for the particular case of the PARAGRIP reconfigurable parallel manipulator. The workspace is obtained by applying a combined geometrical and discretization method. To reduce the possible grasping point combinations and thereby reduce computational cost, we apply the special requirements that the grasping point combinations must fulfil. By solving the inverse kinematic problem for each combination the useful workspace is calculated. HighlightsWe present a method for parallel reconfigurable manipulators.We get the grasping point combinations with the biggest free-singularity workspace.We obtain the combinations that lead to the biggest sphere in the useful workspace.We introduce the method for a general case.We focus on the parallel reconfigurable manipulator PARAGRIP case.

A new approach to determine the maximal singularity-free zone of 3-RPR planar parallel manipulator

SUMMARYThis paper presents a new algorithm to find the singularity-free cylindrical workspace of parallel manipulators. Because of the limited workspace of parallel manipulators cluttered with different types of singularities, a simple and robust technique to determine continuous singularity-free zones in the workspace of parallel manipulators is required. Here, the largest singularity-free cylinder within the workspace for any prescribed orientation ranging around a reference orientation angle of moving platform is determined. To this end, Particle Swarm Optimization is utilized to find the closest point on the singularity surface to the axis of the cylinder. By implementing the algorithm on 3-RPR planar parallel manipulator, the results show that this algorithm improves the efficiency and leads to significantly larger singularity-free workspace than those reported earlier.

Software Tool to Compute, Analyze and Visualize Workspaces of Parallel Kinematics Robots

The aim of this paper is to present a new software tool designed to compute and allow visualization of the different types of workspaces of parallel manipulators in the most user-friendly and efficient way. The graphical interface of this program makes it possible to define the geometrical scheme of the robot. All required parameters of the kinematic model can be set easily and quickly. Given that the workspace of a parallel manipulator is a complex entity, this CAD tool has implemented all the controls needed to visually define all the complicated parameters required to launch a workspace computation. Once the calculations are performed, the challenging task of visualizing the results has been optimized. Due to the circumstance that a workspace can be a higher than three-dimensional (3-D) mathematical entity, which cannot be graphically represented, the user can choose the specific variables (two or three) onto which to project the workspace obtained (2-D or 3-D representations). Within these surfaces and volumes, several color maps, associated with kinematic indicators, can be traced to enable the most efficient path planning of the manipulator analyzed.

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.

3-D Visualization on Workspace of Parallel Manipulators

In parallel mechanisms, the form and volume of workspace also change variously with the attitude of a platform. This paper presents a method to search for the workspace of parallel mechanisms with 6-DOF and 3D visualization of the workspace. Workspace is a search for the movable range of the central point of a platform when it moves with a given orientation. In order to search workspace, geometric analysis based on inverse kinematics is considered. Plots of 2D of calculations are compared with those measured by position sensors. The test results are shown to have good agreement with simulation results. The workspace variations are demonstrated in terms of 3D and 2D plots for prototype mechanisms. The workspace plots are created with OpenGL and Visual C++ by implementation of the algorithm. An application module is developed, which displays workspace of the mechanism in 3D images. The effectiveness and practicability of 3D visualization on workspace are successfully demonstrated by 6-DOF parallel mechanisms.

Increase of singularity-free zones in the workspace of parallel manipulators using mechanisms of variable structure

This paper is focused on the study of singularity of planar parallel manipulators taking into account the force transmission, i.e. study of singularity of planar manipulator by introducing the force transmission factor. Thus the singularity zones in the workspace of the manipulator are defined not only by kinematic criterions from the theoretical perfect model of the manipulator but also by the quality of force transmission. For this purpose, the pressure angle is used as an indicator of force transmission. The optimal control of the pressure angle for a given trajectory of the manipulator is realized by means of legs with variable structure. The suggested procedure to determination of the optimal structure of the planar parallel manipulator 3-RPR is illustrated by two numerical simulations.

Workspace of parallel manipulators with symmetric identical kinematic chains

In this paper, we propound an analogous symmetric theorem of workspace for spatial parallel manipulators with identical kinematic chains, and then present a strict mathematic proof by splitting the problem into planar symmetry, rotational axis symmetry and point symmetry (centrosymmetry). Examples demonstrate that this theorem can be utilized to investigate the geometry shapes of the workspace and to guide the conceptual design of spatial parallel manipulators, especially for those complicated spatial parallel manipulators with full degrees of freedom (DoF). The theorem offers a concrete safeguard for the workspace analysis of any symmetric spatial parallel manipulators.

Uniqueness Domains in the Workspace of Parallel Manipulators

This work investigates new kinematic features of parallel manipulators. It is well known that parallel manipulators admit generally several direct kinematic solutions for a given set of input joint values. The aim of this paper is to characterize the uniqueness domains in the workspace of parallel manipulators, as well as their image in the joint space. The study focuses on the most usual case of parallel manipulators with only one inverse kinematic solution. The notion of aspect introduced for serial manipulators in [Borrel 86] is redefined for such parallel manipulators. Then, it is shown that it is possible to link several solutions to the forward kinematic problem without meeting a singularity, thus meaning that the aspects are not uniqueness domains. An additional set of surfaces, namely the characteristic surfaces , are characterized which divide the workspace into basic regions and yield new uniqueness domains. This study is illustrated all along the paper with a 3-RPR planar parallel manipulator. An octree model of spaces is used to compute the joint space, the workspace and all other newly defined sets.

Trajectory Verification in the Workspace for Parallel Manipulators

We present a fast algorithm for solving the problem of the ver ification of a trajectory for a 6-DOF parallel manipulator with respect to its workspace: i.e., given two different postures for the end effector, is the straight line joining these two postures in the parameters space fully inside the workspace? This al gorithm is based on the analysis of the algebraic inequalities describing the constraints on the workspace and provides a technique for computing those parts of the trajectory that lie outside the workspace. This method is exact if the orientation of the end effector is kept constant along the trajectory and approximate if the orientation is allowed to vary.