Redundant Parallel Manipulator Research Articles

The joint velocity, torque, and power capability evaluation of a redundant parallel manipulator

SUMMARYThe evaluation of joint velocity, torque, and power capability of the 8-PSS redundant parallel manipulator is investigated in this paper. A series of new joint capability indices with obvious physical meanings are presented. The torque index used to evaluate the respective joint dynamic capability of the redundant parallel manipulator is decoupled into the acceleration, velocity, and gravity term. With these velocity, torque, and power indices, it is possible to control the respective joint capability of the redundant parallel manipulator in different directions. The indices have been applied to evaluate the joint capability of the redundant parallel manipulator by simulation. They are general and can be used for other types of parallel manipulators.

DEXTEROUS WORKSPACE OF A 3-PRRR KINEMATICALLY REDUNDANT PLANAR PARALLEL MANIPULATOR

In this work, the dexterous workspace of a general geometry 3-PRRR kinematically redundant planar parallel manipulator with six actuated joints, three of which are redundant, is determined. The 3-P...

Elastodynamic characteristics comparison of the 8-PSS redundant parallel manipulator and its non-redundant counterpart—the 6-PSS parallel manipulator

This paper presents an elastodynamic characteristics comparison of the 8-PSS redundant parallel manipulator and its non-redundant counterpart—the 6-PSS parallel manipulator through simulation. The natural frequency and the displacement response of the moving platform are investigated, respectively. It is shown that the natural frequency of the 8-PSS redundant parallel manipulator is higher than that of the 6-PSS parallel manipulator while its displacement responses of the moving platform are smaller than those of the 6-PSS parallel manipulator.

A new family of constrained redundant parallel manipulators

This paper addresses the description and kinematic analysis of a new family of redundant parallel manipulators. The primary feature of the new family is to have a compact topology consisting of multi-degree of freedom non-identical limbs. In order to simplify the forward position analysis, the motion of the end-effector (platform) is decoupled into translational and rotational components with respect to the base. This kind of topology is in agreement with the parallel manipulator definition of IFToMM—a parallel manipulator “…that controls the motion of its end-effector by means of at least two kinematic chains going from the end effector towards the frame…”. In fact, adding a kinematic pair to a limb of a non-redundant parallel manipulator creates asymmetrical parallel manipulator. Analytical expressions for the forward position, velocity, and acceleration of the parallel manipulators have been obtained and solved for an exemplary 7-DOF redundant parallel manipulator. The numerical results from the analytical expressions are verified by comparing them to the results from a mechanical system simulation software as if a real parallel manipulator is being run to collect the position, velocity, and acceleration data. Finally, based on the velocity formulation, the singularity analysis of the manipulator is also provided.

A New Method to Calculate the Force and Moment Workspaces of Actuation Redundant Spatial Parallel Manipulators

A new method for obtaining the force and moment workspaces of spatial parallel manipulators (PMs) is presented. Force and moment workspaces are regions within which a manipulator can sustain/apply at least a certain value of force or moment in all directions. Here, the force and moment workspaces are found using a method, which explicitly sets the largest possible number of actuators to their maximum limits ensuring that the manipulator is performing at its best possible wrench capabilities. Two cases for obtaining these workspaces are used. The first gives the applicable/sustainable force with a prescribed moment whereas the second one gives the applicable/sustainable moment with a prescribed force. For illustration purposes, the method is applied to a six-degree-of-freedom (DOF) redundantly-actuated spatial PM, the 3-RRṞS. The results are represented graphically as the boundaries of the workspace in the three-dimensional Cartesian space. These workspaces can be used as a powerful tool for path/task planning and PM design.

Dynamic formulation of a planar 3-DOF parallel manipulator with actuation redundancy

In this paper, based on the conventional Newton–Euler approach, a simplification method is proposed to derive the dynamic formulation of a planar 3-DOF parallel manipulator with actuation redundancy. Closed-form solutions are developed for the inverse kinematics. Based on the kinematics, the Newton–Euler approach in simplification form is used to derive the inverse dynamic model of the redundant parallel manipulator. Then, the driving force optimization is performed by minimizing an objective function which is the square of the sum of four driving forces. The dynamic simulations are done for the parallel manipulator with both the redundant and non-redundant actuations. The result shows that the dynamic characteristics of the manipulator in the redundant case are better than that in the non-redundancy. The redundantly actuated parallel manipulator was incorporated into a 4-DOF hybrid machine tool which includes a feed worktable.

Optimum design of 2-DOF parallel manipulators with actuation redundancy

The optimum design of 2-DOF redundant parallel manipulators is investigated in this paper. The planar 2-DOF parallel manipulator with actuation redundancy is treated as non-dimensional structure. The physical model of the solution space is studied. Based on the kinematic model and Jacobian matrix, the global conditioning index, global velocity index and global stiffness index of the 2-DOF parallel manipulators are investigated, and the geometrical parameters without dimension are determined. Based on the optimum non-dimensional result, the optimum dimensional parameters are achieved. The result of this paper is useful for the development of 2-DOF 3-RRR redundant parallel manipulators.

Dynamic formulation and performance evaluation of the redundant parallel manipulator

The dynamic formulation and performance evaluation of the redundant parallel manipulator are presented in this paper. By means of the principle of virtual work and the concept of link Jacobian matrices, the inverse dynamic model of the redundant parallel manipulator is set up. It consists of six linear consistent equations with eight unknown quantities. Then, the optimum solution of the actuating torques is achieved by employing the Moore-Penrose inverse matrix. It is with minimum norm and least quadratic sum among the possible actuating torque vectors. A series of new dynamic performance indices with obvious physical meanings have been proposed in the paper. By decoupling the inverse dynamics in the exhaustive way, a novel dynamic performance index combining the acceleration, velocity and gravity terms of the dynamic equations has been presented to evaluate the dynamic characteristic of the redundant parallel manipulator. With the index, it is possible to control the performance in the different direction. The index has been applied to the dynamic characteristic evaluation of the redundant parallel manipulator in the simulation. It is general and can be used for the dynamic performance evaluation of other types of parallel manipulators.

Dynamic performance comparison of the 8PSS redundant parallel manipulator and its non-redundant counterpart—the 6PSS parallel manipulator

Abstract This paper presents the dynamic performance comparison of the 8PSS redundant parallel manipulator and the 6PSS parallel manipulator. A series of kinematics and rigid dynamics performance indices with obvious physical meanings have been adopted to compare the performance of the 8PSS redundant parallel manipulator and that of the 6PSS parallel manipulator. It is turned out that their kinematics characteristics are equivalent while the dynamic performance of the 8PSS redundant parallel manipulator is better than that of the 6PSS parallel manipulator.

Neural Networks Approaches for Computing the Forward Kinematics of a Redundant Parallel Manipulator

In this paper, different approaches to solve the forward kinematics of a three DOF actuator redundant hydraulic parallel manipulator are presented. On the contrary to series manipulators, the forward kinematic map of parallel manipulators involves highly coupled nonlinear equations, which are almost impossible to solve analytically. The proposed methods are using neural networks identification with different structures to solve the problem. The accuracy of the results of each method is analyzed in detail and the advantages and the disadvantages of them in computing the forward kinematic map of the given mechanism is discussed in detail. It is concluded that ANFIS presents the best performance compared to MLP, RBF and PNN networks in this particular application.

Dynamics and control of a planar 3-DOF parallel manipulator with actuation redundancy

This paper deals with the dynamics and control of a planar 3-DOF parallel manipulator with actuation redundancy. According to the kinematics of the redundant manipulator, the inverse dynamics is derived by using the virtual work principle, and the driving force is optimized by utilizing the least-square method. Based on the dynamic model, a position and force switching control strategy is proposed for the parallel manipulator. In this control strategy, two extendible links are controlled by position and force modes, respectively. Moreover, in the whole workspace, their control modes are switched. The critical angles for switching control modes are planned and the position compensation method is investigated. The control tests show that the contour error of the redundantly actuated parallel manipulator is similar to that of its corresponding non-redundant parallel manipulator without one extendible link. However, the redundant parallel manipulator has a larger orientation workspace and higher stiffness. The redundantly actuated parallel manipulator is incorporated into a 4-DOF hybrid machine tool which also includes a feed worktable.

Performance Analysis and Application of a Redundantly Actuated Parallel Manipulator for Milling

This paper deals with the performance analysis of a 3-degree-of-freedom (3-DOF) planar parallel manipulator with actuation redundancy. Closed-form solutions are developed for both the inverse and direct kinematics about the redundant parallel manipulator. In performance analysis phase, the dexterity is analyzed, three kinds of singularities are investigated, and the stiffness is estimated. Compared with the corresponding non-redundant parallel manipulator with the redundant link removed, the redundantly actuated one has better dexterity, litter singular configurations and higher stiffness. The redundantly actuated parallel manipulator was applied to the design of a 4-DOF hybrid machine tool which also includes a feed worktable to demonstrate its applicability.

Auto-calibration of a redundant parallel manipulator based on the projected tracking error

Utilizing the projected tracking error of the redundant joint angles, we studied the calibration problem of the sensor zero positions of a planar 2-dof parallel manipulator in this paper. Based on the study of the relationship between the projected tracking error of the joint angles and the error of the sensor zero positions, a new error function is proposed for the calibration of the sensor zero positions of the parallel manipulator. It is proved that the error function is robust to the measurement error of the joint sensors, so accurate calibration results can be obtained by minimizing the error function even if the measurement of the joint angles is not accurate. With a simple searching strategy for the minimal value of the error function, we designed an auto-calibration procedure and verified the validity of the calibration procedure through real experiments on a real redundant planar 2-dof parallel manipulator.

Modelling and Control of a Parallel Redundant Manipulator with Hydraulic Actuators

The parallel robotic manipulator, MULTIPOD, is specially designed for carrying out drilling tasks in mines. It is based on two parallel three-degree-of-freedom mechanisms in serial connection. The structure that provides excellent stiffness is hydraulically driven and has six degrees of mobility. The pose of the end-effector is described by five degrees of freedom. In this paper, complete kinematic and dynamic analyses of the manipulator are carried out. In addition, a proportional controller equipped with hydraulic force feedback is designed for the robot. The simulated results that demonstrate the behaviour of the manipulator are presented in this paper.

Kinematic, singularity and stiffness analysis of the hydraulic shoulder: a 3-d.o.f. redundant parallel manipulator

In this paper, kinematic modeling and singularity and stiffness analysis of a 3-d.o.f. redundant parallel manipulator have been elaborated in detail. It is known that, contrary to series manipulators, the forward kinematic map of parallel manipulators involves highly coupled non-linear equations, whose closed-form solution derivation is a real challenge. This issue is of great importance noting that the forward kinematics solution is a key element in closed-loop position control of parallel manipulators. Using the idea of inherent kinematic chains formed in parallel manipulators, both inverse and forward kinematics of the redundant parallel manipulator are fully developed, and a closed-form solution for the forward kinematic map of the parallel manipulator is derived. The closed-form solution is also obtained in detail for the Jacobian of the mechanism and singularity analysis of the manipulator is performed based on the computed Jacobian. Finally, as the first step to develop a control topology based on the overall stiffness property of the manipulator, the stiffness mapping of the manipulator is derived and its configuration dependence is analyzed. It is observed that the actuator redundancy in the mechanism is the major element to improve the Cartesian stiffness and, hence, the dexterity of the hydraulic shoulder. Moreover, loosing one limb actuation reduces the stiffness of the manipulator significantly.

An Internal Force Sensor for Control of a Redundant Parallel Manipulator

This paper describes an internal force sensor for a new redundant parallel manipulator. In convensional control methods of a redundant parallel manipulator, optimal torque minimized actuator torque or maximized manipulability by using evaluation function is decided and used. However, these methods have to use a torque controlled actuator. It's torque is small, also it is expensive. So, we proposed a new control method using a conventional geared actuator. In our method, internal forces produced by actuator redundancy was detected by an internal force sensor and controlled to be zero. This force sensor is designed to detect only internal forces loaded the end-effector. We demonstrate about the structure and the principle of the proposed internal force sensor, and experimental result of the internal force sensor when internal and outer forces are loaded it.

Comparison of Different Methods for Computing the Forward Kinematics of a Redundant Parallel Manipulator

In this paper, three numerical methods are presented to solve the forward kinematics of a three DOF actuator-redundant hydraulic parallel manipulator. It is known, that on the contrary to series manipulators, the forward kinematic map of parallel manipulators involves highly coupled nonlinear equations, whose closed-form solution derivation is a real challenge. This issue is of great importance noting that the forward kinematics solution is a key element in closed loop position control of parallel manipulators. The proposed methods, namely the Neural Network Estimation, the Quasi-closed Solution, and the Taylor series approximation, are using mainly numerical computations, with different ideas to solve the problem in hand. The latter two methods are proposed for the first time in literature to solve the forward kinematics of a parallel manipulator. These methods are compared in detail and the advantages or the disadvantages of each method in computing the forward kinematic map of the given mechanism is discussed. It is shown that a 4th order Taylor series approximation to the problem provides a good compromise for practical applications compared to that of other methods considered in this paper.

Design and analysis of kinematically redundant parallel manipulators with configurable platforms

Redundancy can, in general, improve the ability and performance of parallel manipulators by implementing the redundant degrees of freedom to optimize a secondary objective function. Almost all published researches in the area of parallel manipulators redundancy were focused on the design and analysis of redundant parallel manipulators with rigid (nonconfigurable) platforms and on grasping hands to be attached to the platforms. Conventional grippers usually are not appropriate to grasp irregular or large objects. Very few studies focused on the idea of using a configurable platform as a grasping device. This paper highlights the idea of using configurable platforms in both planar and spatial redundant parallel manipulators, and generalizes their analysis. The configurable platform is actually a closed kinematic chain of mobility equal to the degree of redundancy of the manipulator. The additional redundant degrees of freedom are used in reconfiguring the shape of the platform itself. Several designs of kinematically redundant planar and spatial parallel manipulators with configurable platform are presented. Such designs can be used as a grasping device especially for irregular or large objects or even as a micro-positioning device after grasping the object. Screw algebra is used to develop a general framework that can be adapted to analyze the kinematics of any general-geometry planar or spatial kinematically redundant parallel manipulator with configurable platform.

A Control Algorithm of a Redundant Parallel Manipulator by an Internal Force Sensor

This paper describes a new control method for a redundant parallel manipulator using an internal force sensor. In conventional control methods of a redundant parallel manipulator, optimal torque minimized actuator torque or maximized manipulability by using evaluation function is decided and used. However, these methods have to use a torque controlled actuator. It's torque is small, also it is expensive. So, we propose a new control method using a conventional geared actuator in this paper. In our method, internal forces produced by actuator redundancy is detected by an internal force sensor and controlled to be zero. We demonstrate about the proposed control system and the structure, the principle, and the experimental result of the redundant parallel manipulator using the internal force sensor.

Kinematic Analysis and Design of Kinematically Redundant Parallel Mechanisms

This paper addresses the singularity analysis and the design of three new types of kinematically redundant parallel mechanisms, i.e., the four-degree-of-freedom planar and spherical parallel mechanisms and the seven-degree-of-freedom spatial Stewart platform. The main idea in the design of these parallel manipulators is the addition of one redundant degree of freedom in one of the kinematic chains of the nonredundant manipulator. Such manipulators can be used to avoid the singularities inside the workspace of nonredundant manipulators. After describing the geometry of the manipulators, the velocity equations are derived and the expressions for the Jacobian matrices are obtained. Then, the singularity conditions are discussed. Finally, the expressions of the singularity loci of the kinematically redundant mechanisms are obtained and the singularity loci of the nonredundant and redundant manipulators are compared. It is shown here that the conditions for the singularity of the redundant manipulators are reduced drastically relative to the nonredundant ones. As a result, the proposed kinematically redundant parallel manipulators may be of great interest in several applications.