A 6-DOF reconfigurable hybrid parallel manipulator

This paper presents a case study on a reconfigurable hybrid parallel robot dubbed ReSl-Bot. It addresses the realm of reconfigurable 6-DOF parallel mechanisms, for sustainable manufacturing. It also features a self-reconfigurable architecture. A systematic analysis involving kinematics, constant orientation workspace, singularity and stiffness is developed in detail. Interesting features are discussed, revealing some unique characteristics of the studied architecture. A multi-objective optimization procedure is also carried out with weighted stiffness, dexterity and workspace volume as the performance indices.     

Dynamic modeling and design optimization of a 3-DOF spherical parallel manipulator

This paper deals with the dynamic modeling and design optimization of a three Degree-of-Freedom spherical parallel manipulator. Using the method of Lagrange multipliers, the equations of motion of the manipulator are derived by considering its motion characteristics, namely, all the components rotating about the center of rotation. Using the derived dynamic model, a multiobjective optimization problem is formulated to optimize the structural and geometric parameters of the spherical parallel manipulator. The proposed approach is illustrated with the design optimization of an unlimited-roll spherical parallel manipulator with a main objective to minimize the mechanism mass in order to enhance both kinematic and dynamic performances.     

A 6-DOF adaptive parallel manipulator with large tilting capacity

In this paper, a novel 6 degrees of freedom (DOFs) adaptive parallel manipulator with large tilting capacity is presented. The manipulator consists of four identical peripheral limbs and one center limb connecting the base and the moving platform. Due to the special architecture, the doubly actuated center limb of the manipulator could have infinite inverse solutions. In every configuration of the end-effector, the manipulator can adapt its center limb to the position and orientation with best dexterity. An optimization equation for obtaining the optimized dexterity of the manipulator is introduced to solve this nonholonomic problem, which also makes the manipulator capable of large tilting capacity. Targeting for the application of five-face machining, the detailed kinematic analysis of the manipulator is developed, which includes the closed-form solutions of inverse position problems, the singularity, dexterity, workspace and tilting capability. The analysis developed in this paper shows that the proposed manipulator has large tilting capacity and thus a suitable candidate for five-face machining.     

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.     

Design of a 3-DOF tripod electro-pneumatic parallel manipulator

The objective of the research project was to design and construct a 3DOF tripod-type electro-pneumatic parallel manipulator that could be used for pick-and-place tasks in municipal waste recycling facilities. The fundamental requirement was that the manipulator be simple and cheap to construct, operate and maintain as well as robust and resistant to damage. The forward and inverse kinematic problem as well as working space and strength analysis issues were used for construction of manipulator. The prototype was tested using different payloads and velocities to establish its positioning accuracy and repeatability. The robot behavior was controlled with a commercially available industrial controller, which was reported insufficient for point-to-point operations required during solid waste handling. Conclusions have been drawn on how to optimize the robot structure and control.     

Dynamics analysis for a novel 6-DoF parallel manipulator I with three planar limbs

A novel 6-DoF parallel manipulator I with three planar limbs is proposed and its dynamics is analyzed systematically. First, its characteristics and DoF are analyzed and calculated. Second, the formulae for solving kinematics of the moving platform and the planar limbs are derived. Third, the formulae for solving the inertial wrench applied on the planar limbs and the moving platform are derived, and dynamics formula is derived for solving dynamic active forces applied onto the planar limbs. Fourth, a singularity of the proposed parallel manipulator is determined and analyzed. Fifth, an analytic example is given for solving the kinetostatics and dynamics of the proposed parallel manipulator, and the solved results are analyzed and verified by the simulation mechanism. Finally, a workspace is constructed and analyzed by comparing with an existing 6-DoF parallel manipulator.     

Topology design and kinematic optimization of cyclical 5-DoF parallel manipulator with proper constrained limb

This paper proposes topology design and kinematic optimization of cyclical 5-degree-of-freedom (DoF) parallel manipulator with proper constrained limb. Firstly, a type of cyclical 5-DoF parallel manipulators with proper constrained limb is proposed by analyzing DoF of the proper constrained limb within workspace. Exampled by a cyclical 5-DoF parallel manipulator with the topology 4-UPS&1-RPS, its motion mapping model is formulated. By taking the reciprocal product of a wrench on a twist as the generalized virtual power, the local and global kinematic performance indices are provided. Then, on the basis of the actuated and constrained singularity analysis of the 4-UPS&1-RPS parallel manipulator within the position and pose workspace, the topology design of the manipulator without singularity is carried out, and its reachable and prescribed workspaces are obtained. Finally, by maximizing the global kinematic performance index and subjecting to a set of appropriate constraint conditions, the kinematic optimal design of the 4-UPS&1-RPS parallel manipulator is carried out utilizing the genetic algorithm of MATLAB optimization toolbox.     

Analysis and optimization of the 5-RPUR parallel manipulator

Many industrial applications need less than 6 degrees of freedom (DOF) to manipulate. On one hand, the parallel manipulators (PMs) with lower DOF have some advantages such as low manufacturing and control cost. On the other hand, they have more complicated kinematics. Among PMs with lower DOF, the 5-DOF PMs have particularly many industrial applications. Within the group of 5-DOF PMs, the three translational and two rotational (3T2R) type has more industrial applications than three rotational and two translational type. In this paper, we analyze and optimize the 5-RPUR PM which is a 3T2R type. The kinematic analysis is studied using the screw theory. The boundary and volume of the workspace is obtained using a geometrical method. In addition, singularity analysis is studied. Particle swarm optimization is utilized to optimize the workspace and the accuracy simultaneously, and achieve a roughly homogeneous accuracy index over the workspace. The boundary of the optimized workspace is depicted and we show that the optimized workspace is singularity free. The accuracy index of the manipulator is calculated and depicted in several cross-sections of the workspace.     

6-DOF并联机器人并行控制算法与优化

为了实现对6-DOF并联机器人实时在线控制,并能取得良好的控制效果,对其运动控制算法的结构进行了深入剖析与研究,尤其对上平台中心的运动速度和角速度的计算及液压缸各杆的伸长速度计算矩阵进行了细致的研究,提出了并行算法及CPU的优化分配策略,大大提高了并联机器人的实时控制质量.     

Dynamics analysis of a novel 5-DoF 3SPU+2SPRR type parallel manipulator

A novel 5-DOF 3SPU+2SPRR type parallel manipulator is proposed. First, the formulae are derived for solving the kinematics parameters of the moving platform. Second, the kinematics of the active legs and connection rod are analyzed, and the formulae for solving velocity and acceleration of the active legs and connection rod are derived. Third, the formulae are derived for solving the dynamic active and constrained forces. Finally, an analytic example is given for solving the dynamics, and the analytic solved results are verified by the mechanism simulation. This paper is aimed at laying a solid theoretical and technical foundation for its prototype manufacture and control.     

Dynamic analysis and driving force optimization of a 5-DOF parallel manipulator with redundant actuation

Redundant actuation can improve the performance and ability of parallel manipulator. In order to deal with coordination and distribution of the driving force of the parallel manipulator with redundant actuation and to realize the control strategy based on dynamics, on the basis of the original 5UPS/PRPU parallel manipulator, it increases a drive for the middle PRPU passive constraint branch to make it a redundant actuation branch. It introduces configurations’ redundant types and compositions of 5UPS/PRPU parallel manipulator with redundant actuation, illustrates that the mechanism is redundant actuation from the perspective of degree of freedom and establishes a dynamic model based on Lagrangian method. On the basis of the weighted optimization principle of driving torque, it optimizes the driving torque of the parallel manipulator and calculates the driving force of the redundant driving chain with cutting force. It carries out the simulation by using ADAMS software and proves validity of dynamic model. Finally it detects the dynamic performance of the parallel manipulator by processing experiment of parallel manipulator with redundant actuation and its non-redundant counterpart.     

Singularity analysis and detection of 6-UCU parallel manipulator

6-UCU kind Gough–Stewart platform (GSP) has been used extensively in practice. The singularity of GSP has been studied by many scholars, but their works mainly focused on finding the methods to divide the cases of singularity or searching the solutions with Jacobian matrices. On the other hand, this paper studies the singularities of 6-UCU parallel manipulator caused by not only the active joints but also passive universal joints. Two types of singularity are derived based on a degree of freedom method by using screw theory. Singularity detection is essential to certify the absence of singularity within a prescribed workspace or a reachable workspace for a practical use of the 6-UCU parallel manipulator. Algorithms are proposed by using evolutionary strategy to detect the singularity in the desired or reachable workspace of the 6-UCU parallel manipulator. Case studies are presented to demonstrate the effectiveness of the proposed singularity detection methods.     

Stiffness analysis of a 3CPS parallel manipulator for mirror active adjusting platform in segmented telescope

In order to adjust the pose of mirror in segmented telescope initiatively, an active adjusting platform with a novel 3CPS PM as core module is proposed. It consists of a fixed base and a moving platform that is connected by three cylindrical-prismatic-spherical active legs. In this paper, the stiffness characteristics of the 3CPS PM with six DOF are studied systematically. First, the kinematics and statics are derived by the Rodrigues parameters method. Second, the stiffness matrix is proposed which is derived intuitively based on the principle of virtual work considering the compliances subject to both actuators and legs. Next, the elastic deformations of the moving platform corresponding to a given variation of pose parameters and external workload are analyzed. Moreover, applying a procedure iteratively over the workspace, the stiffness maps at initial height position are obtained. Finally, a FE model of the manipulator is constructed and the elastic deformations of FE model are basically coincident with that of analytic results. Both the analytical and FE results show that the stiffness characteristics of active adjusting platform satisfy the functional requirements of segmented telescope.     

Tri-pyramid Robot: Design and kinematic analysis of a 3-DOF translational parallel manipulator

3-DOF translational parallel manipulators have been developed in many different forms, but they still have respective disadvantages in different applications. To overcome their disadvantages, the structure and constraint design of a 3-DOF translational parallel manipulator is presented and named the Tri-pyramid Robot. In the constraint design of the presented manipulator, a conical displacement subset is defined based on displacement group theory. A triangular pyramidal constraint is presented and applied in the constraint designs between the manipulator?s subchains. The structural properties including the decoupled motions, overconstraint elimination, singularity free workspace, fixed actuators and isotropic configuration are analyzed and compared to existing structures. The Tri-pyramid Robot is constrained and realized by a minimal number of 1-DOF joints. The kinematic position solutions, workspace with variation of structural parameters, Jacobian matrix, isotropic and dexterity analysis are performed and evaluated in the numerical simulations.     

Optimizing the kinematic chains for a spatial parallel manipulator via searching the desired dexterous workspace

This paper exploits a new algorithm to optimize the length of the legs of a spatial parallel manipulator for the purpose of obtaining a desired dexterous workspace rather than the whole reachable workspace. With the analysis of the degree of freedom (DoF) of a manipulator, we can select the least number of variables to depict the kinematic constraints of each leg of a manipulator. The optimum parameters can be obtained by searching the extreme values of the objective functions with the given adroit workspace. Example is utilized to demonstrate the significant advantages of this method in the dexterous workspace synthesis. In applications, this method can be widely used to synthesize, optimize and create all kinds of new spatial parallel manipulator with a desired dexterous workspace.     

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

This paper deals with the dynamics and control of a novel 3-degrees-of-freedom （DOF） parallel manipulator with actuation redundancy. According to the kinematics of the redundant manipulator, the inverse dynamic equation is formulated in the task space by using the Lagrangian formalism, and the driving force is optimized by utilizing the minimal 2-norm method. Based on the dynamic model, a synchronized sliding mode control scheme based on contour error is proposed to implement accurate motion tracking control. Additionally, an adaptive method is introduced to approximate the lumped uncertainty of the system and provide a chattering-free control. The simulation results indicate the effectiveness of the proposed approaches and demonstrate the satisfactory tracking performance compared to the conventional controller in the presence of the parameter uncertainties and un-modelled dynamics for the motion control of manipulators.     

Kinematic calibration of a 2-DOF translational parallel manipulator

Two types of kinematic calibration method for a 2-DOF (degrees of freedom) translational parallel manipulator are proposed using different error models. A calibration experiment is performed on both methods using an Absolute Laser Tracker and the results are compared. Two error models of the 2-DOF translational parallel manipulator are established using differential method and linear perturbation method, respectively. The two error models are solved using both the least squares method and linear equations. The results for the two different calibration methods show that the error model based on differential method is more effective in improving the accuracy of the 2-DOF translational parallel manipulator. Overall, the absolute position error of the 2-DOF translational parallel manipulator is significantly reduced to 0.13?mm from 0.93?mm after kinematic calibration.     

Trajectory tracking control of a 6-DOF hydraulic parallel robot manipulator with uncertain load disturbances

This study addresses the trajectory tracking control of a 6-DOF (degrees of freedom) hydraulic parallel robot manipulator with uncertain load disturbances. As load disturbances are the main external disturbances of the parallel robot manipulators and have a significant impact on system tracking performance, many researchers have been devoted to synthesize advanced control methods for improving the system robustness under the assumption that load disturbances are bounded. However, load disturbances are uncertain and vary in a large range in real situation happening in most hydraulic parallel robot manipulators, which is opposed to the assumption. In this paper, the load disturbances are directly measured by force sensors. Then a sliding mode control with discontinuous projection-based adaptation laws is proposed to improve the tracking performance of the parallel robot manipulator. Simulations and experiments with typical desired trajectory are presented, and the results show that good tracking performance is achieved in the presence of uncertain load disturbances.     

Dimensional synthesis of a 3-DOF parallel manipulator based on dimensionally homogeneous Jacobian matrix

A study of dimensional synthesis of a 3-DOF parallel manipulator with coupling of translation and rotation is carried out.The architecture of the manipulator is composed of a moving platform attached to a fixed base through three identical PRS(prismatic-revolute-spherical) serial limbs,whose unique topology leads to the physical unit inconsistency of the conventional Jacobian matrix and the emergence of the parasitic motion.Then this paper introduces a kinetostatic performance index of the manipulator based...     

A multi-level optimization methodology for determining the dextrous workspaces of planar parallel manipulators

A numerical multi-level optimization methodology is proposed for determining dextrous workspaces of 3-degree-of-freedom (3-dof) planar parallel manipulators, in which it is required that at any point within the workspace, the manipulator is able to assume any orientation in a specified range. The method starts by finding a single initial point on the boundary of the dextrous workspace. This first stage requires the successive solution of three separate optimization sub-problems, where the evaluation of the objective function for the second problem and the constraint functions in the third problem are determined by the solution of appropriate optimization problems at a lower level. Once the boundary point is identified, further successive points along the dextrous workspace boundary are traced by the application of the so-called chord method. In the latter procedure, the determination of each successive boundary point is also obtained via a constrained optimization problem, where the constraint functions are again evaluated via the solution of an optimization problem at a lower level. The proposed method is illustrated by its successful application to three different manipulator design geometries, and for various ranges of dexterity. An abbreviated version of this paper was presented at the 5th ASMO UK/ISSMO conference on Engineering Design Optimization, Stratford upon Avon, UK, July 12–13, 2004.