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.     

Kinematics and dynamics analyses of a parallel manipulator with three active legs and one passive leg by a virtual serial mechanism

A novel CAD variation geometry approach and a virtual serial mechanism approach are proposed for analyzing the kinematics and dynamics of a parallel manipulator with three SPS-type active legs and one PU-type constrained passive leg. First, a simulation mechanism of this parallel manipulator is created, and some kinematic characteristics are analyzed. Second, the inverse formulae for solving pose and Jocabian matrix are derived, and workspace and singularity are determined. Third, a virtual serial mechanism is created, and the analytic formulae for solving active forces and constrained wrench of these parallel manipulators are derived. The analytic results are verified by using its simulation mechanism.     

Mobility properties of a Schoenflies-type parallel manipulator

This paper addresses the mobility properties of a novel Schoenflies-type parallel manipulator. By analyzing the degree of freedom (DoF) of the manipulator, we select a set of independent variables to describe the pose relationship of the manipulator and the fixed base, which is the least in number compared with others. Through coordinate transformation, we can obtain the geometric relationship in the absolute coordinate system via a set of parametric equations. As a result, the least order's Jacobian matrix will be gained and the singularity of the manipulator can be expressed as the determinate of the Jacobian matrix is zero. The distinctive merit of this methodology is that the order of Jacobian matrix is the least compared with others.     

A geometrical workspace calculation method for cable-driven parallel manipulators on minimum tension condition

In this paper, a geometrical expression to delineate the sum of tensions (i.e. minimum 1-norm tensions) of 2-DoF planar cable-driven parallel manipulators (CDPMs) is proposed and proofed, which can be used to reduce calculation time of workspace determination. Furthermore, this paper also presents a systematic analysis on the relation between cable tension and workspace by means of convex analysis. In order to obtain wrench-feasible workspace, a unified and feasible algorithm is adopted in simulation examples of spatial CDPMs with different configurations, which demonstrate that the proposed method is valid and straightforward to calculate workspace.     

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.     

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.     

Kinematics analysis and statics of a 2SPS+UPR parallel manipulator

In this paper, the kinematics and statics of a 2SPS+UPR parallel manipulator are studied systematically. First, its simulation mechanism is created, and formulae for solving the inverse/forward displacement kinematics are derived. Second, formulae for solving inverse/forward velocity and active/constrained forces are derived. Third, formulae for solving inverse/forward acceleration are derived, and a workspace is analysed. The analytic results are verified by its simulation mechanism. The authors would like to acknowledge the financial support of the Natural Sciences Foundation Council of China (NSFC) 50575198 and of Doctoral Fund from National Education Ministry of China No. 20060216006.     

Kinematic analysis of a 3-PRS parallel manipulator

Although the current 3-PRS parallel manipulators have different methods on the arrangement of actuators, they may be considered as the same kind of mechanism since they can be treated with the same kinematic algorithm. A 3-PRS parallel manipulator with adjustable layout angle of actuators has been proposed in this paper. The key issues of how the kinematic characteristics in terms of workspace and dexterity vary with differences in the arrangement of actuators are investigated in detail. The mobility of the manipulator is analyzed by resorting to reciprocal screw theory. Then the inverse, forward, and velocity kinematics problems are solved, which can be applied to a 3-PRS parallel manipulator regardless of the arrangement of actuators. The reachable workspace features and dexterity characteristics including kinematic manipulability and global dexterity index are derived by the changing of layout angle of actuators. Simulation results illustrate that different tasks should be taken into consideration when the layout angles of actuators of a 3-PRS parallel manipulator are designed.     

Jerk analysis of a six-degrees-of-freedom three-legged parallel manipulator

In this work the jerk analysis of a 3-RRPS parallel manipulator to realize six degrees of freedom is approached by means of the theory of screws. The input/output equations of velocity, acceleration and jerk of the moving platform with respect to the fixed platform are obtained systematically by resorting to reciprocal-screw theory. A numerical example is included in order to show the application of the method of kinematic analysis. Furthermore, the numerical results obtained via screw theory are satisfactorily compared with simulations generated with the aid of commercially available software.     

Optimal design and workspace analysis of a mobile welding robot with a 3P3R serial manipulator

This paper presents the design optimization of a mobile welding robot based on the analysis of its workspace. A welding robot has been developed to be used inside the double-hull structure of ships, and it shows good welding functionality. But there is a need to optimize the kinematic variables ensuring that the required welding functions inside the ships are satisfied. The task-oriented workspace, which is the workspace enabling specific rotations, has been defined in order to validate the welding ability of the robot, and incorporating the required rotational capabilities. To calculate the workspace, a geometric approach is adopted which considers the pitching and yawing angles simultaneously. Based on the workspace analysis, a scenario is compiled for considering a mass reduction, and a ratio between the design parameters and the workspace, with constraints on the workspace margins. The proposed optimization procedure is composed of two steps of coarse and fine searching. In the coarse searching step, a feasible parameter region (FPR) is defined, which satisfies the geometrical design constraints, and can be obtained without any considerations of the objective functions. In the fine searching step, the design parameters are determined by using the optimization technique of the conjugate gradient method in the overall FPRs. The suggested approach to calculating the task-oriented workspace, and the procedure of optimal design, are expected to be applied to general industrial robots.     

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.     

Mobility analysis and kinematics of the semi-general 2(3-RPS) series-parallel manipulator

This work reports on the kinematics of a series-parallel manipulator built with two zero-torsion tangential parallel manipulators assembled in series connection. Although this mechanism has been widely studied, there are some topics that must be revised, e.g. the mobility analysis here reported shows that the robot under study is not precisely a six degrees of freedom spatial mechanism as it has been commonly considered. Furthermore, the traditional hexagonal coupler platform is replaced with a three-dimensional platform which yields a mechanism with a more general topology. The forward and inverse displacement analyses of the robot are obtained in semi-closed form solutions based on simple closure equations which are generated upon the coordinates of three points embedded to the moving platform while the input–output equations of velocity and acceleration of the semi-general series-parallel manipulator are easily derived by resorting to reciprocal-screw theory. A case study is included in order to show the application of the method of kinematic analysis.     

Formulation of unified Jacobian for serial-parallel manipulators

This paper presents a general approach for Jacobian analysis of serial-parallel manipulators (S-PMs) formed by two lower mobility parallel manipulators (PMs) connected in serials. Based on the kinematic relation, coupling and constraint properties of each PM, the unified forward and inverse Jacobian matrices for S-PMs are derived in explicit form. It is shown that the Jacobian matrices of S-PMs have unified forms, which include the complete information of each PM. A (3-RPS)+(3-SPS/UP) S-PM is used as an example to demonstrate the proposed approach. The established model is applicable for S-PMs with various architectures.     

六自由度模块化机械臂工作空间量化对比分析*

针对六自由度模块化机械臂的两种不同构型,对其工作空间进行了量化对比分析。首先采用DH法进行了手臂结构建模,得到正运动学模型;然后基于MATLAB机器人工具箱搭建了两种构型手臂的仿真平台,运用蒙特卡洛法求解两种构型手臂的工作空间并采用可视化方法得到其工作空间的点云图,结合计算机辅助设计软件绘制两种手臂构型的3D工作空间,采用SLI指标对两种手臂构型的工作空间进行量化处理分析;最后通过对比两种手臂构型的工作空间点云图、3D工作空间实体和SLI指标性能分析了两种构型手臂的优劣,为后续的模块化机械臂的结构参数优化和空间灵活性研究奠定了基础。     

Design of cable-driven parallel manipulators for a specific workspace using interval analysis

In this paper, we present a method, based on interval analysis, to solve the problem of designing cable-driven parallel manipulators (CDPMs) for a desired workspace. The constraint of having positive cable tensions ensuring the equilibrium of the platform has to be satisfied within the given workspace. The proposed algorithm is based on interval analysis, which covers the entire workspace and hence guarantees a singularity-free workspace. Furthermore, the algorithm is capable of finding all possible solutions for this problem and an optimal one is selected according to the user-defined criterion. Two examples are selected to show the efficiency of the developed algorithm in solving this complex problem. The first one deals with the design of a planar CDPM and the second one considers a spatial CDPM. In both cases, the algorithm succeeded to find all possible designs from which the designer can select a solution that fits best his application.     

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 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.     

Kinematics and statics analysis of a novel 5-DoF parallel manipulator with two composite rotational/linear active legs

A novel 5-DoF parallel manipulator (PM) with two composite rotational/linear active legs is proposed and its kinematics and statics are studied systematically. First, a prototype of this PM is constructed and its displacement is analyzed. Second, the formulas are derived for solving the linear/angular velocity and acceleration of UPS composite active leg. Third, the Jacobian and Hessian matrices are derived and formulas for solving the velocity, statics and acceleration of this PM are derived. Third, a reachable work space is constructed using a CAD variation geometric approach. Finally, the kinematics and statics of this PM are illustrated and solved. The solved results are verified by the simulation results.