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.     

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.     

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.     

A comparison study on the dynamics of planar 3-DOF 4-RRR, 3-RRR and 2-RRR parallel manipulators

This paper presents a comparison study on the dynamics of three planar 3-DOF parallel manipulators, one with 3-RRR structure, and the other two with 2-RRR and 4-RRR structures. The inverse kinematics and Jacobian matrix of these mechanisms are analyzed. The dynamic formulations in the linear form are derived and a dynamic performance index is given to compare their dynamic performances. The results show that the 2-RRR parallel manipulator has the worst dynamic performance.     

Forward kinematics,performance analysis,and multi-objective optimization of a bio-inspired parallel manipulator

In this paper, a bio-inspired parallel manipulator with one translation along z-axis and two rotations along x- and y- axes is developed as the hybrid head mechanism of a groundhog robotic system. Several important issues including forward kinematic modeling, performance mapping, and multi-objective improvement are investigated with specific methods or technologies. Accordingly, the forward kinematics is addressed based on the integration of radial basis function network and inverse kinematics. A novel performance index called dexterous stiffness is defined, derived and mapped. The multi-objective optimization with particle swarm algorithm is conducted to search for the optimal dexterous stiffness and reachable workspace.     

Dimensional optimization of 6-DOF 3-CCC type asymmetric parallel manipulator

In this paper, dimensional optimization of a six-degrees-of-freedom (DOF) 3-CCC (C: cylindrical joint) type asymmetric parallel manipulator (APM) is performed by using particle swarm optimization (PSO). The 3-CCC APM constructed by defining three angle and three distance constraints between base and moving platforms is a member of 3D3A generalized Stewart–Gough platform (GSP) type parallel manipulators. The dimensional optimization purposes to find the optimum limb lengths, lengths of line segments on the base and moving platforms, attachment points of the line segments on the base platform, the orientation angles of the moving platform, and position of the end-effector in the reachable workspace in order to maximize the translational and orientational dexterous workspaces of the 3-CCC APM, separately. The dexterous workspaces are obtained by applying condition number and minimum singular values of the Jacobian matrix. The optimization results are compared with the traditional GSP manipulator for illustrating the kinematic performance of 3-CCC APM. Optimizations show that 3-CCC APM have superior dexterous workspace characteristics than the traditional GSP manipulator.     

Kinematic analysis and optimal design of a novel 1T3R parallel manipulator with an articulated travelling plate

Driven by the requirements of the large-scale component assemblage for the docking platform, this paper proposes a novel one-translational-three-rotational (1T3R) parallel manipulator with an articulated travelling plate, which can provide high stiffness and good accuracy performances in the assemblage. The underlying architecture of this manipulator is briefly addressed with emphasis on the practical realization of the articulated travelling plate. On the basis of the kinematic analysis of the 1T3R parallel manipulator, its optimal design considering the force and motion transmissibility is carried out, in which the generalized virtual power transmissibility of this manipulator is defined. This paper aims at laying a solid theoretical and technical foundation for the prototype design and manufacture of the 1T3R parallel manipulator.     

Design and kinetostatic analysis of a new parallel manipulator

This paper proposes an innovative design for a parallel manipulator that can be applied to a machine tool. The proposed parallel manipulator has three degrees of freedom (DOFs), including the rotations of a moving platform about the x and y axes and a translation of this platform along the z-axis. A passive link is introduced into this new parallel manipulator in order to increase the stiffness of the system and eliminate any unexpected motion. Both direct and inverse kinematic problems are investigated, and a dynamic model using a Newton–Euler approach is implemented. The global system stiffness of the proposed parallel manipulator, which considers the compliance of links and joints, is formulated and the kinetostatic analysis is conducted. Finally, a case study is presented to demonstrate the applications of the kinematic and dynamic models and to verify the concept of the new design.     

A simple method to solve the forward displacement analysis of the general six-legged parallel manipulator

In this work a simple method to solve the forward displacement analysis of the general 6-6 fully parallel manipulator is applied. The method is based on generating closure equations upon the unknown coordinates of three points embedded to the moving platform. The method is easy to follow and it is available for both, planar and three-dimensional moving platforms. Numerical examples are included with the purpose to show the application of the method.