Serial-parallel Manipulator Research Articles

A Transformation Method to Generate the Workspace of an n(3RRS) Serial–Parallel Manipulator

Abstract This paper presents a transformation method to generate the workspace of an n(3RRS) serial–parallel manipulator (S–PM). Firstly, the boundary of the workspace of the 3RRS parallel manipulator (PM) is obtained using the boundary search method and verified by MATLAB/SimMechanics simulation. Secondly, the workspace of the 2(3RRS) S–PM is obtained using the proposed method and verified by MATLAB/SimMechanics simulation. Finally, the workspace of the 3(3RRS) S–PM is obtained using the proposed method. The results indicate that the n(3RRS) S–PM can significantly expand its workspace with the increase in the number of PMs connected in series, and the proposed method can generate the workspaces of n(3RRS) S–PMs efficiently with the advantages of simple operation, high efficiency, and high accuracy. The proposed method is applicable to all S–PMs that are composed of PMs, and it provides a reference for solving the workspaces of other types of redundantly hybrid manipulators.

Terminal constraint and mobility analysis of serial-parallel manipulators formed by 3-RPS and 3-SPR PMs

Although the serial-parallel manipulators(S-PMs) formed by the symmetric 3-RPS and 3-SPR PMs have been widely studied, the terminal constraint and mobility criterion for this class of manipulators are still open questions. This paper solves the terminal constraint and mobility problems of the (3-SPR) + (3-RPS) and the (3-RPS) + (3-SPR) S-PMs. In this paper, the terminal mobility composition principle for the two S-PMs is presented. By analyzing the rank of two types screw systems composed of six constraint forces concerned with the two S-PMs under different geometry conditions, the degree of freedom (DOF) of the two S-PMs are determined. From algebraic and geometric concepts, the approaches for solving the intersection of two sub three order screw systems in determining the terminal constraint are proposed. In addition, the terminal constraint form and mobility property for the two S-PMs under different conditions are discussed. The results show that the terminal constraint of the (3-SPR) + (3-RPS) S-PM is one finite-non-zero pitch screw and the terminal constraint of the (3-RPS) + (3-SPR) S-PM is empty in the general case. This research provides a foundation for the terminal constraint and mobility analysis for S-PMs.

Kinematic analysis of the 3-RPS-3-SPR series–parallel manipulator

SUMMARYThis paper deals with the kinematic analysis and enumeration of singularities of the six degree-of-freedom 3-RPS-3-SPR series–parallel manipulator (S–PM). The characteristic tetrahedron of the S–PM is established, whose degeneracy is bijectively mapped to the serial singularities of the S–PM. Study parametrization is used to determine six independent parameters that characterize the S–PM and the direct kinematics problem is solved by mapping the transformation matrix between the base and the end-effector to a point in ℙ7. The inverse kinematics problem of the 3-RPS-3-SPR S–PM amounts to find the location of three points on three lines. This problem leads to a minimal octic univariate polynomial with four quadratic factors.

Analysis and Optimization of a Spatial Parallel Mechanism for a New 5-DOF Hybrid Serial-Parallel Manipulator

Hybrid manipulators have potentially application in machining industries and attract extensive attention from many researchers on the basis of high stiffness and high dexterity. Therefore, in order to expand the application prospects of hybrid manipulator, a novel 5-degree-of-freedom (DOF) hybrid serial-parallel manipulator (HSPM) is proposed. Firstly, the design plan of this manipulator is introduced. Secondly, the analysis of this manipulator is carried out in detail, including kinematics analysis, statics analysis, and workspace analysis. Especially, an amplitude equivalent method of disposing the over-constrained force/couple to the non-overconstrained force/couple is used in the statics analysis. Then, three performance indices are used to optimize the PM. Two of them have been widely used, and the third one is a new index which considers the characteristics of the actuated force. Based on the performance indices, the performance atlas is drawn and the optimal design of the PM is investigated. In order to satisfy the anticipant kinetic characteristics of the PM, the verification of the optimized physical dimension is done and the workspace based on the optimized physical dimension is carried out. This paper will lay good theoretical foundations for application of this novel HSPM and also can be applied to other hybrid manipulators.

Design of a novel 5-DOF hybrid serial-parallel manipulator and theoretical analysis of its parallel part

Abstract Parallel mechanisms (PMs) with two rotational degrees-of-freedom (DOF) and one translational DOF (2R1T) have gained much attention, in view of their good comprehensive performance in the field of machine tools. In this paper, a novel 2R1T 2UPU/SP PM is presented, and a 5-DOF hybrid serial-parallel manipulator is constructed on the basis of this novel PM. First, to better understand typical 2R1T PMs, a type synthesis method in virtue of the inner properties of PMs are investigated; in particular, the construction principles for the 2UPU/SP PM are introduced. Second, as the 2UPU/SP PM belongs to an over-constrained 2R1T PM, the constraint force and torque generated on the moving platform (MP) are analyzed in detail, and the rotational axes of the 2UPU/SP PM are obtained. Third, the kinematics of the 2UPU/SP PM are studied systematically, including position, velocity and acceleration analysis; based on the kinematic model, an inverse dynamic model is established using the virtual work principle method. The analysis of this PM shows that its kinematic and dynamic models are quite simple. To confirm the correctness of the kinematic and dynamic models, numerical simulations are performed. Next, the workspace is drawn using MATLAB and CAD softwares, which makes it possible to visualize it fully. Finally, the dimensional synthesis on the basis of the motion/force transmissibility is analyzed and relatively optimized physical dimensions are obtained. This study will enhance the research applications of PM and establish good theoretical foundations for the application of this novel manipulator.

Singular Kinetics Analysis of Cartesian Serial-Parallel Manipulator

New type of universal Cartesian serial-parallel manipulator in singular configuration, kinetics equations and Euler’s equations constructed, complete analysis of each jointed points of the moving platform carried out, inverse kinetics solution can be obtained with the given parameters, which include the position and orientation of the manipulator, applied force on the output shaft, parameters of motion of output shaft and connecting bar and sliding block, computer programming adopted to get the valid data and its figure, thus found the perfect show of redundant driving structure on this special mechanism.

Kinetics and Statics Analysis of 2PPPPS-R-2PPPPS Serial-Parallel Manipulator

Based on kinetics equations and Euler's equations, the new organized 2PPPPS-R-2PPPPS serial-parallel manipulator conducts a thorough force analysis of each jointed point of the whole mechanism. Given the position and orientation of the manipulator, applied force on the output shaft, parameters of motion of output shaft and connecting bar and sliding block, we can obtain the inverse solution of force screw of each input jointed point can be found by applying theory of wrench of multi-rigid body. Subsequently, effective data is to be visually presented via computer programming and graphing.

Kinematics and Singularity Analysis of a Four-Degree-of-Freedom Serial-Parallel Hybrid Manipulator

[abstFig src='/00290003/07.jpg' width='300' text='4DOF serial-parallel hybrid manipulator' ] For adapting to the complex working environments of amphibious manipulators, we proposed a serial-parallel hybrid quadruped walking manipulator. We simplified the leg mechanism of the serial-parallel hybrid manipulator as a 2UPU-UPR parallel mechanism, and then analyzed the degree of freedom (DOF) of the parallel mechanism by using the screw theory. The results show that the position of the<span class=”bold”>Y</span>direction and the pose of the<span class=”bold”>Z</span>direction are two independent variables which influence the mechanism movement. We deduced the kinematics inverse solution and the velocity Jacobian matrix of the 2UPU-UPR parallel mechanism. Based on the analysis of the Jacobian matrix, three kinds of kinematic singularities of the 2UPU-UPR parallel mechanism are identified. The results show that the 2UPU-UPR parallel mechanism doesn’t have the kinematic inverse singularity, but it has three kinds of kinematic forward singularities and two kinds of combined singularities. Finally, the variation of motorial parameters of this 2UPU-UPR parallel mechanism was discussed by a calculation example.

Kinematics, dynamics and stiffness analysis of a novel 3-DOF kinematically/actuation redundant planar parallel mechanism

A novel 5-degree-of-freedom (DOF) hybrid serial-parallel manipulator is introduced, and the prototype of its parallel part has been manufactured for pratical testing purpose. The parallel part is a 3-DOF metamorphic planar parallel mechanism (PM) with two different types of configuration: actuation redundancy and kinematic redundancy. First, to establish the inverse dynamic model of the 3-DOF planar PM, its kinematics are studied systematically, including mobility, position, velocity, acceleration, singularity and workspace analysis. Second, an inverse dynamic model of the kinematically redundant planar PM is established by using the virtual work principle method. The actuation forces of the kinematically redundant planar PM are obtained, and the internal forces acting on revolute joints are also obtained by means of separated model blocks. Then, the stiffness matrix is obtained easily by means of the same method used in the dynamics modeling. Finally, kinematics, dynamic numerical simulations considering actuation forces and joint force trends are performed, and the stiffness distributions with contour atlases are also given. The results show the correct of the theoretical kinematic and dynamic models and give reference to know the stiffness performances. A systematic and comprehensive analysis of mentioned planar PM shows that the kinematics of this manipulator with a high degree of modularity are quite simple. And the metamorphic characteristics of kinematic redundancy and actuation redundancy are believed to be able to enhance the research applications of the robot. This research will lay good theoretical foundations for application of this novel manipulator.

Approximate and Widespread Pareto Solutions in the Structure-Control Design of Mechatronic Systems

The structure-control design approach of mechatronic systems requires a different design formulation where the mechanical structure and control system are simultaneously designed. Optimization problems are commonly stated to confront the structure-control design formulation. Nevertheless, these problems are often very complex with a highly nonlinear dependence between the design variables and performance functions. This fact has made the use of evolutionary algorithms, a feasible alternative to solve the highly nonlinear optimization problem; the method to find the best solution is an open issue in the structure-control design approach. Hence, this paper presents a mechanism to exhaustively exploit the solutions in the differential evolution (DE) algorithm in order to find more non-dominated solutions with uniformly distributed Pareto front and better trade-offs in the structure-control design framework. The proposed approach adopts an external population to retain the non-dominated solutions found during the evolutionary process and includes a mechanism to mutate the individuals in their corresponding external population region. As a study case, the structure-control design of a serial-parallel manipulator with its control system is stated as a dynamic optimization problem and is solved by using the proposed approach. A comparative analysis shows that the multi-objective exhaustive exploitation differential evolution obtained a superior performance in the structure-control design framework than a DE algorithm which did not consider the proposal. Hence, the resulting designs provide better trade-offs between the structure-control performance functions.

Kinematics and dynamics analysis of a novel serial-parallel dynamic simulator

A serial-parallel dynamics simulator based on serial-parallel manipulator is proposed. According to the dynamics simulator motion requirement, the proposed serial-parallel dynamics simulator formed by 3-RRS (active revolute joint-revolute joint-spherical joint) and 3-SPR (Spherical joint-active prismatic joint-revolute joint) PMs adopts the outer and inner layout. By integrating the kinematics, constraint and coupling information of the 3-RRS and 3-SPR PMs into the serial-parallel manipulator, the inverse Jacobian matrix, velocity, and acceleration of the serial-parallel dynamics simulator are studied. Based on the principle of virtual work and the kinematics model, the inverse dynamic model is established. Finally, the workspace of the (3-RRS)+(3-SPR) dynamics simulator is constructed.

Type synthesis of the 2R1T parallel mechanism with two continuous rotational axes and study on the principle of its motion decoupling

The two-rotational-degrees-of-freedom and one-translational-degree-of-freedom (2R1T) parallel mechanism (PM) with two continuous rotational axes (CRAs) has a simple kinematic model, and it is therefore easy to implement trajectory planning, parameter calibration, and motion control. However, no systematic analysis on the structural constraints of the 2R1T-PM with two CRAs has been performed. Furthermore, there are few types of 2R1T-PM with two CRAs. Firstly, combining the theories of screw theory and space geometry, we explore the spatial geometrical relationships of the constraint forces supplied by the branches that give the 2R1T-PM two CRAs. Then, type synthesis of the 2R1T-PM with two CRAs is carried out based on the constraint forces meeting special arrangements. In addition, based on the positional relationship between the actuation force and the rotational axe, we analyze the decoupling principle between two rotational degrees of freedom for the 2R1T-PM, and put forward the criteria for distinguishing whether the two rotational degrees of freedom are partially decoupled or completely decoupled. At last, aiming at the different spatial arrangements of the two CRAs for the 2R1T-PM, we propose different configuration modes to construct 5-DOF hybrid serial-parallel manipulator, and get a 5-DOF hybrid serial-parallel manipulator on the basis of one 2R1T-PM.

Design and kinematics analysis of a novel serial–parallel kinematic machine

A novel serial–parallel kinematic machine based on a serial–parallel manipulator is proposed and its kinematics and statics are studied systematically. First, the concept of serial–parallel kinematic machine formed by the 3-PRS parallel manipulator and the 2-UPR + SPR PM is proposed. Second, the displacement is derived in close form based on the geometrical and dimensional constraints existed in the serial–parallel kinematic machine. Third, the Jacobian, velocity and statics of the serial–parallel kinematic machine are derived in the explicit and compact form. Finally, the formulas for solving the acceleration of this serial–parallel kinematic machine are derived. This research will lay a good foundation for the development of the serial–parallel kinematic machine.

Unified solving inverse dynamics of 6-DOF serial–parallel manipulators

The unified inverse dynamics model of serial–parallel manipulators (S–PMs) formed by two parallel manipulators (PMs) connected in series is systematically established based on the constraint and the coupling characteristics of the single PMs in the S–PM. First, the common formulas for solving inverse kinematics of S–PMs is derived. Second, the inverse dynamics model is established based on the principle of virtual work. Finally, a novel (UPR+RPS+SPS)+(3-SPS/UP) S–PM is analyzed to illustrate the generality and effectiveness of the solving procedures.

Inverse and forward dynamics of N-3RPS manipulator with lockable joints

SUMMARYThe N-3 Revolute-Prismatic-Spherical (N-3RPS) manipulator is a kind of serial-parallel manipulator and has higher stiffness and accuracy compared with serial mechanisms, and a larger workspace compared with parallel mechanisms. The locking mechanism in each joint allows the manipulator to be controlled by only three wires. Modeling the dynamics of this manipulator presents an inherent complexity due to its closed-loop structure and kinematic constraints. In the first part of this paper, the inverse kinematics of the manipulator, which consists of position, velocity, and acceleration, is studied. In the second part, the inverse and forward dynamics of the manipulator is formulated based on the principle of virtual work and link Jacobian matrices. Finally, the numerical example is presented for some trajectories.

Kinematics Performance and Structural Analysis for the Design of a Serial-parallel Manipulator Transferring a Billet for a Hot Extrusion Forging Process

To reduce the downtime and optimize the use of energy and manpower, a serial-parallel manipulator is designed for transferring heavy billets for a hot extrusion forging station. With the purpose of...

Position Analysis of a Hybrid Serial-Parallel Manipulator in Immersion Lithography

This paper proposes a novel hybrid serial-parallel mechanism with 6 degrees of freedom. The new mechanism combines two different parallel modules in a serial form. 3-P̲(PH) parallel module is architecture of 3 degrees of freedom based on higher joints and specializes in describing two planes’ relative pose. 3-P̲SP parallel module is typical architecture which has been widely investigated in recent researches. In this paper, the direct-inverse position problems of the 3-P̲SP parallel module in the couple mixed-type mode are analyzed in detail, and the solutions are obtained in an analytical form. Furthermore, the solutions for the direct and inverse position problems of the novel hybrid serial-parallel mechanism are also derived and obtained in the analytical form. The proposed hybrid serial-parallel mechanism is applied to regulate the immersion hood’s pose in an immersion lithography system. Through measuring and regulating the pose of the immersion hood with respect to the wafer surface simultaneously, the immersion hood can track the wafer surface’s pose in real-time and the gap status is stabilized. This is another exploration to hybrid serial-parallel mechanism’s application.

Kinematic Analysis for Hybrid 2-(6-UPU) Manipulator Using Wavelet Neural Network

This paper addresses forward and inverse kinematics of a specific class of serial-parallel manipulators, known as 2(6-UPU) manipulators. This manipulator composed of two modules which consist of elementary manipulators with the parallel structure of Stewart Platform. At first, the Kinematics Model of the hybrid manipulator is obtained. As there is a highly nonlinear relations between joint variables, and position and orientation of the end effectors, the inverse kinematic problem of these manipulators is quite complicated to solve. In this study, wavelet based neural network (WNN) with its inherent learning ability, is used to solve the inverse kinematic problem. Also, proposed wavelet neural network is applied to approximate the paths of mid and upper plates in circle and spiral trajectories. Finally, the results of simulation show high accurate performance of proposed method.

Complete kinematics of a serial–parallel manipulator formed by two Tricept parallel manipulators connected in serials

Complete kinematic is an essential and a challenging work for series–parallel manipulators (S–PMs). This paper studied the complete kinematic of a 2(3-SPS+UP) series–parallel manipulator. First, a S–PM formed by two well-known Tricept parallel manipulators (PMs) connected in serial is presented. Second, the forward and inverse displacements are studied using sylvester dialytic elimination method. Third, the forward and inverse Jacobian matrices are established based on integrating the constraint and coupling information of the single PMs into the S–PM. Fourth, simple and compact formulae for the forward and inverse acceleration are derived using vector approach. Finally, the workspace of this S–PM is constructed using CAD variation geometry approach. The results show that the 2(3-SPS+UP) S-PM has multiple forward and inverse position solutions. The existence and uniqueness of the forward, inverse Jacobian matrices and the acceleration formula are shown from their explicit form. The workspace analysis shows that this S–PM has large workspace. The research works provided a theoretical basis for the novel 2(3-SPS+UP) S–PM, as well as a feasible approach for establishing the complete kinematics for S–PMs.

Error Analysis on Cartesian Serial-Parallel Manipulator with Redundant Drive

The serial-parallel robot can be resolved into the serial combination of two parallel robots. Each branch chain of the parallel robot is all a serial branch chain. By utilizing the kinematics equivalency and considering the influences on posture errors of the final moving platform affected by end errors of each branch, the synthetic analytical method based on dynamic and static factors was put forward. The main affection factor was presented and effectiveness verification has been carried out on the conclusion of study by the form of a living example.