Hierarchical design,laboratory prototype fabrication and machining tests of a novel 5-axis hybrid serial-parallel kinematic machine tool

Hybrid serial-parallel kinematic machine tool (HSPKMT) has been regarded as a promising solution for 5-axis machining in many industrial fields. A typical HSPKMT can be constructed by integrating a parallel functional module with a serial functional module. Following this way, the authors construct a novel 5-axis HSPKMT through the integration of an over constrained redundantly actuated parallel module with a stack-up serial gantry. The proposed HSPKMT can accomplish a 5-axis motion capacity with three translations and two rotations (3T2R). A hierarchical design method is proposed to facilitate the design issues of the 5-axis HSPKMT. According to the hierarchical method, a laboratory prototype is designed with a top-down strategy and then fabricated with a bottom-up strategy. An open-architecture computer numerical control (CNC) system is developed to drive the fabricated prototype. A kinematic analysis is carried out to reveal necessary kinematic properties of the proposed HSPKMT. The reachable workspace and task workspace are defined to graphically illustrate the machine's position-orientation capabilities. A workspace performance index is formulated to compare the proposed 5-axis HSPKMT with several 5-axis machine tools. Based the kinematic analysis, a 5-axis machining methodology is developed and further applied to the laboratory prototype to perform 5-axis machining tasks. The machining tests verify that the proposed novel HSPKMT possesses desirable 5-axis machining capability with the tolerance rang of ±0.05 mm. This also implies that the proposed hierarchical design method as well as the 5-axis machining methodology can be further applied to other types of HSPKMTs with minor modifications.     

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.     

Forward kinematic singularity avoiding design of a Schönflies motion generator by asymmetric attachment of subchains

In most of the previous studies on parallel mechanisms (PMs), architectural design mainly relying on symmetric geometry was investigated without in-depth analysis of its performance. This work demonstrates that such a symmetric geometry of multiple subchains sometimes induces a forward kinematic singularity which degrades the overall kinematic performance of PMs within the desired workspace and claims that an asymmetric attachment of those subchains on a moving platform can effectively resolve such a singularity problem. A 4-Degree-of-Freedom (DOF) PM exhibiting Schönflies motions is examined as an example device. First, its mobility analysis and kinematic modeling via screw theory are conducted. Then a singularity analysis based on Grassmann line geometric conditions is carried out, and the forward kinematic singularities of the mechanism are identified and verified by simulations. Based on these analysis and simulations, a forward kinematic singularity-free design is suggested. To show the high potential of the device in practical applications, its output stiffness and dynamic motion capability are examined. Then a prototype is built and its motions capability is verified through experiments.     

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

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.     

Workspace and dynamic performance evaluation of the parallel manipulators in a spray-painting equipment

The paper deals with the workspace and dynamic performance evaluation of the PRR–PRR parallel manipulator in spray-painting equipment. Functional workspace of planar fully parallel robots is often limited because of interference among their mechanical components. The proposed 3-DOF planar parallel manipulator with two kinematic chains connecting the moving platform to the base can reduce interference while still maintaining 3 DOFs. Based on the kinematics, four working modes are analyzed and singularity is studied. The workspace is investigated and the inverse dynamics is formulated using the virtual work principle. The dynamic performance evaluation indices are designed on the basis of maximum and minimum magnitude of acceleration vector of the moving platform produced by a unit actuated force. The index not only can evaluate the accelerating performance of a manipulator, but also can reflect the isotropy of accelerating performance. Workspace and dynamic performances of the four working modes are compared and the optimal working mode for the painting of a large object with conical surface is determined.     

Joint workspace of parallel kinematic machines

Robot workspace is the set of positions a robot can reach. Workspace is one of the most useful measures for the evaluation of a robot. Workspace is usually defined as the reachable space of the end-effector in Cartesian coordinate system. However, it can be defined in joint coordinate system in terms of joint motions. In this paper, workspace of the end-effector is called task workspace, and workspace of the joint motions is called joint workspace. Joint workspace of a parallel kinematic machine (PKM) is focused, and a tripod machine tool with three degrees of freedom (DOF) is taken as an example. To study the joint workspace of this tripod machine tool, the forward kinematic model is established, and an interpolating approach is proposed to solve this model. The forward kinematic model is used to determine the joint workspace, which occupies a portion of the domain of joint motions. The following contributions have been made in this paper include: (i) a new concept so-called joint workspace has been proposed for design optimization and control of a PKM; (ii) an approach is developed to determine joint workspace based on the structural constraints of a PKM; (iii) it is observed that the trajectory planning in the joint coordinate system is not reliable without taking into considerations of cavities or holes in the joint workspace.     

Kinematic modeling of Exechon parallel kinematic machine

The studies on PKMs have attracted a great attention to robotics community. By deploying a parallel kinematic structure, a parallel kinematic machine (PKM) is expected to possess the advantages of heavier working load, higher speed, and higher precision. Hundreds of new PKMs have been proposed. However, due to the considerable gaps between the desired and actual performances, the majorities of the developed PKMs were the prototypes in research laboratories and only a few of them have been practically applied for various applications; among the successful PKMs, the Exechon machine tool is recently developed. The Exechon adopts unique over-constrained structure, and it has been improved based on the success of the Tricept parallel kinematic machine. Note that the quantifiable theoretical studies have yet been conducted to validate its superior performances, and its kinematic model is not publically available. In this paper, the kinematic characteristics of this new machine tool is investigated, the concise models of forward and inverse kinematics have been developed. These models can be used to evaluate the performances of an existing Exechon machine tool and to optimize new structures of an Exechon machine to accomplish some specific tasks.     

Position and stiffness analysis of a new asymmetric 2PRR–PPR parallel CNC machine

In this paper, structural stiffness analysis of a new 3-axis asymmetric planar parallel manipulator, a 2 P RR–P P R structural kinematic chain, is investigated. The manipulator is proposed as a tool holder for a 5-axis hybrid computer numerical control (CNC) machine. First, the structure of the robot is introduced and inverse kinematics solution is presented. Secondly, stiffness matrix of the robot is determined using a continuous method based on Castigliano’s theorem and calculation of strain energy of the robot components. This method removes the need for commonly used simplifying assumptions and, therefore, results in good accuracy. For this purpose, force and strain energy for each segment of the robot are analyzed. Finally, to verify the analytical results, commercial FEM software is used to simulate the physical structure of the manipulator. A numerical example is presented which confirms the correctness of the analytical formulations.     

Type synthesis of 2T1R-type parallel kinematic mechanisms and the application in manufacturing

This paper investigates the type synthesis of 2T1R-type (T: translational degree of freedom (DoF) and R: rotational DoF) parallel kinematic mechanisms (PKMs). A type synthesis method based on Grassmann Line Geometry and Line-graph Method is introduced. Some basic criterions of Grassmann Line Geometry are briefly summarized, and the Line-graph Method is presented sequentially. In order to uncover the relationship between DoF-line graph and constraint-line graph, the dual rule is brought in and explained in detail. Based on these foundations, the technological process of the type synthesis is given. Thereafter, the type synthesis of 2T1R-type PKMs is carried out and the results are listed. Taken as an application example, a synthesized 3-DoF mechanism is chosen as the parallel module of a five-axis hybrid machine tool, which is capable of five-face machining in one setup. The developed prototype is introduced and applied into the machining of a part with freeform surfaces. The presented type synthesis method is concise and can be used in the type synthesis of other PKMs.     

Forward and inverse kinematics of a 5-DOF hybrid robot for composite material machining

Hybrid robots consist of both serial and parallel mechanisms, which have advantages in stiffness and workspace compared with serial/parallel robots when machining composite material. However, the forward and inverse kinematics of hybrid robots generally do not have analytic solutions. This paper deals with the analytic forward and inverse kinematics solutions of a 5-degree-of-freedom (DOF) hybrid robot which consists with a 3-DOF 2UPU/SP parallel mechanism (PM) and a 2-DOF rotating head. In the forward kinematic problem, a method is proposed to transfer the high order kinematic equation to a 4th-order polynomial based on the Sylvester's dialytic elimination, and the analytic solutions can be further obtained by Ferrari's method. In the inverse problem, the redundant Euler angles expressed by four rotations are firstly proposed for decoupling different motions, then, the closed-form solution of inverse kinematics can be found. Finally, a simulation trajectory is given, and the result shows that the accuracy of the solutions’ calculation reaches femtometer grade and the efficiency reaches microsecond grade; furthermore, an experiment is performed on the prototype to validate the effectiveness of the proposed forward and inverse kinematics.     

Simulation and computer-aided kinematic design of three-degree-of-freedom spherical parallel manipulators

Parallel robotic manipulators are complex mechanical systems that lead to involved kinematic and dynamic equations. Hence, the design of such systems is in general not intuitive, and advanced simulation and design tools specialized for this type of architecture are highly desirable. This article discusses the kinematic simulation and computer-aided design of three-degree-of-freedom spherical parallel manipulators with either prismatic or revolute actuators. The kinematic analysis of spherical parallel manipulators is first reviewed. Solutions for the direct and inverse kinematic problems are given, and the expressions for the singularity loci are then introduced. The determination of the workspace of this type of manipulator is also addressed. Finally, a computer package developed specifically for the CAD of spherical parallel manipulators is presented. This package allows the interactive analysis of manipulators of arbitrary architecture including the representation of the workspace, the representation of singularities, and the graphic animation of trajectories specified either by the direct or the inverse kinematic module. It can be used for the design of any spherical parallel three-degree-of-freedom actuated mechanism, which can find many applications in high-performance robotic systems. © 3995 John Wiley & Sons, Inc.     

Constrained multi-objective trajectory planning of parallel kinematic machines

This paper presents a new approach to multi-objective dynamic trajectory planning of parallel kinematic machines (PKM) under task, workspace and manipulator constraints. The robot kinematic and dynamic model, (including actuators) is first developed. Then the proposed trajectory planning system is introduced. It minimizes electrical and kinetic energy, robot traveling time separating two sampling periods, and maximizes a measure of manipulability allowing singularity avoidance. Several technological constraints such as actuator, link length and workspace limitations, and some task requirements, such as passing through imposed poses are simultaneously satisfied. The discrete augmented Lagrangean technique is used to solve the resulting strong nonlinear constrained optimal control problem. A decoupled formulation is proposed in order to cope with some difficulties arising from dynamic parameters computation. A systematic implementation procedure is provided along with some numerical issues. Simulation results proving the effectiveness of the proposed approach are given and discussed.     

Kinematics,Singularity Study and Optimization of an Innovative Spherical Parallel Manipulator with Large Workspace

A novel design for three degree of freedom (DoF) mechanical arm, i.e. a 3-PUS/S Spherical Parallel Manipulator (SPM) with three rotational motions is proposed in this article. In addition, its kinematic equations, singularity and design optimization are studied according to its application. The proposed parallel robot that has three legs with three prismatic joints can rotate about Z-axis unlimitedly. Therefore, the manipulator has large workspace and good flexibility, hence being attractive to study. To complete the kinematic analysis of the manipulator, three stages are considered as follows. At the first, the kinematics of the SPM is explained to obtain the positions, velocities, and accelerations. Furthermore, the Jacobian and Hessian matrices of the 3-PUS/S Parallel Manipulator are derived. The results are verified by the use of CAD and Adams software. Next, the Jacobian matrix obtained from the kinematic equations is utilized to study the different types of singularities. Finally, the optimum dimensions of the manipulator based on kinematic and singularity features are studied by Genetic Algorithm (GA), and the Global Condition Index (GCI) is maximized. The results help the designers to achieve an ideal geometry for the parallel manipulator with good workspace and minimum singularity.     

Analysis of parallel kinematic machine with kinetostatic modelling method

A new method, called Kinetostatic Modelling Method is proposed for analysis of parallel kinematic machines (PKMs) in the paper. First, system modelling includes mobility study, kinematic model and inverse kinematic is conducted. Then, kinetostatic modelling is presented. It includes a complete compliant model developed for the analysis of the PKMs with fixed-length legs, with the model, two global compliance indices are introduced to provide a new mean of measuring the PKM's compliance over the workspace. These two global indices are the mean value and the standard deviation of the trace of the generalized compliance matrix. The mean value represents the average compliance of the PKM over the workspace, while the standard deviation indicates the compliance fluctuation relative to the mean value. The effect of three types of compliance is investigated in order to identify a dominant factor. The proposed method is implemented to analyze the compliance of the Tripod-based PKM prototype built at the Integrated Manufacturing Technologies Institute of the National Research Council of Canada. It is shown that the proposed method is an effective means for evaluating the kinetostatic behaviour of PKMs globally.     

Uniqueness domains and regions of feasible paths for cuspidal manipulators

This paper addresses the kinematics of cuspidal manipulators, i.e., nonredundant manipulators which can change posture without meeting a singularity. It focuses on the uniqueness domains and on the regions of feasible paths in the workspace. For cuspidal manipulators, the uniqueness domains are not the singularity-free regions of the joint space. It is shown that additional surfaces, called characteristic surfaces, separate the inverse kinematic solutions in the joint space. The uniqueness domains define the regions of feasible paths in the workspace. Joint limits are taken into account in this paper. This paper should help the reader better understand the kinematics of cuspidal manipulators.     

Dynamic visual servo control of a 4-axis joint tool to track image trajectories during machining complex shapes

A large part of the new generation of computer numerical control systems has adopted an architecture based on robotic systems. This architecture improves the implementation of many manufacturing processes in terms of flexibility, efficiency, accuracy and velocity. This paper presents a 4-axis robot tool based on a joint structure whose primary use is to perform complex machining shapes in some non-contact processes. A new dynamic visual controller is proposed in order to control the 4-axis joint structure, where image information is used in the control loop to guide the robot tool in the machining task. In addition, this controller eliminates the chaotic joint behavior which appears during tracking of the quasi-repetitive trajectories required in machining processes. Moreover, this robot tool can be coupled to a manipulator robot in order to form a multi-robot platform for complex manufacturing tasks. Therefore, the robot tool could perform a machining task using a piece grasped from the workspace by a manipulator robot. This manipulator robot could be guided by using visual information given by the robot tool, thereby obtaining an intelligent multi-robot platform controlled by only one camera.     

Open-architecture of CNC system and mirror milling technology for a 5-axis hybrid robot

This paper presents an open-architecture of CNC system and mirror milling technology for a new-type 5-axis hybrid robot named TriMule. The CNC system with dual CPUs is developed first to achieve human-computer interaction and motion control. Then, three key technologies are integrated in the system for improving the control quality, including singularity avoidance, feedforward control considering joint couplings and real-time error compensation by using externally mounted encoders. Based on these control technologies for single robot system, a collaborative machining strategy on the mirror milling system that consists of two TriMule robots is proposed to control the machining wall thickness of large thin-walled structural parts. Experiments on the TriMule robot and mirror milling system verify that the acceptable machining accuracy on the NAS test part and large thin-walled structural part can be ensured by using the developed CNC system and technologies. The root mean square of wall thickness error using the collaborative machining strategy can be 41.67% lower than the case without using the strategy.     

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.