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.     

Type synthesis,unified kinematic analysis and prototype validation of a family of Exechon inspired parallel mechanisms for 5-axis hybrid kinematic machine tools

To fully disclose potential configurations of parallel mechanisms (PMs) that are performance-comparable to the commercially successful Exechon, a family of one translational two rotational (1T2R) over-constrained Exechon inspired PMs is synthesized through the screw theory. The synthesized PMs are further comparatively analyzed in terms of inverse kinematics, singularity occurrence and reachable workspace based on a unified kinematic model. The kinematic analyses indicate that the inherited overconstraints benefit for eliminating the constraint singularity of all synthesized Exechon inspired PMs and the workspace distribution of an Exechon inspired PM is closely related to its topological arrangement. Based on the kinematic evaluations, a preferred configuration of 2UPR-1RPS PM (‘R’: revolute joint, ‘U’: universal joint, ‘S’: spherical joint, ‘P’: prismatic actuated joint) is selected as a candidate for 1T2R spindle head. A laboratory prototype is fabricated and experimentally tested to verify the feasibility of the type synthesis and the correctness of the kinematic analyses. By integrating the selected PM with a 2-degree of freedom sliding gantry, a full scale prototype of a novel hybrid kinematic machine tool is developed to perform 5-axis machining tasks. The well match between the machined workpiece and its designed shape fully proves the engineering potential of the synthesized PMs that are expected to be employed as the functional module to construct 5-axis serial-parallel hybrid machining devices.     

Type synthesis of 5‐DOF parallel manipulators based on screw theory

With the introduction of virtual chains to represent the motion patterns of 5‐DOF motions, a classification of 5‐DOF PMs (parallel manipulators) is proposed at first. A general method for the type synthesis of 5‐DOF PMs is then proposed based on screw theory and using the concept of virtual chains. The type synthesis of US‐equivalent PMs is presented in detail to show the application of the proposed approach. US‐equivalent PMs are the parallel counterparts of the 5‐DOF US serial manipulators. For a US‐equivalent PM, the moving platform can rotate arbitrarily about a point moving along a spherical surface. The type synthesis of legs for US‐equivalent PKCs (parallel kinematic chains), the type synthesis of US‐equivalent PKCs, as well as the selection of actuated joints of US‐equivalent PMs are dealt with in sequence. US‐equivalent PKCs with and without inactive joints are synthesized. Several US‐equivalent PMs as well as other classes of 5‐DOF PMs with identical type of legs are obtained. © 2005 Wiley Periodicals, Inc.     

Structural synthesis of 5 DoFs 3T2R parallel manipulators with prismatic actuators on the base

A method is presented to synthesize 5 degrees of freedom (DoFs) of 3 translational and 2 rotational (3T2R) parallel kinematic structures. This method is based on the theory of linear transformation and geometrical analysis. Central to this method is a set of novel 5 DoFs 3T2R parallel mechanisms (PMs). Based on the legs configuration, the generated mechanisms are classified. Moreover, the promising mechanisms of each class are introduced with respect to some criteria, i.e.: (a) degree of coupling between the actuators and degrees of freedom; (b) easy kinematics and control command; (c) easy construction (or low cost construction); and, (d) manufacturability. With reference to these criteria, some discussions are given on the promising mechanisms. Finally, to demonstrate the role of legs configuration in relation to the characteristics of a manipulator, the kinematic analysis of two of the introduced mechanisms is compared.     

A Family of Symmetrical Lower‐Mobility Parallel Mechanisms with Spherical and Parallel Subchains

This paper presents a new family of symmetrical lower‐mobility parallel mechanisms (PMs) with spherical and parallel subchains, which consists of two 5‐DOF (degrees of freedom) PMs, one 4‐DOF PM and five 3‐DOF PMs. The basic feature of this family is that each limb consists of five revolute pairs and can be constructed with two subchains, a 2R pointing subchain and a 3R parallel subchain, or a 3R spherical subchain and a 2R parallel subchain. Different geometrical arrangements of the limbs lead to different degrees of freedom. All the PMs of this family can be modularized easily due to the simple structure of the subchains. © 2003 Wiley Periodicals, Inc.     

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.     

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.     

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.     

Conceptual design and analysis of the 2T1R mechanism for a cooking robot

This paper deals with the design and analysis of a two-translation and one-rotation (2T1R) mechanism for a novel cooking robot. Firstly the motions involved in stir-fry, the most representative operation in the cooking processes used in Chinese cuisine, are analyzed in details. Then the featured motions are decomposed into four main movements that are used as a design base for a wok motion mechanism. Several three-degrees-of-freedom (DOF) parallel manipulators are considered. From these, a 2T1R mechanism is selected as an ideal candidate. A 4-DOF (2T1R+1T) cooking robot is constructed by combining the 2T1R parallel manipulator with a 1-DOF linear feed mechanism. It is shown that the combined 4-DOF robot can perform the required cooking operations, particularly the stir-fry. The analysis conducted on the proposed 2T1R parallel manipulator includes inverse kinematics, forward kinematics, the velocity analysis, the constant orientation workspace, and the total orientation workspace. A prototype of the cooking robot is developed. The experiments verify that the proposed cooking robot is suitable for performing the required operations.     

Inverse Dynamic Model and a Control Application of a Novel 6-DOF Hybrid Kinematics Manipulator

Kinematics with six degrees of freedom can be of several types. This paper describes the inverse dynamic model of a novel hybrid kinematics manipulator. The so-called Epizactor consists of two planar disk systems that together move a connecting element in 6 DOF. To do so each of the disk systems has a linkage point equipped with a homokinetic joint. Each disk system can be described as a serial 3-link planar manipulator with unlimited angles of rotation. To compensate singularities, a kinematic redundancy is introduced via a fourth link. The kinematic concept leads to several technical advantages for compact 6-DOF-manipulators when compared to established parallel kinematics: The ratio of workspace volume and installation space is beneficial, the number of kinematic elements is smaller, and rotating drives are used exclusively. For a singularity-robust control-approach, the inverse dynamic model is derived using the iterative Newton–Euler-method. Feasibility is shown by the application of the model to an example where excessive actuator velocities and torques are avoided.     

Parametric design optimization of 2-DOF R–R planar manipulator—A design of experiment approach

This work illustrates simulation approach for optimizing the parametric design and performance of a 2-DOF R–R planar manipulator. Using dynamic and kinematic models of a manipulator different performance measures for the manipulator are obtained for different combination of parameters with effect of noise incorporated to imitate the real time performance of the manipulator. A novel approach has been proposed to model, the otherwise difficult to model, noise effects. The data generated during simulation for various parameter combinations are utilized to analyze the statistical significance of kinematic and dynamic parameters on performance of manipulator using ANOVA technique. The parameter combinations, which give optimum performance measures obtained for different points in workspace, are compared and reported.     

Description of Instantaneous Restriction Space for Multi-DOFs Bilateral Teleoperation Systems Using Position Sensors in Unstructured Environments

This paper investigates a novel position-sensor-based force reflection framework for multi-degree-of-freedom (DOF) bilateral teleoperation systems in unstructured environments. The conventional position-sensor-based force reflection method, which is known as position error feedback, may generate grossly inaccurate force reflection directions during collisions involving the slave manipulator links. The proposed restriction space projection framework calculates the instantaneous restriction space to provide the accurate force reflection, regardless of kinematic dissimilarity (KDS) conditions of bilateral teleoperation systems. Simulation results confirmed the validity of the proposed framework in a KDS bilateral teleoperation system under various constraint conditions.     

Visual servoing of redundant manipulator with Jacobian matrix estimation using self-organizing map

Vision based redundant manipulator control with a neural network based learning strategy is discussed in this paper. The manipulator is visually controlled with stereo vision in an eye-to-hand configuration. A novel Kohonen’s self-organizing map (KSOM) based visual servoing scheme has been proposed for a redundant manipulator with 7 degrees of freedom (DOF). The inverse kinematic relationship of the manipulator is learned using a Kohonen’s self-organizing map. This learned map is shown to be an approximate estimate of the inverse Jacobian, which can then be used in conjunction with the proportional controller to achieve closed loop servoing in real-time. It is shown through Lyapunov stability analysis that the proposed learning based servoing scheme ensures global stability. A generalized weight update law is proposed for KSOM based inverse kinematic control, to resolve the redundancy during the learning phase. Unlike the existing visual servoing schemes, the proposed KSOM based scheme eliminates the computation of the pseudo-inverse of the Jacobian matrix in real-time. This makes the proposed algorithm computationally more efficient. The proposed scheme has been implemented on a 7 DOF PowerCube? robot manipulator with visual feedback from two cameras.     

Visual motor control of a 7 DOF robot manipulator using a fuzzy SOM network

A fuzzy self-organizing map (SOM) network is proposed in this paper for visual motor control of a 7 degrees of freedom (DOF) robot manipulator. The inverse kinematic map from the image plane to joint angle space of a redundant manipulator is highly nonlinear and ill-posed in the sense that a typical end-effector position is associated with several joint angle vectors. In the proposed approach, the robot workspace in image plane is discretized into a number of fuzzy regions whose center locations and fuzzy membership values are determined using a Fuzzy C-Mean (FCM) clustering algorithm. SOM network then learns the inverse kinematics by on-line by associating a local linear map for each cluster. A novel learning algorithm has been proposed to make the robot manipulator to reach a target position. Any arbitrary level of accuracy can be achieved with a number of fine movements of the manipulator tip. These fine movements depend on the error between the target position and the current manipulator position. In particular, the fuzzy model is found to be better as compared to Kohonen self-organizing map (KSOM) based learning scheme proposed for visual motor control. Like existing KSOM learning schemes, the proposed scheme leads to a unique inverse kinematic solution even for a redundant manipulator. The proposed algorithms have been successfully implemented in real-time on a 7 DOF PowerCube robot manipulator, and results are found to concur with the theoretical findings.     

Kinematics analysis of a hybrid manipulator for computer controlled ultra-precision freeform polishing

As one of the final processing steps of precision machining, polishing process is a very key decision for surface quality. This paper presents a novel hybrid manipulator for computer controlled ultra-precision (CCUP) freeform polishing. The hybrid manipulator is composed of a three degree-of-freedom (DOF) parallel module, a two DOF serial module and a turntable providing a redundant DOF. The parallel module gives the workpiece three translations without rotations. The serial module holds the polishing tool and gives it no translations on the polishing contact area due to its particular mechanical design. A detailed kinematics model is established for analyzing the kinematics of the parallel module and the serial module, respectively. For the parallel module, the inverse kinematics, the forward kinematics, the Jacobian matrix, the workspace and the dexterity distribution are analyzed systematically. Workspaces are also investigated for varying structural parameters. For the serial module, the inverse kinematics, the forward kinematics, the workspace and the precession motion analysis are carried out. An example of saddle surface finishing with this manipulator is given and the movement of actuators with respect to this shape is analyzed theoretically. These analysis results illustrate that the proposed hybrid manipulator is a very suitable machine structure for CCUP freeform polishing.     

Collaborative Multi-MSA Multi-Target Tracking and Surveillance: a Divide &; Conquer Method Using Region Allocation Trees

This work deals with the problem of the accurate task space control subject to finite-time convergence. Kinematic and dynamic equations of a rigid robotic manipulator are assumed to be uncertain. Moreover, unbounded disturbances, i.e., such structures of the modelling functions that are generally not bounded by construction, are allowed to act on the manipulator when tracking the trajectory by the end-effector. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we derive a class of absolutely continuous (chattering-free) robust controllers based on the estimation of a Jacobian transpose matrix, which seem to be effective in counteracting uncertain both kinematics and dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the robot trajectory. The numerical simulations carried out for a 2DOF robotic manipulator with two revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers.     

Kinematic design of a 6-DOF parallel manipulator with decoupled translation and rotation

A new three-limb, six-degree-of-freedom (DOF) parallel manipulator (PM), termed a selectively actuated PM (SA-PM), is proposed. The end-effector of the manipulator can produce 3-DOF spherical motion, 3-DOF translation, 3-DOF hybrid motion, or complete 6-DOF spatial motion, depending on the types of the actuation (rotary or linear) chosen for the actuators. The manipulator architecture completely decouples translation and rotation of the end-effector for individual control. The structure synthesis of SA-PM is achieved using the line geometry. Singularity analysis shows that the SA-PM is an isotropic translation PM when all the actuators are in linear mode. Because of the decoupled motion structure, a decomposition method is applied for both the displacement analysis and dimension optimization. With the index of maximal workspace satisfying given global conditioning requirements, the geometrical parameters are optimized. As a result, the translational workspace is a cube, and the orientation workspace is nearly unlimited.     

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.     

Disturbance rejection for space‐based manipulators

Most industrial manipulators operate from a fixed base. Hence, there are no disturbances from the environment to alter the position of the end‐effector. On the other hand, manipulators that are mounted on mobile platforms are subject to disturbances emerging from unwanted motion at the base. Similarly, manipulators that perform delicate operations in space while on board in‐orbit spacecraft experience disturbances. This article describes the design and implementation of a disturbance rejection controller for a 6 degree‐of‐freedom (DOF) programable universal manipulator for assembly (PUMA) manipulator mounted on a 3‐DOF platform. A control algorithm is designed to track the desired position and attitude of the end‐effector in inertial space, subject to unknown disturbances in the platform axes. Experimental results are presented for step, sinusoidal, and random disturbances in the platform rotational axis and in the neighborhood of kinematic singularities. ©1999 John Wiley & Sons, Inc.