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.     

GEHEIMSCHREIBER

World War II's “Fish” cipher was a British cover word for all kinds of encrypted German radio teleprinter messages. The GC&CS at Bletchley, Buckinghamshire, did not only attack successfully Enigma traffic (Morse signals on radio links) by the electromechanical deciphering machines called BOMBES. In addition, Bletchley's electronic text processor COLOSSUS broke the German “Tunny” ciphers, generated by TELEPRINTER ATTACHMENTS “SZ”, employed by the ‘Heer’ (Army) on HF radio links.     

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.     

Dynamics analysis for a novel 6-DoF parallel manipulator I with three planar limbs

A novel 6-DoF parallel manipulator I with three planar limbs is proposed and its dynamics is analyzed systematically. First, its characteristics and DoF are analyzed and calculated. Second, the formulae for solving kinematics of the moving platform and the planar limbs are derived. Third, the formulae for solving the inertial wrench applied on the planar limbs and the moving platform are derived, and dynamics formula is derived for solving dynamic active forces applied onto the planar limbs. Fourth, a singularity of the proposed parallel manipulator is determined and analyzed. Fifth, an analytic example is given for solving the kinetostatics and dynamics of the proposed parallel manipulator, and the solved results are analyzed and verified by the simulation mechanism. Finally, a workspace is constructed and analyzed by comparing with an existing 6-DoF parallel 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.     

Retrieval of atmospheric and oceanic properties from MERIS measurements: A new Case‐2 water processor for BEAM

A freely available data processor for the B asic E RS & ENVISAT ( A )ATSR and M ERIS Toolbox (BEAM) was developed to retrieve atmospheric and oceanic properties above and of Case‐2 waters from Medium Resolution Imaging Spectrometer (MERIS) Level1b data. The processor was especially designed for European coastal waters and uses MERIS Level1b Top‐Of‐Atmosphere (TOA) radiances to retrieve atmospherically corrected remote sensing reflectances at the Bottom‐Of‐Atmosphere (BOA), spectral aerosol optical thicknesses (AOT) and the concentration of three water constituents, namely chlorophyll‐a (CHL), total suspended matter (TSM) and the absorption of yellow substance at 443 nm (YEL). The retrieval is based on four separate artificial neural networks which were trained on the basis of the results of extensive radiative transfer (RT) simulations by taking various atmospheric and oceanic conditions into account. The accuracy of the retrievals was acquired by comparisons with concurrent in situ ground measurements and was published in full detail elsewhere. For the remote sensing reflectance product a mean absolute percentage error (MAPE) of 18% was derived within the spectral range 412.5–708.75 nm while the accuracy of the AOT at 550 nm in terms of MAPE was calculated to be 40%. The accuracies for CHL, TSM and YEL were derived from match‐up analysis with MAPEs of 50%, 60% and 71%, respectively.     

Optimal motion planning for parallel robots via convex optimization and receding horizon

In this paper, the problem of motion planning for parallel robots in the presence of static and dynamic obstacles has been investigated. The proposed algorithm can be regarded as a synergy of convex optimization with discrete optimization and receding horizon. This algorithm has several advantages, including absence of trapping in local optimums and a high computational speed. This problem has been fully analyzed for two three-DOF parallel robots, ie 3s-RPR parallel mechanism and the so-called Tripteron, while the shortest path is selected as the objective function. It should be noted that the first case study is a parallel mechanism with complex singularity loci expression from a convex optimization problem standpoint, while the second case is a parallel manipulator for which each limb has two links, an issue which increases the complexity of the optimization problem. Since some of the constraints are non-convex, two approaches are introduced in order to convexify them: (1) A McCormick-based relaxation merged with a branch-and-prune algorithm to prevent it from becoming too loose and (2) a first-order approximation which linearizes the non-convex quadratic constraints. The computational time for the approaches presented in this paper is considerably low, which will pave the way for online applications.     

Architecture Selection and Singularity Analysis of a Three-Degree-of-Freedom Planar Parallel Manipulator

A three degree-of-freedom planar parallel manipulator, intended for high-speed, high-precision wire-bonding and electronic-component placement tasks, has been developed in our laboratory. In this paper, the work related to the kinematic manipulator-architecture selection is presented. The reachable workspace and effective base area metrics of the parallel manipulator were utilized for selecting the best possible architecture amongst six potential configurations. Constant platform-orientation regions, within the reachable workspace of the selected manipulator, were identified based on the manipulator task requirements. Simulation results for the workspace analyses (reachable workspace, effective base areas, and constant-orientation regions) are presented in this paper. Once the optimal-workspace architecture was selected, both workspace-boundary and internal singularities were further investigated in order to have a clear view of the set of uncontrollable poses of the manipulator. Singularity analyses examples are also included herein.     

Piece wise linear least–squares approximation of planar curves

Two algorithms for solving the piecewise linear least–squares approximation problem of plane curves are presented. The first is for the case when the L ₂ residual (error) norm in any segment is not to exceed a pre–assigned value. The second algorithm is for the case when the number of segments is given and a (balanced) L ₂ residual norm solution is required. The given curve is first digitized and either algorithm is then applied to the discrete points. For each segment, we obtain the upper triangular matrix R in the QR factorization of the (augmented) coefficient matrix of the resulting system of linear equations. The least–squares solutions are calculated in terms of the R (and Q) matrices. The algorithms then work in an iterative manner by updating the least–squares solutions for the segments via up dating the R matrices. The calculation requires as little computational effort as possible. Numerical results and comments are given. This, in a way, is a tutorial paper.     

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.     

Learning accurate very fast decision trees from uncertain data streams

Most existing works on data stream classification assume the streaming data is precise and definite. Such assumption, however, does not always hold in practice, since data uncertainty is ubiquitous in data stream applications due to imprecise measurement, missing values, privacy protection, etc. The goal of this paper is to learn accurate decision tree models from uncertain data streams for classification analysis. On the basis of very fast decision tree (VFDT) algorithms, we proposed an algorithm for constructing an uncertain VFDT tree with classifiers at tree leaves (uVFDTc). The uVFDTc algorithm can exploit uncertain information effectively and efficiently in both the learning and the classification phases. In the learning phase, it uses Hoeffding bound theory to learn from uncertain data streams and yield fast and reasonable decision trees. In the classification phase, at tree leaves it uses uncertain naive Bayes (UNB) classifiers to improve the classification performance. Experimental results on both synthetic and real-life datasets demonstrate the strong ability of uVFDTc to classify uncertain data streams. The use of UNB at tree leaves has improved the performance of uVFDTc, especially the any-time property, the benefit of exploiting uncertain information, and the robustness against uncertainty.     

Dual Integral Sliding Mode Control Loop for Mechanical Error Correction in Trajectory-Tracking of a Planar 3-<Emphasis Type="Underline">P</Emphasis>RP Parallel Manipulator

This paper presents a dual-loop control scheme based on an integral sliding mode control scheme for the task-space pose error correction in trajectory-tracking of a planar 3-PRP parallel manipulator due to mechanical inaccuracies. The proposed dual-loop control scheme uses redundant sensor feedback, i.e., individual active joint displacements, velocities (at the joint-space level) and, end-effector positions and orientation (at the task-space level) are obtained as feedback signals using appropriate sensors. Using the redundant feedback information, the actual pose errors of the end-effector are computed in the outer-loop (kinematic) control and rectified in joint-space inner-loop (dynamic) control to achieve the given desired task-space trajectory. To demonstrate the efficacy and show complete performance of the controllers, real-time experiments are executed on an in-house fabricated planar 3-PRP parallel manipulator. The experimentation results show that the manipulator tracing performance is considerably improved with the proposed dual-loop control scheme. In addition, the controller parameter sensitivity and robustness analyses are also accomplished.     

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.     

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.     

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.     

Workspace evaluation of manipulators through finite-partition of SE(3)

Workspace analysis and optimization are important in a manipulator design. As the complete workspace of a 6-DOF manipulator is embedded into a 6-D space, it is difficult to quantify and qualify it. Most literatures only considered the 3-D sub workspaces of the complete 6-D workspace. In this paper, a finite-partition approach of the Special Euclidean group SE(3) is proposed based on the topology properties of SE(3), which is the product of Special Orthogonal group SO  (3) and R³${\mathbb{R}}^3$. It is known that the SO(3) is homeomorphic to a solid ball D³ with antipodal points identified while the geometry of R³${\mathbb{R}}^3$ can be regarded as a cuboid. The complete 6-D workspace SE(3) is at the first time parametrically and proportionally partitioned into a number of elements with uniform convergence based on its geometry. As a result, a basis volume element of SE  (3) is formed by the product of a basis volume element of R³${\mathbb{R}}^3$ and a basis volume element of SO(3), which is the product of a basis volume element of D³ and its associated integration measure. By this way, the integration of the complete 6-D workspace volume becomes the simple summation of the basis volume elements of SE(3). Two new global performance indices, i.e., workspace volume ratio (W_r) and global condition index (GCI), are defined over the complete 6-D workspace. A newly proposed 3RP PS parallel manipulator is optimized based on this finite-partition approach. As a result, the optimal dimensions for maximal workspace are obtained, and the optimal performance points in the workspace are identified.     

WHY GERMANY LOST THE CODE WAR

This paper was presented for discussion at the Baltimore-Washington German History Seminar, 8 November 1980, Towson State University, Towson, Maryland. It is a slightly revised form of a portion of “Codebreaking in World Wars I and II: The Major Successes and Failures, Their Causes and Their Effects,” The Historical Journal, 23 (September, 1980), 617–639, which lists all sources. The technical reasons given below owe a great deal to the kind help of Dr. Cipher A. Deavonrs.