Fault tolerance of parallel manipulators using task space and kinematic redundancy

When a parallel manipulator suffers from failures, its performance can be significantly affected. Thus, fault tolerance is essential for task-critical applications or applications in which maintenance is hard to implement. In this paper, we consider three types of common strut failures corresponding to stuck joints, unactuated actuators, or the complete loss of struts, respectively. The impacts of different failures on the kinematics of a manipulator are examined, and the task space redundancy and kinematic redundancies are used to help overcome these failures. In addition, local measures of fault tolerance and their properties are analyzed. These measures can be helpful in architecture design and path planning.     

Estimation model for kinematic calibration of manipulators with a parallel structure

This article provides an estimation model for calibrating the kinematics of manipulators with a parallel geometrical structure. Parameter estimation for serial link manipulators is well developed, but fail for most structures with parallel actuators, because the forward kinematics is usually not analytically available for these. We extend parameter estimation to such parallel structures by developing an estimation method where errors in kinematical parameters are linearly related to errors in the tool pose, expressed through the inverse kinematics, which is usually well known. The method is based on the work done to calibrate the MultiCraft robot. This robot has five linear actuators built in parallel around a passive serial arm, thus making up a two-layered parallel-serial manipulator, and the unique MultiCraft construction is reviewed. Due to the passive serial arm, for this robot conventional serial calibration must be combined with estimation of the parameters in the parallel actuator structure. The developed kinematic calibration method is verified through simulations with realistic data and real robot kinematics, taking the MultiCraft manipulator as the case. © 1994 John Wiley & Sons, Inc.     

Optimization design of general triglide parallel manipulators

Optimization design of parallel manipulators has attracted much interest from researchers in recent years. The reported methodologies attempted to achieve optimal design of parallel manipulators considering several properties, such as dexterity, stiffness, and space utilization, which are important parameters to be considered. However, stiffness analysis considered by many researchers generally ignores the deformation of the mobile platform. For space utilization, there is no reported method to consider the variation in the physical size caused by different postures of the manipulator. Additionally, although optimization of a linear delta and an orthoglide has been presented by several researchers, optimization of a general triglide has not been reported. In order to address these issues, this paper presents a multi-objective optimization addressing dexterity, stiffness, and space utilization of a general triglide. Its stiffness matrix is obtained considering the deformation of mobile platform, limbs, and actuators. A novel stiffness index is used to evaluate its stiffness property considering external wrench applied on the manipulator. The physical size of the triglide is represented using both a constant size and a variable size. Comparing with a reported optimization methodology, it is proven that the proposed method is capable of providing optimal solutions with better properties.     

Some kinematic considerations for the design of robot manipulators

This work deals with the optimization of the link lengths and ranges of motion of the joint coordinates of the major linkage of a robot manipulator. On the basis of some simple modifications of the mechanism the characteristics of the workspace are improved. The optimization criteria are expressed by robot workspace volume and compactness. In order to evaluate the results obtained, a comparison is made with an anthropomorphic mechanism.     

Numerical direct kinematic analysis of fully parallel linearly actuated platform type manipulators

This article presents a new numerical approach for solving the direct kinematics problem of fully parallel, linearly actuated platform manipulators. The solution procedure consists of two stages. The first stage transforms the direct kinematics problem into an equivalent nonlinear programming program, and a robust search algorithm is developed to bring the moving platform from arbitrary initial approximation to a feasible configuration that is near to the true solution. The second stage uses the Newton‐Raphson iterative method to converge the solution to the desired accuracy. This approach is numerically stable and computationally efficient. In addition, by randomly perturbing the initial approximations, it can be implemented successively to find multiple solutions to the direct kinematics problem. Two numerical examples are presented to demonstrate the stability and efficiency of this approach. © 2002 Wiley Periodicals, Inc.     

Calibration of stewart platforms and other parallel manipulators by minimizing inverse kinematic residuals

This paper focuses on the accuracy enhancement of Stewart platforms through kinematic calibration. The calibration problem is formulated in terms of a measurement residual, which is the discrepancy between the measured leg length and the computed leg length. With this formulation, one is able to identify kinematic error parameters of the Stewart platform without the necessity of solving the forward kinematic problem; thus avoiding the numerical problems associated with any forward kinematic solution. By this formulation, a concise differential error model with a well-structured identification Jacobian, which relates the pose measurement residual to the errors in the parameters of the platform, is derived. Experimental studies confirmed the effectiveness of the method. It is also shown in this paper that the proposed approach can be applied to other types of parallel manipulators, assuming that their inverse kinematic solution is simpler than its forward kinematic solution. Because this condition is satisfied by almost all parallel manipulators, the method is very useful for kinematic calibration of such machines. © 1998 John Wiley & Sons, Inc.     

Design of a spherical parallel kinematic machine for ankle rehabilitation

Existing ankle rehabilitation robots have the limitations of insufficient motion ranges and coupled translations. An improved spherical robot has been proposed to overcome these limitations. The forward and inverse kinematic problems of this new machine are formulated and solved; the dexterity of the workspace is evaluated and the workspace has been optimized with the consideration of the motion ranges of passive joints. The operation of machine has been simulated; it will be further expanded as a control program to run the rehabilitation robot.     

Experimental kinematic calibration of parallel manipulators using a relative position error measurement system

Because of errors in the geometric parameters of parallel robots, it is necessary to calibrate them to improve the positioning accuracy for accurate task performance. Traditionally, to perform system calibration, one needs to measure a number of robot poses using an external measuring device. However, this process is often time-consuming, expensive and difficult for robot on-line calibration. In this paper, a methodical way of calibration of parallel robots is introduced. This method is performable only by measuring joint variable vector and positioning differences relative to a constant position in some sets of configurations that the desired positions in each set are fixed, but the moving platform orientations are different. In this method, measurements are relative, so it can be performed by using a simple measurement device. Simulations and experimental studies on a Hexaglide parallel robot built in the Sharif University of Technology reveal the convenience and effectiveness of the proposed robot calibration method for parallel robots.     

Experimental results on kinematic calibration of parallel manipulators using a partial pose measurement device

This paper presents kinematic calibration of parallel manipulators with partial pose measurements, using a device that measures a rotation of the end-effect or along with its position. The device contains a linear variable differential transformer, a biaxial inclinometer, and a rotary sensor. The device is designed in a modular fashion, and links of different lengths can be used. Two additional kinematic parameters required for the measurement device are discussed, kinematic relations are derived, and cost function is established to perform calibration with the proposed device. The study is performed for a six-degree-of-freedom fully parallel HexaSlide mechanism (HSM). Experimental results show significant improvement in the accuracy of the HSM.     

Performance investigations on optimum mechanical design aspects of planar parallel manipulators

This paper presents a comparative analysis of three degrees of freedom planar parallel robotic manipulators (x, y and θ_z motion platforms) namely 2PRP-PPR, 2PRR-PPR, 3PPR (Hybrid), 3PRP (Hephaist) and 3PPR U-base in terms of optimal kinematic design performance, static structural stiffness and dynamic performance (energy and power consumption). Kinematic and dynamic performance analyses of these platforms have been done using multibody dynamics software (namely ADAMS/View). Static stiffness of the above-mentioned manipulators have been analysed, compared using the conventional joint space Jacobian stiffness matrix method, and this method has been verified through a standard finite-element software (namely NASTRAN) as well. The size of the fixed base or aspect ratio (width/height) can be varied for various working conditions to understand its design parameters and optimal design aspects which are depending on the fixed base structure. Different aspect ratios (fixed base size) are considered for the comparative analyses of isotropy, manipulability and stiffness for the above-mentioned planar parallel manipulators. From the numerical simulation results, it is observed that the 2PRP-PPR manipulator is associated with a few favourable optimum design aspects such as singularity-free workspace, better manipulability, isotropy, higher stiffness and better dynamic performance in terms of power and energy requirement as compared to other planar parallel manipulators.     

Structures and characteristics of parallel manipulators

Parallel structures have remarkable characteristics such as high precision, high load capacity, high rigidity and high speed. Therefore, they have received a lot of attention as alternative structures for robot manipulators. This paper reviews the recent results on properties of the parallel manipulator. First, the basics of the link mechanism, which is necessary to understand the structure of the parallel manipulator, is summarized before the structure of the parallel manipulator is defined. Then, the parallel manipulator is compared with the serial manipulator. The singular point of the parallel manipulator and the optimum design of the structure of the parallel manipulator are also discussed.     

The optimum design of 6‐DOF isotropic parallel manipulators

How to obtain 6‐DOF parallel manipulators with optimum global isotropy is investigated in this paper. A systematic method is first presented to get isotropic parallel designs. A measure for spatial isotropy is then proposed to evaluate and compare the global isotropy of obtained manipulators. Efficient methods to find the minimum and maximum singular values of matrices are developed to facilitate the evaluation process. © 2005 Wiley Periodicals, Inc.     

Simulation of biological ion channels with technology computer-aided design

Computer simulations of realistic ion channel structures have always been challenging and a subject of rigorous study. Simulations based on continuum electrostatics have proven to be computationally cheap and reasonably accurate in predicting a channel's behavior. In this paper we discuss the use of a device simulator, SILVACO, to build a solid-state model for KcsA channel and study its steady-state response. SILVACO is a well-established program, typically used by electrical engineers to simulate the process flow and electrical characteristics of solid-state devices. By employing this simulation program, we have presented an alternative computing platform for performing ion channel simulations, besides the known methods of writing codes in programming languages. With the ease of varying the different parameters in the channel's vestibule and the ability of incorporating surface charges, we have shown the wide-ranging possibilities of using a device simulator for ion channel simulations. Our simulated results closely agree with the experimental data, validating our model.     

Six-Dimensional space expression of workspace of six-DoF parallel manipulators using hyper spherical coordinates (HSC)

A closed-form formulation for the workspace of N-Degrees-of-Freedom (DoF) parallel mechanisms is presented using least-square curve fitting. The concepts of multi-dimensional polynomial (MDP) and in hyper spherical coordinates (HSC) are introduced. The boundary of workspaces of those parallel linkages which are surfaces without voids and concavities can be well approximated by the MDPs in the HSC. First, the boundary points are obtained in HSC considering all physical constrains and probable singularities. Then, an MDP with proper order consisting of sine and cosine functions is fitted to those points. The presented method is general and applicable to all DoF. Three case studies of 2, 3, and 6-DoF mechanisms are investigated to demonstrate the effectiveness of the method.     

Classification of kinematic singularities in planar robot manipulators

In [13, 14] we have proclaimed a singularity theory based programme of investigations of kinematic singularities in robot manipulators. The main achievement of the programme consists in providing local candidate models of kinematic singularities. However, due to the specific form of the manipulator kinematics, fitting the candidate models into the prescribed robot kinematics is a fairly open problem. The problem is easily solvable only around non-singular configurations of manipulators, where locally the kinematics can be modelled by linear injections or projections. In this paper we are concerned with planar manipulator kinematics, and prove that, under a mild geometric condition, such kinematics can be transformed around singular configurations to simple quadratic models of the Morse type. The models provide a complete local classification of generic planar kinematics of robot manipulators.     

Definition of a kinematic metric for robot manipulators

Using a Riemannian metric in the special Euclidean group we define a kinematic metric on the space of kinematics of robot manipulators. Prospective applications of the metric in kinematic design and performance evaluation of robot manipulators are indicated. For exemplary kinematics, including the PUMA 600, explicit formulas are provided describing the dependence of the metric on manipulator's geometric parameters. © 1994 John Wiley & Sons, Inc.     

Direct displacement analysis of parallel manipulators

A new numerical method for the direct position analysis of the parallel manipulators is presented. The main feature of the method, making it attractive with respect to the method available in the literature, is the ability to search out the direct solution under any precision quickly. © 2000 John Wiley & Sons, Inc.     

Vibration analysis of cable-driven parallel manipulators

A cable-driven parallel manipulator is a manipulator whose end-effector is driven by a number of parallel cables instead of rigid links. Since cables always have more flexibility than rigid links, a cable manipulator bears a concern of possible vibration. Thus, investigation of vibration of cable manipulators caused by cable flexibility is important for applications requiring high system stiffness or bandwidth. This paper provides a vibration analysis of general 6-DOF cable-driven parallel manipulators. Based on the analysis of the natural frequencies of the multibody system, the study demonstrates that a cable manipulator can be designed stiff enough for special applications like the cable-manipulator based hardware-in-the-loop simulation of contact dynamics. Moreover, under an excitation, a cable may vibrate not only in its axial direction, but also in its transversal direction. The paper also analyzes the vibration of cable manipulators caused by cable flexibilities in both axial and transversal directions. It is shown that the vibration of a cable manipulator due to the transversal vibration of cables can be ignored comparing to that due to the axial flexibility of cables.     

Dynamic modeling and design optimization of a 3-DOF spherical parallel manipulator

This paper deals with the dynamic modeling and design optimization of a three Degree-of-Freedom spherical parallel manipulator. Using the method of Lagrange multipliers, the equations of motion of the manipulator are derived by considering its motion characteristics, namely, all the components rotating about the center of rotation. Using the derived dynamic model, a multiobjective optimization problem is formulated to optimize the structural and geometric parameters of the spherical parallel manipulator. The proposed approach is illustrated with the design optimization of an unlimited-roll spherical parallel manipulator with a main objective to minimize the mechanism mass in order to enhance both kinematic and dynamic performances.