Transactions of the Canadian Society for Mechanical Engineering

Volume 33 (2009), Issue 4

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In this article, the workspace of planar wire-actuated parallel manipulators is studied. The investigation is based on two methods: an analytical method which formulates the workspace envelope by means of Cramer’s rule pertaining to the Jacobian matrix and the null space method from static analysis of manipulator. The workspace envelope method is extended to analyzing redundant planar manipulators and planar manipulators with an external wrench or gravity modelled as an additional wire. It is discussed that the null space method gives a more realistic workspace formulation as it takes into account wire tension limits, while the workspace generated by the workspace envelope method assumes very large wire tensions are possible. The workspace envelope method plots an analytical function as the border of the workspace so a much higher resolution representation of the wrench closure workspace is possible.

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Redundant manipulators have potential advantages of using their degree(s) of redundancy to satisfy additional task(s). To achieve desirable performance criteria, various optimization techniques can be applied to redundant manipulators. In the work presented, the redundancy resolution of planar wire-actuated parallel manipulators is investigated at the kinematic and dynamic levels in order to perform desirable tasks while maintaining positive tensions in the wires. Local optimization routines are used in the simulations in order to minimize the norm of actuator forces/torques or to minimize the norm of the mobile platform velocity, subject to positive tension in the wires. This paper presents techniques to alter wire tensions, mobile platform trajectory, mobile platform velocity, and length rate of wires, in order to maintain positive wire tensions. The effectiveness of the presented approaches is studied through simulations of an example planar wire-actuated manipulator. The presented approaches can be utilized in the design of controllers, trajectory planning, and dynamic workspace analysis.

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A unified approach for the description of multibody systems is presented, relying on a rotationless formulation for rigid bodies. The set of differential algebraic equations governing the motion of multibody dynamics does not only beneficially offer the design of energy-momentum schemes but it also bears the advantage to be extended by vital modeling features. In this spirit we present within this paper the modeling of friction phenomena such as joint friction and the incorporation of control constraints. Both features rely on a specific augmentation technique which introduces rotational degrees of freedom into the rotationless formulation. An example of a partially controlled movement of a free floating parallel platform with joint friction will demonstrate the performance of the newly developed energy-momentum consistent scheme.

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A novel architecture of planar closed-loop cable-driven parallel mechanism is introduced in this paper. In this architecture, instead of being wound on spools, the cables form closed loops attached to the end-effector and whose motion is controlled by sliders. By eliminating the spools, it is expected that the new mechanisms will lead to a better accuracy than conventional cable-driven parallel mechanisms. This paper presents the inverse kinematics, the Jacobian matrices and the static equilibrium equations for the new architecture. Using the Jacobian matrices, the singularities of the mechanism are also analyzed. Also, based on the static equation, the available wrench set is determined. It is pointed out that the trajectory of the endpoint of a given cable loop is a portion of ellipse. The intersection of the ellipses provides the assembly modes. There can be more than one intersection point of the ellipses at a given position of the sliders. This geometric characteristic is analyzed at the end of the paper.

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This paper presents an obstacle avoidance method for discretely-actuated planar manipulators with a large number of serially connected modules. The method uses a direct combination of the manipulator workspace density functions and obstacle density maps to solve the inverse kinematics of the manipulator, thus avoiding the geometrical modelling of obstacles and the computation of the nearest point distance between the manipulator and the obstacles. Simulations on a seventeen-module planar manipulator operating in a workspace with circular obstacles have demonstrated the viability of the obstacle avoidance algorithm. This paper presents a detailled description of the proposed method and a summary of the results.

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This paper presents an algorithm, based on a geometric approach, to obtain the workspace of a parallel manipulator. For several steps in the process, a short review of different methods is presented, along with the presentation of the preferred algorithm. This work was performed in the context of the design of a robot for human-robot collaboration, which is also presented as an example.

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This paper explores the pose selection for the kinematic calibration of the constraining linkage of a 4 degrees of freedom parallel manipulator. The aim is to select a set of poses out of a larger pool of possible poses which improve the calibration accuracy. Five different criteria have been suggested in the literature and are investigated in this article. The results show that the pose selection criteria did not significantly improve the calibration of this parallel manipulator. There was very little difference between applying the criteria and not applying it and some of the results using the criteria were worse than not using any criteria.

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Cet article présente une méthode rapide et efficace d’optimisation de l’architecture d’un mécanisme entraîné par câbles, qui permet d’en maximiser l’espace atteignable et de minimiser les risques d’interférences. La contribution principale de ces travaux est la détermination de l’architecture optimale d’un mécanisme à câble servant de plate-forme de génération de mouvement pour un nouveau concept de simulateur de vol. La méthode d’optimisation utilise un algorithme génétique multicritériel qui permet également de dégager quelques règles générales de design des mécanismes à câbles.

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In this work, the dexterous workspace of a general geometry 3-PRRR kinematically redundant planar parallel manipulator with six actuated joints, three of which are redundant, is determined. The 3-PRRR manipulator is an adaptation of the 3-RRR manipulator with a redundant prismatic actuator added to each leg. Obtaining the dexterous workspace by discretizing a large area around the manipulator and determining if each point is in the workspace is relatively simple though computationally inefficient. This work proposes a geometrical method to determine the dexterous workspace of a 3-PRRR planar parallel manipulator. With this method, an exact solution of the workspace boundaries is obtained. The geometrical method uses the four-bar mechanism analogy to determine the dexterous workspace. Though the method is applied to a 3-PRRR planar manipulator, it can be readily applied to any n-PRRR planar manipulator, where n is the number of chains.

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For translational parallel manipulators (TPMs), topology synthesis methods that can be found in the literature are mainly based on screw theory, instantaneous kinematics, or group theory. In this work, finite displacement equations are used for the topology synthesis of TPM. Serial chains with less than 6 degrees of freedom (DOF) are first investigated and, topological conditions for them to generate 3D translations while its end-effector (EE) is under a constant orientation constraint are derived. Then the parallel manipulators (PM) composed of these serial chains are analyzed to find out whether and under what conditions the EE will keep a constant orientation throughout a finite workspace.

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This work focuses on the geometric synthesis of planar 3-RPR parallel mechanisms in order to guarantee a singularity-free workspace for a desired orientation range. The effects of the orientation angle, the minimal leg length as well as the base shape on the singularity-free workspace are analyzed using the Gauss divergence theorem. The results show that for every orientation angle, there exists an optimal minimal leg length which leads to the maximal singularity-free workspace. If the optimal minimal leg lengths are used, the equilateral triangle base yields the maximal singularity-free workspace for any orientation angle. However, for a prescribed working range of the orientation angle, the optimal minimal leg length may be different from the individual optimal minimal leg lengths. Based on the optimal minimal leg length determined for a prescribed working range of the orientation angle, a geometric synthesis procedure is proposed in order to guarantee a singularity-free workspace.

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Un manipulateur est dit isotrope si le produit de sa matrice jacobienne par sa transposée est un multiple de la matrice identité. Dans cet état, le manipulateur démontre des propriétés cinématiques optimales. Dans cet article, nous montrons qu’il existe un manipulateur sériel 6R sphérique dont l’effecteur peut atteindre toutes orientations en état constant d’isotropie. Les articulations 2 et 5 sont fixes, alors que les 4 autres permettent d’atteindre toutes les orientations. À notre connaissance, ce manipulateur est le seul manipulateur sériel sphérique dans la littérature à conserver une configuration isotrope sur tout son espace de travail.

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The development of a path-planning algorithm for the robot-assisted rapid prototyping (RP) of ice structures is reported here. The algorithm, written in Matlab code, first imports a stereolithography (STL) file, which contains the geometry of the part to be built, and a text file containing other configuration parameters. The algorithm then finds intersection contours between evenly-spaced horizontal planes and the part; these contours define the boundaries of the areas to be filled for each layer. Each contour is then grouped with the other contours that define the same area. Subsequently, support structure contours are generated automatically from the part model; a support structure CAD model is not required. Then, part and support areas are filled by iteratively shrinking each outer contour until inner boundaries are reached.

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This paper presents the isotropic conditions for the topological class of H4 parallel manipulators with an articulated traveling plate which has four degrees of freedom. First, a generic kinematic model of this class of manipulators is developed, then we impose isotropic conditions on the Jacobian matrix. From the newly obtained equations, design constraints and a design procedure allowing the determination of all isotropic geometries are obtained. The proposed procedure allows the successive choice and computation of each and all geometrical parameters of an isotropic manipulator of the H4 class.

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The design and implementation of an indoor absolute localization system for a novel threedegree-of-freedom (DOF) omni-directional mobile platform is presented. This localization system is a modification of the Cricket indoor localization system developed at the Massachusetts Institute of Technology (MIT) and is similar to the Global Positioning System (GPS) used in outdoor applications. The designed system has an active mobile architecture with actively transmitting beacons mounted on the mobile platform, and receivers (listeners) fixed at known positions on the ceiling of the operating environment. Position estimates of the mobile beacons, relative to a global coordinate system, are obtained using trilateration; a technique that determines the position of a beacon using distance estimates between the beacon and the fixed listeners. The distance estimates between the beacons and listeners are calculated using the time-of-flight of radio frequency and ultrasonic signals. Testing of the localization system was performed and experimental results are presented. These preliminary results indicate that the modified Cricket system has improved accuracy in distance and position estimation compared to the original system, as well as a higher position update rate when performing tracking of the mobile platform.

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In underwater remote vehicle-manipulator system (URVM) applications, it is beneficial to have the underwater remote vehicle (URV) hold station using its thrusters while a human pilot operates the serial manipulator. This provides a stable platform for the manipulator and eases the pilot’s job drastically when current and/or tether disturbances are present. The contribution of this work is twofold: Firstly, the reduction of dynamic coupling in the URVM systems is realized using two robust control techniques namely Sliding-mode control and H∞ control, and the performance of both controllers in the dynamic coupling reduction problem is reported. Secondly, a new control scheme is proposed that involves both controllers in the control loop. Numerical case studies are developed to demonstrate the effectiveness of the controllers. It is concluded that sliding-mode and H∞ controller combined approach provides superior dynamic coupling reduction performance.

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Kinematic and dynamic models of a human body are presented. The models intend to represent paraplegics wearing a powered exoskeleton. The proposed exoskeleton fully controls the motion of the hip and knee joints, i.e., each lower extremity contains four actuators, three at the hip joint and one at the knee joint. A spring-loaded ankle-foot orthosis completes the exoskeleton. The kinematic model involves a large number of degrees of freedom, 34-DOF. The dynamic model presents a general formulation that can be implemented for any human task – walking, running, jumping, climbing stairs, etc. Traditional dynamic models simplify the motion of bipeds by considering a limited number of movements contained in the sagittal plane and by focusing on a particular task. A 3D model of a human body has been developed to simulate motion.

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There is much research on the poles of the transfer function (between the beam-end displacement and base torque) of slewing single-flexible beams. However, there is no comprehensive report on their zeros. The study on the zeros is of great importance, especially from the controller design perspective, because some of these zeros are in the right-hand-side (RHS) of the domain S in the Laplace transform. These RHS zeros limit the control bandwidth; deteriorate the trade-off between the robustness and the desirable control performance. They also create challenges in the beam-end trajectory-tracking. It is for these reasons that a comprehensive study on the zeros is of valuable significance which for the first time is reported in this paper. It is shown here that the physical parameters of the slewing flexible beamfall into three categories with respect to the locations of the zeros. In the first category, an increase (or decrease) in values of physical parameters move the zeros further from (or closer to) the imaginary axis. The second category is composed of physical parameters where an increase (or decrease) in their values move the zeros closer to (or further from) the imaginary axis. The third category includes the physical parameters where the locations of the zeros are independent of their values.