Sensitivity Analysis of Serial and Parallel Manipulator - A Review (original) (raw)
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Sensitivity comparison of planar parallel manipulators
Mechanism and Machine Theory, 2010
This paper deals with the sensitivity comparison of three Degree-of-Freedom planar parallel manipulators. First, a methodology is described to obtain the sensitivity coefficients of the pose of the moving platform of the manipulators to variations in their geometric parameters and actuated variables. Their sensitivity coefficients are derived and expressed algebraically for a matter of analysis simplicity. Moreover, two aggregate sensitivity
Sensitivity Analysis of 3-RPR Planar Parallel Manipulators
Journal of Mechanical Design, 2009
This paper deals with the sensitivity analysis of 3-RPR planar parallel manipulators (PPMs). First, the sensitivity coefficients of the pose of the manipulator moving platform to variations in the geometric parameters and in the actuated variables are expressed algebraically. Moreover, two aggregate sensitivity indices are determined, one related to the orientation of the manipulator moving platform and another one related to its position. Then, a methodology is proposed to compare 3-RPR PPMs with regard to their dexterity, workspace size and sensitivity. Finally, the sensitivity of a 3-RPR PPM is analyzed in detail and four 3-RPR PPMs are compared as illustrative examples. NOMENCLATURE a i Distance between points O and A i ρ i Distance between points A i and C i c i Distance between points C i and P α i Angle between vectors Ox and OA i β i Angle between vectors C 1 C 2 and PC i θ i Angle between vectors Ox and A i C i 1 hal-00456135, version 1 -
Sensitivity analysis of parallel manipulators using an interval linearization method
Mechanism and Machine Theory, 2014
The subject of this paper is about an interval linearization method for the sensitivity analysis of manipulators to variations in their geometric parameters. First, the proposed method is presented. Then, three manipulators are used as illustrative examples: The five-bar mechanism, the 3-RRR planar parallel manipulator and the Orthoglide. The benefits and restrictions of the proposed method are also discussed and appropriate indices are derived to show the efficiency of the method. The obtained results are also compared with the results obtained with frequently used methods. The proposed method is simple to implement and provides verified results in low computational time and thus can be applied to complex robots such as the Orthoglide. In particular, the standard linearization method computes unreliable results near singularities, whereas the proposed interval linearization method automatically detects such situations.
Sensitivity and Dexterity Comparison of 3-RRR planar parallel manipulators
Computational Kinematics, 2009
This paper deals with the sensitivity comparison of three Degree-of-Freedom planar parallel manipulators. First, a methodology is described to obtain the sensitivity coefficients of the pose of the moving platform of the manipulators to variations in their geometric parameters and actuated variables. Their sensitivity coefficients are derived and expressed algebraically for a matter of analysis simplicity. Moreover, two aggregate sensitivity indices are determined, the first one is related to the orientation of the moving platform of the manipulator and the other one to its position. Then, a methodology is proposed to compare PPMs with regard to their workspace size and sensitivity. Finally, 3-RPR, 3-RPR, 3-RRR, 3-RRR and 3-PRR PPMs are compared in order to highlight the contributions of the paper.
Meccanica, 2011
This paper deals with the sensitivity analysis of 3-RPR planar parallel manipulators. First, the manipulators under study as well as their degeneracy conditions are presented. Then, an optimization problem is formulated in order to obtain their maximal regular dexterous workspace. Moreover, the sensitivity coefficients of the pose of the manipulator moving platform to variations in the geometric parameters and in the actuated variables are expressed algebraically. Two aggregate sensitivity indices are determined, one related to the orientation of the manipulator moving platform and another one related to its position. Then, we compare two non-degenerate and two degenerate 3-RPR planar parallel manipulators with regard to their dexterity, workspace size and sensitivity. Finally, two actuating modes are compared with regard to their sensitivity.
This paper presents the results of a comprehensive study on the efficiency of planar parallel mechanisms, considering their kinetostatic performance and also, their workspace. This aim is approached upon proceeding single-and multi-objective optimization procedures. Kinetostatic performances of ten different planar parallel mechanisms are analyzed by resorting to a recent index, kinematic sensitivity. Moreover, the greatest possible continuous circle in the constant-orientation workspace of the latter mechanisms is considered as another objective for the optimization procedures. Seeking the set of design parameters which compromises simultaneous optimal values for the two aforementioned objectives, i.e., kinematic sensitivity and workspace, necessitates launching a multi-objective optimization process. The mathematical framework adopted for the optimization problem is based on genetic algorithm. The results of multi-objective optimization are based on the sets of Pareto points, offering the most reliable decisions to reconciliate between some conflicting objectives. To this end, the ten planar parallel mechanisms are sorted into two sets based on their type of actuator, some of them with prismatic actuators and the other ones with revolute actuators. Finally, a comparison between performances of these mechanisms, according to the obtained results, is carried out.
Optimum transmission performance of 3-RRR planar parallel manipulators and sensitivity analysis
Journal of Advanced Mechanical Design, Systems, and Manufacturing, 2021
In this paper, a parametric model of 3-RRR planar parallel manipulators (PPMs) is presented, aiming to optimize the overall transmission performance with optimum shapes and sizes of platforms, including the base and the mobile platform. By utilizing the duality of motion and force spaces, an analytical approach is presented through the formalities of linear algebra so as to evaluate transmission performance of planar 3-RRR manipulators, upon which an optimum design is conducted. Moreover, sensitivity analysis is accomplished to reveal the influences of the design parameters on the overall performance of manipulators. With the developed fully parameterized model, optimal configurations of 3-RRR PPMs are studied. In total, six configurations with optimal transmission quality are identified, most of them having mobile platforms of either opened, or folded shape. An optimal design case is finally included to demonstrate further its transmission performance.
On Robust Mechanical Design of a PAR2 Delta-Like Parallel Kinematic Manipulator
Journal of Mechanisms and Robotics, 2021
Sensitivity analysis of manipulators aims at studying the influence of variations in its own geometric parameters on its performance. This information is useful for evaluating the position error of the end-effector as well as for the synthesis of tolerances. Indeed, the synthesis of tolerances is a very important issue in the design and manufacturing of robot manipulators. In this paper, a sequential procedure for modeling, dimensioning, and tolerance synthesis of the Parallel Kinematic Manipulator (PKM) PAR2 is proposed. For optimal dimensional design, an approach based on the optimization of the workspace is proposed, taking into account several constraints, followed by a numerical matrix analysis-based deterministic method for sensitivity analysis whose performance is studied in terms of accuracy. To calculate the optimal dimensional tolerances, a new tolerance synthesis method is used. The effect of geometric tolerance on accuracy is analyzed.
Journal of Mechanical Science and Technology, 2017
In this paper, the kinematic performance of a planar parallel manipulator 3-RPR is investigated. Based on the constraint equations, robot geometric Jacobian matrix is calculated. Since the end-effector of the 3-RPR planar parallel manipulator performs both translational and rotational motions, robot geometric Jacobian matrix is transformed to a homogeneous form. This method defines a new Jacobian that transforms the linear velocities of two points on the end-effector to the actuator velocities. The velocity manipulability index is used for studying the ability of the manipulator to move. The manipulator distance singularity and kinematic accuracy is checked out by using the Local conditioning index (LCI) and Global conditioning index (GCI). The effect of Jacobian matrix homogenization on both the LCI and manipulability index is investigated in detail. Furthermore, the relation between LCI and the manipulability ellipsoids for certain moving platform orientations is studied. The paper is finally concluded by checking out the shapes of the manipulability ellipsoids for different moving platform orientations over the whole workspace.
Geometric analysis of the kinematic sensitivity of planar parallel mechanisms
2011
The kinematic sensitivity is a unit-consistent measure that has been recently proposed as a mechanism performance index to compare robot architectures. This paper presents a robust geometric approach for computing this index for the case of planar parallel mechanisms. The physical meaning of the kinematic sensitivity is investigated through different combinations of the Euclidean and infinity norms and by means of several illustrative examples. Finally, this paper opens some avenues to the dimensional synthesis of parallel mechanisms by exploring the meaning of the global kinematic sensitivity index.