Optimum design of 3-RRR planar parallel manipulators

2010 ◽  
Vol 224 (2) ◽  
pp. 411-418 ◽  
Author(s):  
Runliang Dou
Keyword(s):  
Optimum Design ◽  
Design Space ◽  
Jacobian Matrix ◽  
Kinematic Model ◽  
Parallel Manipulators ◽  
Stiffness Index ◽  
Geometrical Parameters ◽  
Dimensional Parameter ◽  
Planar Parallel Manipulators

This article deals with the optimum design of 3-RRR planar parallel manipulators. Based on the kinematic model and Jacobian matrix, the global conditioning index, global velocity index and global stiffness index of 3-RRR parallel manipulators are investigated. The corresponding atlases are represented graphically in the established design space, and the geometrical parameters without dimension are determined. An example is presented to achieve the optimum dimensional parameter based on the optimum non-dimensional result. The result of this article is not only useful for the development of 3-RRR planar parallel manipulators, but also helpful for the optimum design of other parallel manipulators.

Optimum design of a 4-PSS-PU redundant parallel manipulator based on kinematics and dynamics

2015 ◽  
Vol 230 (13) ◽  
pp. 2273-2284 ◽  
Author(s):  
Liping Wang ◽  
Binbin Zhang ◽  
Jun Wu
Keyword(s):  
Optimum Design ◽  
Parallel Manipulator ◽  
Design Space ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Search Method ◽  
Kinematics And Dynamics ◽  
Performance Indices ◽  
Maximum Acceleration ◽  
High Acceleration

This paper presents an optimum design of a 4-PSS-PU redundant parallel manipulator by taking the workspace, conditioning performance, and acceleration into account. On the basis of rank of the Jacobian matrix, a method to directly find out the workspace is presented, rather than the search method. Based on the dynamic model, a maximum acceleration index is defined. The corresponding atlases of these performance indices are represented graphically in the established design space. Based on these atlases, the optimum design is performed and the optimum region is determined. It is expected to realize the high acceleration of parallel manipulators by using the optimum method.

Optimum Design of a 3-RRR Planar Parallel Manipulator with a Singularity-Free Workspace

2011 ◽  
Vol 86 ◽  
pp. 606-610 ◽  
Author(s):  
Ming Wang Gao ◽  
Xian Min Zhang ◽  
Zhi Wei Wu
Keyword(s):  
Parallel Manipulator ◽  
Design Space ◽  
Parallel Manipulators ◽  
Design Strategy ◽  
Geometrical Parameters ◽  
Kinematic Parameters ◽  
Planar Parallel Manipulator ◽  
Singular Loci ◽  
Reliable Design ◽  
Planar Parallel Manipulators

In this paper, a reliable design strategy, capable of optimally picking out the geometrical parameters of the 3-RRR planar parallel manipulators, is presented. The distribution charts for singular loci and usable workspace shape are obtained in the non-dimensional design space. Based on the singularity-free workspace and good force transition capacity, the optimum kinematic parameters are determined by means of the global conditioning index. An example shows that the strategy is useful for realizing the singularity-free workspace optimally.

A geometric approach for singularity analysis of 3-DOF planar parallel manipulators using Grassmann–Cayley algebra

Robotica ◽  
2015 ◽  
Vol 35 (3) ◽  
pp. 511-520 ◽  
Author(s):  
Kefei Wen ◽  
TaeWon Seo ◽  
Jeh Won Lee
Keyword(s):  
Jacobian Matrix ◽  
Screw Theory ◽  
Geometric Approach ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Singular Configurations ◽  
Cayley Algebra ◽  
Grassmann Cayley Algebra ◽  
Planar Parallel Manipulators

SUMMARYSingular configurations of parallel manipulators (PMs) are special poses in which the manipulators cannot maintain their inherent infinite rigidity. These configurations are very important because they prevent the manipulator from being controlled properly, or the manipulator could be damaged. A geometric approach is introduced to identify singular conditions of planar parallel manipulators (PPMs) in this paper. The approach is based on screw theory, Grassmann–Cayley Algebra (GCA), and the static Jacobian matrix. The static Jacobian can be obtained more easily than the kinematic ones in PPMs. The Jacobian is expressed and analyzed by the join and meet operations of GCA. The singular configurations can be divided into three classes. This approach is applied to ten types of common PPMs consisting of three identical legs with one actuated joint and two passive joints.

Statics, Instantaneous Kinematics and Singularity Analysis of Planar Parallel Manipulators via Grassmann-Cayley Algebra

2014 ◽  
Vol 532 ◽  
pp. 378-381 ◽  
Author(s):  
Ke Fei Wen ◽  
Jeh Won Lee
Keyword(s):  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
New Approach ◽  
Coordinate Method ◽  
Cayley Algebra ◽  
Symbolic Formula ◽  
Grassmann Cayley Algebra ◽  
Planar Parallel Manipulators

The wrench Jacobian matrix plays an important role in statics and singularity analysis of planar parallel manipulators (PPMs). It is easy to obtain this matrix based on plücker coordinate method. In this paper, a new approach is proposed to the analysis of the forward and inverse wrench Jacobian matrix used by Grassmann-Cayley algebra (GCA). A symbolic formula for the inverse statics and a coordinate free formula for the singularity analysis are obtained based on this Jacobian. As an example, this approach is implemented for the 3-RPR PPMs.

Comparative Kinematic Analysis and Design Optimization of Redundant and Nonredundant Planar Parallel Manipulators Intended for Haptic Use

Robotica ◽  
2019 ◽  
Vol 38 (8) ◽  
pp. 1463-1477 ◽  
Author(s):  
Houssem Saafi ◽  
Houssein Lamine
Keyword(s):  
Design Optimization ◽  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Kinematic Model ◽  
Parallel Manipulators ◽  
Geometric Parameters ◽  
Analysis And Design ◽  
Planar Parallel Manipulator ◽  
Forward Kinematic ◽  
Planar Parallel Manipulators

SUMMARYThis paper investigates a comparative kinematic analysis between nonredundant and redundant 2-Degree Of Freedom parallel manipulators. The nonredundant manipulator is based on the Five-Bar mechanism, and the redundant one is a 3-RRR planar parallel manipulator. This study is aimed to select the best structure for a haptic application. This latter requires a mechanism with a desired workspace of 10 cm × 10 cm and an admissible force of 5 N in all directions. The analysis criteria are the accuracy of the forward kinematic model and the required actuator torques. Thereby, the geometric parameters of the two structures are optimized in order to satisfy the required workspace such that parallel singularities are overcome. The analysis showed that the nonredundant optimally designed manipulator is more suitable for the haptic application.

Sensitivity Analysis of Planar Parallel Manipulators

2008 ◽  
Author(s):  
Ste´phane Caro ◽  
Nicolas Binaud ◽  
Philippe Wenger
Keyword(s):  
Sensitivity Analysis ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Geometric Parameters ◽  
Sensitivity Coefficients ◽  
Planar Parallel Manipulator ◽  
Moving Platform ◽  
Conditioning Number ◽  
Planar Parallel Manipulators

This paper deals with the sensitivity analysis of planar parallel manipulators. A methodology is introduced to derive the sensitivity coefficients by means of the study of 3-RPR manipulators. As a matter of fact, the sensitivity coefficients of the pose of its moving platform to variations in the geometric parameters are expressed algebraically, the variations being defined both in Polar and Cartesian coordinates. The dexterity of the manipulator is also studied by means of the conditioning number of its normalized kinematic Jacobian matrix. As an illustrative example, the sensitivity of a symmetrical planar parallel manipulator is analyzed in detail. Finally, the accuracy of the manipulator is compared with its dexterity.

MOTION RECOVERY AFTER JOINT FAILURE IN PARALLEL MANIPULATORS

2011 ◽  
Vol 35 (4) ◽  
pp. 559-571 ◽  
Author(s):  
Leila Notash
Keyword(s):  
Failure Modes ◽  
Jacobian Matrix ◽  
Null Space ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Partial Recovery ◽  
Joint Failure ◽  
Motion Recovery ◽  
Motion Performance ◽  
Planar Parallel Manipulators

In this paper, the failure of parallel manipulators is investigated. Failure modes of parallel manipulators and their causes and effects from the kinematics point of view are discussed. Methodologies for investigating the effect of failures, due to joint failure or singularity, on the motion performance of manipulators are presented, and the criteria for full and partial recovery from these failures are established. The proposed methodologies are based on the projection of the lost motion onto the orthogonal complement of the null space of the Jacobian matrix after failure. The procedure is simulated for planar parallel manipulators to examine if after joint failure the required motion of manipulator could be fully recovered; as well as to calculate the corrections to the motion of remaining joints for recovering the lost motion.

Synthesis of planar parallel manipulators including dexterity, force transmission and stiffness index

2019 ◽  
Vol 47 (6) ◽  
pp. 680-702 ◽  
Author(s):  
Héctor Fabio Quintero-Riaza ◽  
Luz Adriana Mejía-Calderón ◽  
Miguel Díaz-Rodríguez
Keyword(s):  
Parallel Manipulators ◽  
Stiffness Index ◽  
Force Transmission ◽  
Planar Parallel Manipulators

scholarly journals Performance Analysis and Optimum Design of a Redundant Planar Parallel Manipulator

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 908 ◽  
Author(s):  
Xiaoyong Wu
Keyword(s):  
Optimum Design ◽  
Parallel Manipulator ◽  
Optical Design ◽  
Kinematic Model ◽  
Parallel Manipulators ◽  
Performance Comparison ◽  
Design Parameters ◽  
Redundant Manipulator ◽  
Symmetrical Structure ◽  
Planar Parallel Manipulator

This work presents a comprehensive performance evaluation and optimum design of a novel symmetrical 4-PPR (P indicates the prismatic joint, R denotes the revolute joint, and the letter with underline represents an active joint) redundant planar parallel manipulator. The kinematic model is established, upon which the inverse position and singularity are analyzed. Based on the evaluation of dexterity, velocity, and stiffness performance, the optimum region is achieved. With the optical design parameters, a case study for the analysis of dynamic behavior is conducted. Performance comparison between the redundant manipulator and another two non-redundant 3-PPR planar parallel manipulators, one with a Δ-shape symmetrical structure and the other with U-shape symmetrical structure, is presented. Simulation results reveal that the U-shape manipulator has the greatest velocity performance. Moreover, the redundant manipulator possesses the best dexterity, stiffness, and dynamic performance.

scholarly journals Workspace Analysis and Optimal Design of 3-PRR Planar Parallel Manipulators

2020 ◽  
Author(s):  
Shivakumar M.R. ◽  
R. Srikri ◽  
R. Sr ◽  
Sree Sailesh ◽  
Manoj Kumar Reddy ◽  
...  
Keyword(s):  
Optimal Design ◽  
Design Procedure ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Closed Form Expression ◽  
Geometrical Parameters ◽  
Geometrical Approach ◽  
Workspace Analysis ◽  
Planar Parallel Manipulators

Abstract In the optimum design of parallel manipulators, workspace of the manipulator is of greater importance. The shape and area of the workspace are the main parameters under this. In this paper, a new geometrical approach is presented to determine the shape and size of the constant orientation workspace for the 3-PRR planar parallel manipulators. All possibilities of shapes of workspaces are determined with variation of different parameters. For each shape of workspace corresponding geometrical conditions are also put forth. Closed from area expression of workspace is derived by geometrical approach for each shape. Such closed form expression of area is not possible with non-dimensional approach. This becomes extremely useful during optimal design procedure. A look-up table is also presented seeing which the designer can choose geometrical conditions between different parameters which will ensure a void free workspace. A case study is presented wherein a user gives his required workspace area and an algorithm is presented which gives all possible combinations of geometrical parameters satisfying the workspace area requirement. Then based on various considerations including singularity analysis an optimal parallel manipulator is offered for the task which does not have any void within the workspace having least/nil singularities.

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