Optimization of the Singularity Locus of a Novel Kinematically Redundant Spherical Parallel Manipulator

2017 ◽  
Author(s):  
Jérôme Landuré ◽  
Clément Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Parallel Robot ◽  
Point Of View ◽  
Design Parameters ◽  
Redundant Robot ◽  
Jacobian Matrices ◽  
Geometric Point ◽  
Singularity Locus ◽  
Spherical Parallel Manipulator

This article introduces a new architecture of spherical parallel robot which significantly extends the workspace when compared to existing architectures. To this end, the singularity locus is studied and the design parameters are chosen so as to confine the singularities to areas already limited by other constraints such as mechanical interferences. First, the architecture of the spherical redundant robot is presented and the Jacobian matrices are derived. Afterwards, the analysis of the singularities is addressed from a geometric point of view, which yields a description of the singularity locus expressed as a function of the architectural parameters. Then, the results are applied to an example set of architectural parameters chosen in order to illustrate the advantages of the redundant architecture over current designs in terms of workspace.

Kinematic Analysis of a Novel Kinematically Redundant Spherical Parallel Manipulator

2018 ◽  
Vol 10 (2) ◽  
Author(s):  
Jérôme Landuré ◽  
Clément Gosselin
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Parallel Robot ◽  
Point Of View ◽  
Design Parameters ◽  
Redundant Robot ◽  
Jacobian Matrices ◽  
Geometric Point ◽  
Singularity Locus ◽  
Spherical Parallel Manipulator

This paper introduces a new architecture of spherical parallel robot which significantly extends the workspace when compared to existing architectures. To this end, the singularity locus is studied and the design parameters are chosen so as to confine the singularities to areas already limited by other constraints such as mechanical interferences. First, the architecture of the spherical redundant robot is presented and the Jacobian matrices are derived. Afterwards, the analysis of the singularities is addressed from a geometric point of view, which yields a description of the singularity locus expressed as a function of the architectural parameters. Then, the results are applied to an example set of architectural parameters, which are chosen in order to illustrate the advantages of the redundant architecture over current designs in terms of workspace.

A new family of spherical parallel manipulators

Robotica ◽  
2002 ◽  
Vol 20 (4) ◽  
pp. 353-358 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
End Effector ◽  
Singular Configurations ◽  
New Family ◽  
Geometric Conditions ◽  
Singularity Locus ◽  
The Given ◽  
Spherical Parallel Manipulator ◽  
Spherical Motion

In the literature, 3-RRPRR architectures were proposed to obtain pure translation manipulators. Moreover, the geometric conditions, which 3-RRPRR architectures must match, in order to make the end-effector (platform) perform infinitesimal (elementary) spherical motion were enunciated. The ability to perform elementary spherical motion is a necessary but not sufficient condition to conclude that the platform is bound to accomplish finite spherical motion, i.e. that the mechanism is a spherical parallel manipulator (parallel wrist). This paper demonstrates that the 3-RRPRR architectures matching the geometric conditions for elementary spherical motion make the platform accomplish finite spherical motion, i.e. they are parallel wrists (3-RRPRR wrist), provided that some singular configurations, named translation singularities, are not reached. Moreover, it shows that 3-RRPRR wrists belong to a family of parallel wrists which share the same analytic expression of the constraints which the legs impose on the platform. Finally, the condition that identifies all the translation singularities of the mechanisms of this family is found and geometrically interpreted. The result of this analysis is that the translation singularity locus can be represented by a surface (singularity surface) in the configuration space of the mechanism. Singularity surfaces drawn by exploiting the given condition are useful tools in designing these wrists.

scholarly journals Kinematic Analysis Of Tricept Parallel Manipulator

2012 ◽  
Vol 12 (5) ◽  
Author(s):  
Mir Amin Hosseini ◽  
Hamid-Reza Mohammadi Daniali
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Geometric Constraints ◽  
Design Parameters ◽  
Forward Kinematics ◽  
Jacobian Matrices ◽  
Moving Platforms ◽  
Workspace Optimization

Parallel manipulators consist of fixed and moving platforms connected to each other with some actuated links. They have some significant advantages over their serial counterparts. While, they suffer from relatively small workspaces, complex kinematics relations and highly singular points within their workspaces. In this paper, forward kinematics of Tricept parallel manipulator is solved analytically and its workspace optimization is performed. This parallel manipulator has a complex degree of freedom, therefore leads to dimensional in-homogeneous Jacobian matrices. Thus, we divide some entries of the Jacobian by units of length, thereby producing a new Jacobian that is dimensionally homogeneous. Moreover, its workspace is parameterized using some design parameters. Then, using GA method, the workspace is optimized subjects to some geometric constraints. Finally, dexterity of the design is evaluated. Keywords- Kinematic, Workspace, Singularity, TriceptABSTRAK - Manipulator selari terdiri daripada platform tetap dan bergerak yang bersambung antara satu sama lain dengan beberapa pautan bergerak. Manipulator selari mempunyai beberapa kebaikan tertentu dibandingkan dengan yang bersamaan dengannya. Walaupun ia mempunyai ruang kerja yang sempit, hubungan kinematik kompleks dan titik tunggal tinggi dalam linkungan ruang kerjanya. Dalam kajian ini, kinematik ke hadapan manipulator selari Tricept diselesaikan secara analisa dan pengoptimuman ruang kerja dijalankan. Manipulator selari ini mempunyai darjah kebebasan yang kompleks, yang menyebabkan ia mendorong kepada kehomogenan dimensi matriks Jacobian. Catatan Jacobian dibahagikan kepada unit panjang, dimana ia menghasilkan Jacobian baru yang homogen dimensinya. Tambahan, ruang kerjanya diparameterkan dengan menggunakan beberapa parameter reka bentuk. Kemudian, dengan kaedah GA, ruang kerja mengoptimakan subjek kepada beberapa kekangan geometrik. Akhirnya, kecakatan reka bentuk dinilaikan.Keywords- Kinematic, Workspace, Singularity, Tricept

scholarly journals Influence of design parameters on the singularities and workspace of a 3-RPS parallel robot

2018 ◽  
Vol 42 (1) ◽  
pp. 30-37 ◽  
Author(s):  
Ranjan Jha ◽  
Damien Chablat ◽  
Luc Baron
Keyword(s):  
Design Parameter ◽  
Parallel Manipulator ◽  
Decomposition Method ◽  
Parallel Robot ◽  
Joint Space ◽  
Mobile Platform ◽  
Design Parameters ◽  
Cylindrical Algebraic Decomposition ◽  
Parasitic Motion

This paper presents variations in the workspace, singularities, and joint space with respect to design parameter k, which is the ratio of the dimensions of the mobile platform to the dimensions of the base of a 3-RPS parallel manipulator. The influence of the design parameters on parasitic motion, which is important when selecting a manipulator for a desired task, is also studied. The cylindrical algebraic decomposition method and Gröbner-based computations are used to model the workspace and joint space with parallel singularities in 2R1T (two rotational and one translational) and 3T (three translational) projection spaces, where the orientation of the mobile platform is represented using quaternions. These computations are useful in selecting the optimum value for the design parameter k such that the parasitic motions can be limited to specific values. Three designs of the 3-RPS parallel robot, based on different values of k, are analyzed.

Evaluation of the Position Error of Four Non-Overconstrained Spherical Parallel Manipulators

2012 ◽  
Vol 162 ◽  
pp. 194-203
Author(s):  
A. Chaker ◽  
A. Mlika ◽  
M.A. Laribi ◽  
L. Romdhane ◽  
S. Zeghloul
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Position Error ◽  
Point Of View ◽  
Good Precision ◽  
End Effector ◽  
High Rigidity ◽  
Manufacturing Errors ◽  
Position And Orientation ◽  
Spherical Parallel Manipulator

The 3-RRR spherical parallel manipulator is known to be highly overconstrained, which causes several problems of mounting the mechanism, but has the advantage of having high rigidity thus a good precision. Several works in the literature proposed non-overconstrained versions of this mechanism. However, very few works dealt with the problem of the consequence of modifying an overconstrained mechanism into a non-overconstrained one, mainly from an accuracy point of view. In this work, we present an analysis of the accuracy of four different non-overconstrained SPMs, i.e., 3-RSR, 3-RCC, 3-RRS, and 3-RUU. These four SPM are then evaluated in translational and rotational accuracy due to manufacturing errors. The error on the position and orientation of the end-effector, due to manufacturing errors, are computed in 100 different configurations within their workspace. These SPMs are then compared among each other and we showed that the 3-RRS has the best compromise between the translational and rotational accuracy.

Designing a Translational Parallel Manipulator Based on the 3SS Kinematic Joint

2019 ◽  
Vol 11 (5) ◽  
Author(s):  
Erik Macho ◽  
Mónica Urízar ◽  
Víctor Petuya ◽  
Alfonso Hernández
Keyword(s):  
Condition Number ◽  
Parallel Manipulator ◽  
Modular Design ◽  
Parallel Manipulators ◽  
Industrial Applications ◽  
Point Of View ◽  
Pick And Place ◽  
Prismatic Joints ◽  
Singularity Locus ◽  
Kinematic Joint

Abstract Nowadays, translational parallel manipulators are widely used in industrial applications related to pick and place tasks. In this paper, a new architecture of a translational parallel manipulator without floating prismatic joints and without redundant constraints is presented, which leads to a robust design from the manufacturing and maintenance point of view. The frame configuration has been chosen with the aim of achieving the widest and most regular operational workspace completely free of singularities. Besides, the position equations of the proposed design are obtained in a closed form, as well as the singularity locus. It will be shown that the proposed design owns a very simple kinematics so that the related equations can be efficiently implemented in the control of the robot. In addition, the Jacobian condition number assessment shows that a wide part of the operational workspace is well-conditioned, and also the existence of an isotropic configuration will be proved. Finally, a prototype has been built by following a modular design approach.

scholarly journals Social spider optimization algorithm for tuning parameters in PD-like Interval Type-2 Fuzzy Logic Controller applied to a parallel robot

2021 ◽  
Vol 54 (3-4) ◽  
pp. 303-323
Author(s):  
Amjad J Humaidi ◽  
Huda T Najem ◽  
Ayad Q Al-Dujaili ◽  
Daniel A Pereira ◽  
Ibraheem Kasim Ibraheem ◽  
...  
Keyword(s):  
Fuzzy Logic ◽  
Trajectory Tracking ◽  
Fuzzy Logic Controller ◽  
Optimization Technique ◽  
Parallel Robot ◽  
Design Parameters ◽  
Social Spider ◽  
Social Spider Optimization ◽  
Interval Type

This paper presents control design based on an Interval Type-2 Fuzzy Logic (IT2FL) for the trajectory tracking of 3-RRR (3-Revolute-Revolute-Revolute) planar parallel robot. The design of Type-1 Fuzzy Logic Controller (T1FLC) is also considered for the purpose of comparison with the IT2FLC in terms of robustness and trajectory tracking characteristics. The scaling factors in the output and input of T1FL and IT2FL controllers play a vital role in improving the performance of the closed-loop system. However, using trial-and-error procedure for tuning these design parameters is exhaustive and hence an optimization technique is applied to achieve their optimal values and to reach an improved performance. In this study, Social Spider Optimization (SSO) algorithm is proposed as a useful tool to tune the parameters of proportional-derivative (PD) versions of both IT2FLC and T1FLC. Two scenarios, based on two square desired trajectories (with and without disturbance), have been tested to evaluate the tracking performance and robustness characteristics of proposed controllers. The effectiveness of controllers have been verified via numerical simulations based on MATLAB/SIMULINK programming software, which showed the superior of IT2FLC in terms of robustness and tracking errors.

Task-based torque minimization of a 3-PṞR spherical parallel manipulator

Robotica ◽  
2021 ◽  
pp. 1-30
Author(s):  
Soheil Zarkandi
Keyword(s):  
Closed Form ◽  
Dynamic Modeling ◽  
Dynamic Equation ◽  
Parallel Manipulator ◽  
Optimization Problem ◽  
Dynamic Constraints ◽  
Part C ◽  
Euler Approach ◽  
Three Degree Of Freedom ◽  
Spherical Parallel Manipulator

Abstract A comprehensive dynamic modeling and actuator torque minimization of a new symmetrical three-degree-of-freedom (3-DOF) 3-PṞR spherical parallel manipulator (SPM) is presented. Three actuating systems, each of which composed of an electromotor, a gearbox and a double Rzeppa-type driveshaft, produce input torques of the manipulator. Kinematics of the 3-PṞR SPM was recently studied by the author (Zarkandi, Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 2020, https://doi.org/10.1177%2F0954406220938806). In this paper, a closed-form dynamic equation of the manipulator is derived with the Newton–Euler approach. Then, an optimization problem with kinematic and dynamic constraints is presented to minimize torques of the actuators for implementing a given task. The results are also verified by the SimMechanics model of the manipulator.

Optimal design of a redundant spherical parallel manipulator

Robotica ◽  
1997 ◽  
Vol 15 (4) ◽  
pp. 399-405 ◽  
Author(s):  
Sylvie Leguay-Durand ◽  
Claude Reboulet
Keyword(s):  
Optimal Design ◽  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Structure Optimization ◽  
Kinematic Design ◽  
Spherical Wrist ◽  
Redundant Structure ◽  
Spherical Parallel Manipulator

A new kinematic design of a parallel spherical wrist with actuator redundancy is presented. A special feature of this parallel manipulator is the arrangement of co-axial actuators which allows unlimited rotation about any axis inside a cone-shaped workspace. A detailed kinematic analysis has shown that actuator redundancy not only removes singularities but also increases workspace while improving dexterity. The structure optimization has been performed with a global dexterity criterion. Using a conditioning measure, a comparison with a non-redundant structure of the same type was performed and shows that a significant improvement in dexterity has been obtained.

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