Forward Kinematics Solution Distribution and Analytic Singularity-Free Workspace of Linear-Actuated Symmetrical Spherical Parallel Manipulators

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Dongming Gan ◽  
Jian S. Dai ◽  
Jorge Dias ◽  
Lakmal Seneviratne
Keyword(s):  
Coordinate System ◽  
Optimization Design ◽  
Parallel Manipulators ◽  
Geometric Constraints ◽  
Forward Kinematics ◽  
Kinematics Model ◽  
Analytic Singularity ◽  
Dynamics And Control ◽  
Rotation Motion ◽  
Forward Kinematic

This paper presents a new kinematics model for linear-actuated symmetrical spherical parallel manipulators (LASSPMs) which are commonly used considering their symmetrical kinematics and dynamics properties. The model has significant advantages in solving the forward kinematic equations, and in analytically obtaining singularity loci and the singularity-free workspace. The Cayley formula, including the three Rodriguez–Hamilton parameters from a general rotation matrix, is provided and used in describing the rotation motion and geometric constraints of LASSPMs. Analytical solutions of the forward kinematic equations are obtained. Then singularity loci are derived, and represented in a new coordinate system with the three Rodriguez–Hamilton parameters assigned in three perpendicular directions. Limb-actuation singularity loci are illustrated and forward kinematics (FK) solution distribution in the singularity-free zones is discussed. Based on this analysis, unique forward kinematic solutions of LASSPMs can be determined. By using Cayley formula, analytical workspace boundaries are expressed, based on a given mechanism structure and input actuation limits. The singularity-free workspace is demonstrated in the proposed coordinate system. The work gives a systematic method in modeling kinematics, singularity and workspace analysis which provides new optimization design index and a simpler kinematics model for dynamics and control of LASSPMs.

A Novel Parallel Mechanism With 3-RRUR Legs

2007 ◽  
Author(s):  
Yanwen Li ◽  
Yueyue Zhang ◽  
Lumin Wang ◽  
Zhen Huang
Keyword(s):  
Machine Tools ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Symmetrical Structure ◽  
Forward Kinematic ◽  
Accumulated Error

This paper investigates a novel 4-DOF 3-RRUR parallel manipulator, the number and the characteristics of its degrees of freedom are determined firstly, the rational input plan and the invert and forward kinematic solutions are carried out then. The corresponding numeral example of the forward kinematics is given. This type of parallel manipulators has a symmetrical structure, less accumulated error, and can be used to construct virtual-axis machine tools. The analysis in this paper will play an important role in promoting the application of such manipulators.

Forward Kinematics of Nonpolyhedral Parallel Manipulators

1993 ◽  
Vol 115 (4) ◽  
pp. 938-940 ◽  
Author(s):  
Jean-Pierre Merlet
Keyword(s):  
Symmetry Axis ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Forward Kinematic

Forward kinematics has been studied for polyhedral parallel manipulators. We present here an algorithm for the forward kinematic of nonpolyhedral manipulators the plates of which have a symmetry axis. We show that there will be at most 352 possible solutions and exhibit a configuration with eight solutions.

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

Forward Kinematics of 3-GPR Planar Parallel Manipulators With Circular Rolling Contact Joints

2003 ◽  
Author(s):  
Curtis L. Collins
Keyword(s):  
Relative Motion ◽  
Parallel Manipulators ◽  
Solution Procedure ◽  
Rolling Contact ◽  
Degree Of Freedom ◽  
Forward Kinematics ◽  
Prismatic Joint ◽  
Forward Kinematic ◽  
Planar Parallel Manipulators ◽  
Circular Contact

In this work, we investigate the geometry and position kinematics of planar parallel manipulators composed of three GPR serial sub-chains, where G denotes a rolling contact, or geared joint, P denotes a prismatic joint, and R denotes a revolute joint. The rolling contact joints provide a passive one degree-of-freedom relative motion between the base and the prismatic links. It is shown, both theoretically and numerically, that when all the G-joints have equal circular contact profiles, there are at most 48 real forward kinematic solutions when the P joints are actuated. The solution procedure is general and can be used to predict and solve for the kinematics solutions of 3-GPR manipulators with any combination of rational contact ratios.

Performing Nonsingular Transitions Between Assembly Modes in Analytic Parallel Manipulators by Enclosing Quadruple Solutions

2015 ◽  
Vol 137 (12) ◽  
Author(s):  
Adrián Peidró ◽  
José María Marín ◽  
Arturo Gil ◽  
Óscar Reinoso
Keyword(s):  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Joint Space ◽  
Parallel Robots ◽  
Forward Kinematics ◽  
Characteristic Polynomials ◽  
Forward Kinematic ◽  
Three Degrees Of Freedom

This paper analyzes the multiplicity of the solutions to forward kinematics of two classes of analytic robots: 2RPR-PR robots with a passive leg and 3-RPR robots with nonsimilar flat platform and base. Since their characteristic polynomials cannot have more than two valid roots, one may think that triple solutions, and hence nonsingular transitions between different assembly modes, are impossible for them. However, the authors show that the forward kinematic problems of these robots always admit quadruple solutions and obtain analytically the loci of points of the joint space where these solutions occur. Then, it is shown that performing trajectories in the joint space that enclose these points can produce nonsingular transitions, demonstrating that it is possible to design simple analytic parallel robots with two and three degrees-of-freedom (DOF) and the ability to execute these transitions.

New Resolution Scheme of the Forward Kinematics of Parallel Manipulators Using Extra Sensors

1996 ◽  
Vol 118 (2) ◽  
pp. 214-219 ◽  
Author(s):  
Kilryong Han ◽  
Wankyun Chung ◽  
Y. Youm
Keyword(s):  
Closed Form ◽  
Real Time ◽  
Parallel Manipulators ◽  
Stewart Platform ◽  
Forward Kinematics ◽  
Numerical Examples ◽  
Resolution Scheme ◽  
Real Time Applications ◽  
Forward Kinematic Problem ◽  
Forward Kinematic

This paper presents a new closed-form resolution scheme of the forward kinematics of parallel manipulators based on two concepts, local structurization and mechanism partition. This scheme is applied to 6-DOF Stewart platform manipulators and the effectiveness of this scheme is verified through numerical examples. It is shown that one extra sensor is sufficient for both 3-3 SPM and 6-3 SPM to exactly resolve the forward kinematic problem (FKP) in closed form and two sensors for 6-6 SPM. In previous research, at least three extra sensors were needed for closed-form resolution of the FKP for 6-6 SPM. Consequently, the new resolution scheme is efficient to implement and easy for real-time applications for the control of parallel manipulators.

Unified Kinematics Analysis and Analytic Singularity-Free Workspace of a Metamorphic Parallel Mechanism With Controllable Rotation Center

2014 ◽  
Author(s):  
Dongming Gan ◽  
Jian S. Dai ◽  
Jorge Dias ◽  
Lakmal D. Seneviratne
Keyword(s):  
Coordinate System ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Central Line ◽  
Kinematics Analysis ◽  
Base Plane ◽  
Analytic Singularity ◽  
Rotation Center ◽  
Pure Rotation ◽  
Rotation Motion

This paper presents a metamorphic parallel mechanism with controllable rotation center in its pure rotation topology. Based on reconfiguration of a reconfigurable Hooke (rT) joint, the rotational center of the mechanism can be altered along the central line perpendicular to the base plane. A unified Dixon resultant based method is proposed to solve the forward kinematics analytically by covering all configurations with variable rotation centers while the rotation motion is expressed using Cayley formula. Then singularity loci are derived and represented in a new coordinate system with the three Rodrigues-Hamilton parameters assigned in three perpendicular directions. Limb-actuation singularity loci are also obtained from row vectors of the Jacobian matrix. By using Cayley formula, analytical workspace boundaries are expressed by including the mechanism structure parameters and input actuation limits. Finally, singularity-free workspace of configurations with variable rotation centers is demonstrated in the proposed coordinate system.

A three translational DoFs parallel cube-manipulator

Robotica ◽  
2003 ◽  
Vol 21 (6) ◽  
pp. 645-653 ◽  
Author(s):  
Xin-Jun Liu ◽  
Jay il Jeong ◽  
Jongwon Kim
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Cartesian Coordinate System ◽  
Micro Motion ◽  
Moving Platform ◽  
Delta Robot ◽  
Cartesian Coordinate

This paper concerns the presentation and analysis of a type of three translational degrees of freedom (DoFs) parallel cube-manipulator. The parallel manipulators are the topology architectures of the DELTA robot and Tsai's manipulator, respectively, which have three translational DoFs. In the design, the three actuators are arranged according to the Cartesian coordinate system, which means that the actuating directions are normal to each other, and the joints connecting to the moving platform are located on three sides of a cube, for such reason we call this type of manipulator the parallel cube-manipulator. The kinematics problems, singularity, workspace, compliance characteristic of the manipulator are investigated in the paper. The analysis results show that the manipulators have the advantages of no singularities in the workspace, relatively more simple forward kinematics, and existence of a compliance center. The parallel cube-manipulator can be applied to the fields of micro-motion manipulators, remote center compliance (RCC) devices, assembly, and so on.

Solving kinematics and stiffness of a novel n(2-UPS/PS+RPS) spatial hyper-redundant manipulator

Robotica ◽  
2015 ◽  
Vol 34 (10) ◽  
pp. 2386-2399 ◽  
Author(s):  
Bo Hu ◽  
Yin Wang ◽  
Jingjing Yu ◽  
Yi Lu
Keyword(s):  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Spherical Joint ◽  
Redundant Manipulator ◽  
Universal Joint ◽  
Revolute Joint ◽  
Kinematics Model ◽  
Prismatic Joint ◽  
In Series ◽  
Close Form

SUMMARYA novel n(2-UPS/PS+RPS) spatial hyper-redundant manipulator (SHRM) formed by an optional number of 2-UPS/PS+RPS(2-universal joint-prismatic joint-spherical joint/prismatic joint-spherical joint+revolute joint-prismatic joint-spherical joint) parallel manipulators(PMs) connected in series is proposed and analyzed in this paper. First, the forward kinematics of the 2-UPS/PS+RPS PM is derived in close form. By extending this result to the whole SHRM, the forward kinematics model of the n(2-UPS/PS+RPS) SHRM is established. Second, the compact and elegant expressions for solving the forward velocity of the n(2-UPS/PS+RPS) SHRM are derived. Third, the statics and stiffness of the n(2-UPS/PS+RPS) SHRM are analyzed systematically by considering both active forces and constrained forces existed in each 2-UPS/PS+RPS PM. Finally, an analytically solved example is given for a 4(2-UPS/PS+RPS) SHRM formed by four 2-UPS/PS+RPS PMs. The analytical results are verified by CAD software.

Forward Kinematic Modeling of Conical-Shaped Continuum Manipulators

Robotica ◽  
2021 ◽  
pp. 1-19
Author(s):  
A. H. Bouyom Boutchouang ◽  
Achille Melingui ◽  
J. J. B. Mvogo Ahanda ◽  
Othman Lakhal ◽  
Frederic Biya Motto ◽  
...  
Keyword(s):  
Neural Networks ◽  
Data Collection ◽  
Robot Control ◽  
Deep Neural Networks ◽  
Forward Kinematics ◽  
Kinematic Modeling ◽  
Experimental Platform ◽  
Continuum Manipulators ◽  
Forward Kinematic

SUMMARY Forward kinematics is essential in robot control. Its resolution remains a challenge for continuum manipulators because of their inherent flexibility. Learning-based approaches allow obtaining accurate models. However, they suffer from the explosion of the learning database that wears down the manipulator during data collection. This paper proposes an approach that combines the model and learning-based approaches. The learning database is derived from analytical equations to prevent the robot from operating for long periods. The database obtained is handled using Deep Neural Networks (DNNs). The Compact Bionic Handling robot serves as an experimental platform. The comparison with existing approaches gives satisfaction.

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