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.

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 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.

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.

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.

Gröbner basis and resultant method for the forward displacement of 3-DoF planar parallel manipulators in seven-dimensional kinematic space

Robotica ◽  
2015 ◽  
Vol 34 (11) ◽  
pp. 2610-2628 ◽  
Author(s):  
Davood Naderi ◽  
Mehdi Tale-Masouleh ◽  
Payam Varshovi-Jaghargh
Keyword(s):  
Euclidean Space ◽  
Gröbner Basis ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Dimensional Euclidean Space ◽  
Grobner Basis ◽  
Kinematic Space ◽  
Forward Kinematic Problem ◽  
Forward Kinematic

SUMMARYIn this paper, the forward kinematic analysis of 3-degree-of-freedom planar parallel robots with identical limb structures is presented. The proposed algorithm is based on Study's kinematic mapping (E. Study, “von den Bewegungen und Umlegungen,” Math. Ann.39, 441–565 (1891)), resultant method, and the Gröbner basis in seven-dimensional kinematic space. The obtained solution in seven-dimensional kinematic space of the forward kinematic problem is mapped into three-dimensional Euclidean space. An alternative solution of the forward kinematic problem is obtained using resultant method in three-dimensional Euclidean space, and the result is compared with the obtained mapping result from seven-dimensional kinematic space. Both approaches lead to the same maximum number of solutions: 2, 6, 6, 6, 2, 2, 2, 6, 2, and 2 for the forward kinematic problem of planar parallel robots; 3-RPR, 3-RPR, 3-RRR, 3-RRR, 3-RRP, 3-RPP, 3-RPP, 3-PRR, 3-PRR, and 3-PRP, respectively.

scholarly journals Forward kinematic analysis of Dobot using closed-loop method

2020 ◽  
Vol 9 (3) ◽  
pp. 153
Author(s):  
Javier Dario Sanjuan De Caro ◽  
Mohammad Rahman ◽  
Ivan Rulik
Keyword(s):  
Analytical Solution ◽  
Kinematic Analysis ◽  
Closed Loop ◽  
Dynamical Model ◽  
Forward Kinematics ◽  
Loop Method ◽  
Serial Robots ◽  
Forward Kinematic

Dobot is a hybrid robot that combines features from parallel and serial robots. Because of this characteristic, the robot excels for is reliability, allowing its implementation in diverse applications. Therefore, researchers have studied its kinematics to improve its capabilities. However, to the extent of our knowledge, no analysis has been reported taking into consideration the closed-loop configuration of Dobot. Thus, this article presents the complete analytical solution for the forward kinematics of Dobot, considering each link. The results are expected to be utilized in the development of a dynamical model that contemplates the dynamics of each element of the robot.

Analyses of Error and Precision of 6-DOF Platform

2012 ◽  
Vol 591-593 ◽  
pp. 2081-2086 ◽  
Author(s):  
Rui Ren ◽  
Chang Chun Ye ◽  
Guo Bin Fan
Keyword(s):  
Inverse Kinematics ◽  
Newton Iteration ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
End Effector ◽  
C Programming Language ◽  
C Programming ◽  
Manufacturing Tolerances ◽  
Parallel Robotics ◽  
Forward Kinematic

A particular subset of 6-DOF parallel mechanisms is known as Stewart platforms (or hexapod). Stewart platform characteristic analyzed in this paper is the effect of small errors within its elements (strut lengths, joint placement) which can be caused by manufacturing tolerances or setting up errors or other even unknown sources to end effector. The biggest kinematics problem is parallel robotics which is the forward kinematics. On the basis of forward kinematic of 6-DOF platform, the algorithm model was built by Newton iteration, several computer programs were written in the MATLAB and Visual C++ programming language. The model is effective and real-time approved by forwards kinematics, inverse kinematics iteration and practical experiment. Analyzing the resource of error, get some related spectra map, top plat position and posture error corresponding every error resource respectively. By researching and comparing the error spectra map, some general results is concluded.

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