Forward kinematic problem and constant orientation workspace of 5-RP̲RRR (3T2R) parallel mechanisms

In this paper, a general methodology is introduced in order to formulate the FKP of symmetrical parallel mechanisms in a 7-dimensional projective space by the means of the so-called Study’s parameters. The main objective is to consider rigid-body displacement, and consequently the FKP, based on algebraic geometry, rather than rely on classical recipes, such as Euler angles, to assist in problem-solving. The state of the art presented in this paper is general and can be extended to other types of symmetrical mechanisms. In this paper, we limit the concept of kinematic mapping to topologically symmetrical mechanisms, i.e., mechanisms with limbs having identical kinematic arrangement. Exploring the FKP in a higher dimensional space is more challenging since it requires the use of a larger number of coordinates. There are, however, advantages in adopting a large set of coordinates, since this approach leads to expressions with lower degree that do not involve trigonometric functions.

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Forward kinematic problem of 5-RPUR parallel mechanisms (3T2R) with identical limb structures

Mechanism and Machine Theory ◽

10.1016/j.mechmachtheory.2011.02.005 ◽

2011 ◽

Vol 46 (7) ◽

pp. 945-959 ◽

Cited By ~ 30

Author(s):

Mehdi Tale Masouleh ◽

Clément Gosselin ◽

Manfred Husty ◽

Dominic R. Walter

Keyword(s):

Parallel Mechanisms ◽

Forward Kinematic Problem ◽

Forward Kinematic

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Solving the Forward Kinematic Problem of 4-DOF Parallel Mechanisms (3T1R) With Identical Limb Structures and Revolute Actuators Using the Linear Implicitization Algorithm

Volume 6: 35th Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2011-47884 ◽

2011 ◽

Cited By ~ 2

Author(s):

Mehdi Tale Masouleh ◽

Dominic R. Walter ◽

Manfred Husty ◽

Cle´ment Gosselin

Keyword(s):

Linear Equations ◽

Linear Constraint ◽

Mathematical Framework ◽

Parallel Mechanisms ◽

Novel Approach ◽

Kinematic Space ◽

Forward Kinematic Problem ◽

Rotation Motion ◽

Forward Kinematic ◽

General Architecture

This paper investigates the forward kinematic problem of 4-DOF parallel mechanisms with revolute actuators and identical limb structures and performing a three translations and one rotation motion pattern. The general architecture of all the mechanisms under study in this paper originates from the type synthesis performed for 4-DOF parallel mechanisms with identical limb structures. The mathematical framework used in this paper is based on algebraic geometry where the forward kinematics and constraint expressions are explored in a seven-dimensional kinematic space by means of the so-called Study parameters (dual quaternions). In this paper, the algorithm applied for obtaining the forward kinematic and constraint expressions is based on a recent and novel approach, called linear implicitization algorithm, which is based on solving systematically a system of linear equations to determine the coefficients of the non-linear constraint equations. This paper presents also an example of a 4-DOF parallel mechanism.

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An Optimization-Based Algorithm for Determination of Inclusive and Constant Orientation Workspace of Parallel Mechanisms

Volume 10: Mechanical Systems and Control, Parts A and B ◽

10.1115/imece2009-11148 ◽

2009 ◽

Author(s):

Gholamreza Vossoughi ◽

Soroosh Hassanpour ◽

Amir Fazeli ◽

Mehdi Paak

Keyword(s):

Optimization Technique ◽

Optimization Methods ◽

Optimization Approach ◽

Parallel Mechanisms ◽

End Effector ◽

Boundary Determination ◽

Spatial Parallel Mechanism ◽

Forward Kinematic ◽

Orientation Workspace

Workspace of a mechanism is generally defined as the region of space which end-effector of that mechanism can reach. Determination of workspace is an important task in the design of a mechanism. However, for parallel mechanisms, due to the complexity of solving the forward kinematic equations, determination of workspace is much more complicated than for serial mechanisms. In the literature, time-consuming numerical methods, such as point-by-point searching, are usually employed for this purpose. In this paper, an optimization-based algorithm is introduced for the boundary determination of inclusive and constant orientation workspaces of parallel mechanisms. In the proposed algorithm, thanks to applying the optimization approach along with point-by-point searching, the dimension of the point-by-point searched space (and hence, the consumed time) are significantly reduced. While different optimization methods can be used in the proposed algorithm, Particle Swarm Optimization is utilized as the optimization technique in this paper. The proposed algorithm is illustrated through its application to a planar and a spatial parallel mechanism.

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Forward Kinematic Problem of 5-PRUR Parallel Mechanisms Using Study Parameters

Advances in Robot Kinematics: Motion in Man and Machine ◽

10.1007/978-90-481-9262-5_23 ◽

2010 ◽

pp. 211-221 ◽

Cited By ~ 7

Author(s):

Mehdi Tale Masouleh ◽

Manfred Husty ◽

Clèment Gosselin

Keyword(s):

Parallel Mechanisms ◽

Forward Kinematic Problem ◽

Forward Kinematic

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Kinematic effects of number of legs in 6-DOF UPS parallel mechanisms

Robotica ◽

10.1017/s0263574716000862 ◽

2017 ◽

Vol 35 (12) ◽

pp. 2257-2277 ◽

Cited By ~ 4

Author(s):

Mohammad H. Abedinnasab ◽

Farzam Farahmand ◽

Bahram Tarvirdizadeh ◽

Hassan Zohoor ◽

Jaime Gallardo-Alvarado

Keyword(s):

Parallel Manipulators ◽

Optimum Number ◽

Parallel Mechanisms ◽

Performance Indices ◽

Singular Configurations ◽

Redundantly Actuated ◽

Forward Kinematic Problem ◽

Kinematic Measures ◽

Forward Kinematic ◽

Legged Mechanism

SUMMARYIn this paper, we study the kinematic effects of number of legs in 6-DOF UPS parallel manipulators. A group of 3-, 4-, and 6-legged mechanisms are evaluated in terms of the kinematic performance indices, workspace, singular configurations, and forward kinematic solutions. Results show that the optimum number of legs varies due to priorities in kinematic measures in different applications. The non-symmetric Wide-Open mechanism enjoys the largest workspace, while the well-known Gough–Stewart (3–3) platform retains the highest dexterity. Especially, the redundantly actuated 4-legged mechanism has several important advantages over its non-redundant counterparts and different architectures of Gough–Stewart platform. It has dramatically less singular configurations, a higher manipulability, and at the same time less sensitivity. It is also shown that the forward kinematic problem has 40, 16, and 1 solution(s), respectively for the 6-, 3-, and the 4-legged mechanisms. Superior capabilities of the 4-legged mechanism make it a perfect candidate to be used in more challenging 6-DOF applications in assembly, manufacturing, biomedical, and space technologies.

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

Robotica ◽

10.1017/s0263574715000259 ◽

2015 ◽

Vol 34 (11) ◽

pp. 2610-2628 ◽

Cited By ~ 1

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.

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Analyses of Error and Precision of 6-DOF Platform

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.591-593.2081 ◽

2012 ◽

Vol 591-593 ◽

pp. 2081-2086 ◽

Cited By ~ 1

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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A 6-DOF Ship-Borne Antenna Platform With Large Orientation Workspace

Volume 6B: Ocean Engineering ◽

10.1115/omae2020-18024 ◽

2020 ◽

Author(s):

Yuhang He ◽

Weijia Li ◽

Yaozhong Wu ◽

Jinbo Wu ◽

Zhiyuan Cheng

Keyword(s):

Particle Swarm Optimization ◽

Particle Swarm ◽

Weight Ratio ◽

Stewart Platform ◽

Design Parameters ◽

Parallel Mechanisms ◽

Swarm Optimization ◽

Pitch Range ◽

Orientation Workspace ◽

Load Weight

Abstract Compared with traditional antenna platform with two axes, Stewart platform can search airspace with no tracking blind district. And the advantages of high accuracy, high stiffness and high load-weight ratio also make it be a better solution for antenna platforms. This paper designed a 6-DOF ship-borne antenna platform based on the Stewart platform to overcome the difficulties that to realize a large orientation workspace (azimuth range is from 0° to 360°, pitch range is from 0° to 100°) under the compact dimensions of parallel mechanisms. A novel joint structure has been proposed which can provide a larger rotation angle than common Hooke joints to realize the large orientation workspace without the inter-mechanism interference. In addition, this paper defined the concept of working height and working radius then proposed a trajectory based on that to obtain the complete pose (translation and orientation) of antenna platform by azimuth and pitch angles. After that, the particle swarm optimization algorithm is employed to seek the optimal geometrical design parameters. A prototype of the 6-DOF ship-borne antenna platform adopted the particle swarm optimization results has been constructed. And the results show that it not noly meets the design requirements, but also provides a good performance.

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