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

2011 ◽  
Vol 46 (7) ◽  
pp. 945-959 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Clément Gosselin ◽  
Manfred Husty ◽  
Dominic R. Walter
Keyword(s):  
Parallel Mechanisms ◽  
Forward Kinematic Problem ◽  
Forward Kinematic

A General Methodology for the Forward Kinematic Problem of Symmetrical Parallel Mechanisms and Application to 5-PRUR Parallel Mechanisms (3T2R)

2010 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Manfred Husty ◽  
Cle´ment Gosselin
Keyword(s):  
Dimensional Space ◽  
Large Set ◽  
Parallel Mechanisms ◽  
General Methodology ◽  
Higher Dimensional ◽  
Kinematic Mapping ◽  
Rigid Body Displacement ◽  
Forward Kinematic Problem ◽  
Dimensional Projective Space ◽  
Forward Kinematic

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.

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

2011 ◽  
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.

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

Robotica ◽  
2017 ◽  
Vol 35 (12) ◽  
pp. 2257-2277 ◽  
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.

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.

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.

On the Stability of the Quadruple Solutions of the Forward Kinematic Problem in Analytic Parallel Robots

2016 ◽  
Vol 86 (3-4) ◽  
pp. 381-396 ◽  
Author(s):  
Adrián Peidró ◽  
Arturo Gil ◽  
José María Marín ◽  
Luis Payá ◽  
Óscar Reinoso
Keyword(s):  
Parallel Robots ◽  
The Stability ◽  
Forward Kinematic Problem ◽  
Forward Kinematic

scholarly journals On the Design of Mobile Parallel Robots for Large Workspace Applications

2011 ◽  
Author(s):  
Hai Yang ◽  
Se´bastien Krut ◽  
Franc¸ois Pierrot ◽  
Ce´dric Baradat
Keyword(s):  
Parallel Robots ◽  
Legged Robots ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
Design Constraints ◽  
And Performance ◽  
Forward Kinematic

In this paper, several considerations for designing industry oriented robots which combine the mobility of legged robots and advantages of parallel mechanisms are outlined. For designing such optimized robots in terms of simplicity and performance, a topology study is done based on the mobility analysis. Applying some design constraints, potential topologies of such robots are identified. One architecture is chosen for designing a tripod robot. Both inverse and forward kinematic problems of this robot are derived in order to simulate its gait motion. The analysis and simulations show that: integrating some clamping devices and some lockable passive joints, six actuators are enough to build a legged manipulator which can not only perform 6-axis machining but can also walk on a curved supporting media.

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