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

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.

Forward Kinematic Analysis of Kinematically Redundant Hybrid Parallel Robots

2020 ◽  
Vol 12 (6) ◽  
Author(s):  
Kefei Wen ◽  
Clément M. Gosselin
Keyword(s):  
Real Time ◽  
Unique Solution ◽  
Kinematic Analysis ◽  
Parallel Robots ◽  
Degree Of Freedom ◽  
Real Time Control ◽  
The Real ◽  
Time Control ◽  
Forward Kinematic Problem ◽  
Forward Kinematic

Abstract This paper focuses on the forward kinematic analysis of (6 + 3)-degree-of-freedom kinematically redundant hybrid parallel robots. Because all of the singularities are avoidable, the robot can cover a very large orientational workspace. The control of the robot requires the solution of the direct kinematic problem using the actuator encoder data as inputs. Seven different approaches of solving the forward kinematic problem based on different numbers of extra encoders are developed. It is revealed that five of these methods can produce a unique solution analytically or numerically. An example is given to validate the feasibility of these approaches. One of the provided approaches is applied to the real-time control of a prototype of the robot. It is also revealed that the proposed approaches can be applied to other kinematically redundant hybrid parallel robots proposed by the authors.

Solving 3-6 Parallel Robots by Dixon Resultant

2012 ◽  
Vol 235 ◽  
pp. 158-163 ◽  
Author(s):  
Wei Kun Sun
Keyword(s):  
Original System ◽  
Parallel Robot ◽  
Stewart Platform ◽  
Parallel Robots ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
System Equations ◽  
Forward Kinematic Problem ◽  
Forward Kinematic ◽  
Necessary And Sufficient

In this paper, we investigated the forward kinematic problem of the 3-6 parallel robots (Stewart platform) via a symbolic computation tool called Dixon resultant. 3-6 parallel robot is a variation of the classic 6-6 Stewart platform. First we constructed the system equations of 3-6 parallel robots with a certain coordinate system, and then gave the necessary and sufficient condition for the existence of roots of this system by resultant. With the expression of resultant, we could find the solution of the original system and determined the position of mobile platform. We also discussed how to deal with the extraneous roots.

Unified Kinematic Analysis of General Planar Parallel Manipulators

2004 ◽  
Vol 126 (5) ◽  
pp. 866-874 ◽  
Author(s):  
M. J. D. Hayes ◽  
P. J. Zsombor-Murray ◽  
C. Chen
Keyword(s):  
Parallel Manipulators ◽  
Inverse Kinematic ◽  
Parallel Robots ◽  
Kinematic Mapping ◽  
Forward Kinematic Problem ◽  
Forward Kinematic ◽  
Three Degree Of Freedom ◽  
Generalized Constraint ◽  
First Time ◽  
Planar Parallel Manipulators

A kinematic mapping of planar displacements is used to derive generalized constraint equations having the form of ruled quadric surfaces in the image space. The forward kinematic problem for all three-legged, three-degree-of-freedom planar parallel manipulators thus reduces to determining the points of intersection of three of these constraint surfaces, one corresponding to each leg. The inverse kinematic solutions, though trivial, are implicit in the formulation of the constraint surface equations. Herein the forward kinematic solutions of planar parallel robots with arbitrary, mixed leg architecture are exposed completely, and in a unified way, for the first time.

scholarly journals A stable proportional–proportional integral tracking controller with self-organizing fuzzy-tuned gains for parallel robots

2019 ◽  
Vol 16 (1) ◽  
pp. 172988141881995
Author(s):  
Francisco G Salas ◽  
Jorge Orrante-Sakanassi ◽  
Raymundo Juarez-del-Toro ◽  
Ricardo P Parada
Keyword(s):  
Stability Analysis ◽  
Performance Index ◽  
Closed Loop ◽  
Tracking Error ◽  
Parallel Robots ◽  
Control Loop ◽  
Closed Loop System ◽  
Proportional Integral ◽  
The Stability ◽  
Self Organizing

Parallel robots are nowadays used in many high-precision tasks. The dynamics of parallel robots is naturally more complex than the dynamics of serial robots, due to their kinematic structure composed by closed chains. In addition, their current high-precision applications demand the innovation of more effective and robust motion controllers. This has motivated researchers to propose novel and more robust controllers that can perform the motion control tasks of these manipulators. In this article, a two-loop proportional–proportional integral controller for trajectory tracking control of parallel robots is proposed. In the proposed scheme, the gains of the proportional integral control loop are constant, while the gains of the proportional control loop are online tuned by a novel self-organizing fuzzy algorithm. This algorithm generates a performance index of the overall controller based on the past and the current tracking error. Such a performance index is then used to modify some parameters of fuzzy membership functions, which are part of a fuzzy inference engine. This fuzzy engine receives, in turn, the tracking error as input and produces an increment (positive or negative) to the current gain. The stability analysis of the closed-loop system of the proposed controller applied to the model of a parallel manipulator is carried on, which results in the uniform ultimate boundedness of the solutions of the closed-loop system. Moreover, the stability analysis developed for proportional–proportional integral variable gains schemes is valid not only when using a self-organizing fuzzy algorithm for gain-tuning but also with other gain-tuning algorithms, only providing that the produced gains meet the criterion for boundedness of the solutions. Furthermore, the superior performance of the proposed controller is validated by numerical simulations of its application to the model of a planar three-degree-of-freedom parallel robot. The results of numerical simulations of a proportional integral derivative controller and a fuzzy-tuned proportional derivative controller applied to the model of the robot are also obtained for comparison purposes.

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.

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.

A Real Time Solution to the Forward Kinematic Problem of a General Spherical Three-Degree-of-Freedom Parallel Manipulator

1995 ◽  
Author(s):  
Roger Boudreau
Keyword(s):  
Real Time ◽  
Parallel Manipulator ◽  
Computation Time ◽  
Degree Of Freedom ◽  
Learning Networks ◽  
Time Solution ◽  
Forward Kinematic Problem ◽  
Time Required ◽  
Forward Kinematic ◽  
Three Degree Of Freedom

Abstract In this paper, a real time solution to the forward kinematic problem of a general spherical three-degree-of-freedom parallel manipulator is presented using polynomial learning networks. These networks learn the forward kinematic problem based on a database of input-output examples. After the learning process has been achieved, the networks exhibit very little error when presented with inputs which were not part of the learning database. The computation time required to compute the forward kinematics is very small since the networks consist only of additions and multiplications.

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