Solution of forward kinematics in Stewart platform using six rotary sensors on joints of three legs

Mahmoodi, A.; Sayadi, Amir; Menhaj, Mohammad Bagher

doi:10.1080/01691864.2013.854455

Cited by 11 publications

(6 citation statements)

References 10 publications

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“…Choosing any two from the above three equations, we can eliminate variable z and obtain two equations with variables x and y. Subtracting equation ( 22) from equation (23) and equation (22) from equation (24), the following two equations are obtained, which eliminated variable z, and we get the following equations in variables x and y…”

Section: Polynomial Solutions For the Fpksmentioning

confidence: 99%

“…Subtracting equation (22) from equation (23) and equation (22) from equation (24), the following two equations are obtained, which eliminated variable z, and we get the following equations in variables x and y…”

Section: Polynomial Solutions For the Fpksmentioning

confidence: 99%

“…The numerical methods [18][19][20][21][22][23][24] were introduced to overcome this problem, such as Newton-Raphson method, continuation methods, neural networks, genetic algorithms, interval analysis, and alternative approach. Although numerical methods are accurate and can provide unique solution to the forward kinematics problem, the main challenge such as Newton-Raphson method is difficult to ascertain the number of iterations and to select the initial estimation of the task space, while some of these approaches rely on powerful computer hardware.…”

Section: Introductionmentioning

confidence: 99%

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Forward kinematics solutions of a special six-degree-of-freedom parallel manipulator with three limbs

Gao

Pan

et al. 2015

Advances in Mechanical Engineering

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This article presents a special 6-degree-of freedom parallel manipulator, and the mechanical structure of this robot has been introduced; with this structure, the kinematic constrain equations are decoupled. Based on this character, the polynomial solutions of the forward kinematics problem are also presented. In this method, the closed-loop kinematic chain of the manipulator is divided into two parts, the solution forward position kinematics is obtained by a first-degree polynomial equation first, and then an eighth-degree polynomial equation in a single variable for the forward orientation kinematics is obtained. Based on those solutions, the configurations of the robot, including position and orientation of the end-effector, are graphically displayed. A numerical simulation is given to verify the algorithm, and the result implies that for a given set of input values, the manipulator can be assembled in eight different configurations at most. And a set of experiments illustrate the motion ability for forward kinematics of the prototype of this manipulator.

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Section: Polynomial Solutions For the Fpksmentioning

confidence: 99%

Section: Polynomial Solutions For the Fpksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Forward kinematics solutions of a special six-degree-of-freedom parallel manipulator with three limbs

Gao

Pan

et al. 2015

Advances in Mechanical Engineering

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“…• Employing extra sensors In this approach, researchers pay the cost of more complex hardware to provide more information. It enables them to calculate the current position of the platform faster [1,13]. • Artificial intelligence These methods, which have been increasingly used especially in the last decade, may be employed within the concepts of neural networks, [23,33], genetic algorithm, [20,25], and machine learning [18,34].…”

Section: Introductionmentioning

confidence: 99%

Screw theory-based mobility analysis and projection-based kinematic modeling of a 3-CRRR parallel manipulator

Nazari

Hasani

Beedel

2018

J Braz. Soc. Mech. Sci. Eng.

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Forward kinematics analysis of parallel manipulators requires solving highly complicated nonlinear equations, which deriving a closed-form solution is often a real challenge. Being used in closed loop position control of mechanisms, the forward kinematics solution of parallel manipulators is of great importance. Here, we investigate the mobility, forward kinematics, and inverse kinematics of a previously introduced three-degree-of-freedom spatial parallel manipulator from a new perspective. The manipulator is a 3-CRRR parallel mechanism proposed for object manipulation tasks. The mobility of the mechanism is, first, discussed using screw theory, showing that the robot has only three translational degrees of freedom. Next, the forward kinematics of the robot is analyzed based on a geometric approach. Using this method, which is the main novelty of our article, the spatial representation of the manipulator is transformed to a simpler planar representation by a projection-based interpretation, to reduce the complexity of kinematic equations. Afterward, the position of the end-effector is extracted by some algebraic expressions written based on geometrical properties of the robot. Then, the inverse kinematics of the mechanism is analyzed through the same approach. Finally, the kinematic modeling is verified using numerical and analytical methods. The results show that the obtained kinematic model has high accuracy.

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“…The obtained simulation results show that the proposed algorithm can achieve a superior real-time performance compared with other reported algorithms. Mahmoodi et al 13 proposed a novel method for real-time FKP solution of the SGP using six measurements on three legs joints consisting of the rotations of three legs in two directions. After the application of the method on a laboratory sample SGP, it is observed that while the method has reasonable accuracy, it is simpler in implementation, more practical, less expensive, and easier in maintenance in comparison with the conventional method that uses the length measurements of all six legs.…”

Section: Introductionmentioning

confidence: 99%

ADAMS-MATLAB co-simulation for kinematics, dynamics, and control of the Stewart–Gough platform

Sosa-Méndez

Lugo-González

Arias-Montiel

et al. 2017

International Journal of Advanced Robotic Systems

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The mechanical structure known as Stewart-Gough platform is the most representative parallel robot with a wide variety of applications in many areas. Despite the intensive study on the kinematics, dynamics, and control of the Stewart-Gough platform, many details about these topics are still a challenging problem. In this work, the use of automatic dynamic analysis of multibody systems software for the kinematic and dynamic analysis of the Stewart-Gough platform is proposed. Moreover, a co-simulation automatic dynamic analysis of multibody systems (ADAMS)-MATLAB is developed for motion control of the Stewart-Gough platform end-effector. This computational approach allows the numerical solution for the kinematics, dynamics, and motion control of the Stewart-Gough platform and a considerable reduction on the analytical and programming effort. The obtained results in the three topics (kinematics, dynamics, and control) are validated by comparing them with analytical results reported in the literature. This kind of computational approach allows for the creation of virtual prototypes and saves time and resources in the development of Stewart-Gough platform-based robots applications.

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Solution of forward kinematics in Stewart platform using six rotary sensors on joints of three legs

Cited by 11 publications

References 10 publications

Forward kinematics solutions of a special six-degree-of-freedom parallel manipulator with three limbs

Forward kinematics solutions of a special six-degree-of-freedom parallel manipulator with three limbs

Screw theory-based mobility analysis and projection-based kinematic modeling of a 3-CRRR parallel manipulator

ADAMS-MATLAB co-simulation for kinematics, dynamics, and control of the Stewart–Gough platform

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