Forward analysis of some special Stewart platforms

Selfridge, R. G.; Matthew, G. K.

doi:10.1002/1097-4563(200010)17:10<517::aid-rob1>3.0.co;2-e

Cited by 12 publications

(4 citation statements)

References 7 publications

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“…Analytical approaches have been largely devoted to find all the solutions on basis of a simplified structure to reduce the nonlinearity of the loop closure equations, and hence, they are always not universal and may be practically infeasible. 15,16 Some numerical methods, 17–23 which rely on the numerical continuation method, exhaustive search algorithms, interval analysis, or neural network optimization, have also been proposed for the most general case. However, these methods usually cannot be used for forward kinematics in real time as they involve heavy computation.…”

Section: Introductionmentioning

confidence: 99%

An algorithm for real-time forward kinematics of 6-degree-of-freedom parallel mechanisms

Gao

Yang

Zheng

et al. 2017

Proceedings of the Institution of Mechanical Engineers, Part I:

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This article proposes a forward kinematics algorithm based on closed-loop feedback solution for real-time pose estimation of 6-degree-of-freedom parallel mechanisms. First, a feedback forward kinematics algorithm with second-order error dynamics built in joint space is presented and its convergence is analyzed. Taking a Stewart platform as an example, fast convergence and high solving accuracy of the algorithm are shown in simulation. However, while applying the algorithm to forward kinematics of a 6-degree-of-freedom redundantly actuated parallel mechanisms, solving errors will be growing slowly and non-convergent, which is caused by redundancy character of the parallel mechanisms. Then a modified algorithm, of which second-order error dynamics is built in Cartesian space, is developed. Considering velocity information is usually difficult to measure or estimate accurately in reality, the performance of feedback forward kinematics algorithm without joint velocity feedforward is also evaluated. Finally, the algorithm is implemented into real-time degree of freedom control of the redundant parallel mechanisms which is calibrated by a coordinate measuring machine. Experiment results show that the proposed algorithm can solve the pose with relatively high accuracy under static conditions and is effective and feasible for real-time pose estimation of parallel mechanisms.

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Section: Introductionmentioning

confidence: 99%

An algorithm for real-time forward kinematics of 6-degree-of-freedom parallel mechanisms

Gao

Yang

Zheng

et al. 2017

Proceedings of the Institution of Mechanical Engineers, Part I:

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show abstract

“…Recently, most researchers have investigated the forward position problem, and several methods have been proposed [7−9]. Since the number of real solutions is not known, many of these studies are established on the basis of a simplified structure to reduce the nonlinearity of the loop closure equations, such that an analytical approach can be performed to obtain the complete solution set [10]. However, due to manufacturing errors and technology limitations, the simplified or idealized structures may be practically infeasible.…”

Section: Introductionmentioning

confidence: 99%

Forward kinematics analysis of parallel manipulator using modified global Newton-Raphson method

Yang

Zheng

Jin

et al. 2010

J. Cent. South Univ. Technol.

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In order to obtain direct solutions of parallel manipulator without divergence in real time, a modified global Newton-Raphson (MGNR) algorithm was proposed for forward kinematics analysis of six-degree-of-freedom (DOF) parallel manipulator. Based on geometrical frame of parallel manipulator, the highly nonlinear equations of kinematics were derived using analytical approach. The MGNR algorithm was developed for the nonlinear equations based on Tailor expansion and Newton-Raphson iteration. The procedure of MGNR algorithm was programmed in Matlab/Simulink and compiled to a real-time computer with Microsoft visual studio .NET for implementation. The performance of the MGNR algorithms for 6-DOF parallel manipulator was analyzed and confirmed. Applying the MGNR algorithm, the real generalized pose of moving platform is solved by using the set of given positions of actuators. The theoretical analysis and numerical results indicate that the presented method can achieve the numerical convergent solution in less than 1 ms with high accuracy (1×10 −9 m in linear motion and 1×10 −9 rad in angular motion), even the initial guess value is far from the root.

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“…Parallel manipulators are a strong current research topic, as seen in the recent literature: work has been presented concerning generation of and forward pose solution for analytic parallel manipulators (Kong and Gosselin, 2001), parallel manipulator dynamics (Perreira, 1999), modular platform manipulators (Zhiming and Zhenqun, 1999), singularity determination in spatial platform manipulators (Hao and McCarthy, 1998), parallel manipulator application to inertial measurement unit calibration (Hall and Williams, 2000), and symbolic closed-form forward pose kinematics for special-geometry platform manipulators (Selfridge and Matthew, 2000). A Dutch company has implemented an automated robotic cell featuring a parallel robot for manufacturing propellers (Kochan, 1998).…”

Section: Introductionmentioning

confidence: 99%

Kinematics, design and control of the 6‐PSU platform

Hopkins

Williams

2002

Industrial Robot: An International Journal

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The Department of Mechanical Engineering at Ohio University has designed, constructed, and controlled a new 6‐dof in‐parallel‐actuated platform, a combination and modification of existing designs. The 6‐PSU platform consists of six legs with a prismatic joint, spherical joint, and universal joint connecting links in each leg which move the platform in the six Cartesian freedoms with respect to the base. The prismatic joint is actuated while the other two joints in each leg are passive. The six prismatic joints move vertically with respect to the base, which appears to be a big improvement over the standard Gough/Stewart platform. Experimental results from the Ohio University manipulator are presented.

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Forward analysis of some special Stewart platforms

Cited by 12 publications

References 7 publications

An algorithm for real-time forward kinematics of 6-degree-of-freedom parallel mechanisms

An algorithm for real-time forward kinematics of 6-degree-of-freedom parallel mechanisms

Forward kinematics analysis of parallel manipulator using modified global Newton-Raphson method

Kinematics, design and control of the 6‐PSU platform

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