Modular Method for Kinematic Analysis of Parallel Manipulators Based on Ordered SOCs

Based on the new viewpoint of structural decomposion that any multi-loop mechanism are made up of by a series of ordered single opened chains(SOCs), a new method for kinematic analysis of parallel manipulators, i.e, the SOCs modular method has been presented in the paper. The new method has the following features: (1) The dimensions of sets of the nonlinear kinematic analysis equations are reduced to the minimum, and the kinematic analysis equation often contains only one unknown variable for most parallel manipulators generally applied now. Accordingly, all the real solutions to forward kinematics problem of parallel mechanisms can be easily obtained by using one-dimension searching algorithm; (2) Compared with algebraic method, it has evidently reduced the difficulty of deducing formulas; (3) Compared with homotopy continuation method, it has higher computing efficiency.

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A Simple Method for Inverse Kinematic Analysis of the General 6R Serial Robot

Volume 2: 30th Annual Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2006-99088 ◽

2006 ◽

Cited By ~ 1

Author(s):

Zhi Xin Shi ◽

Yu Feng Luo ◽

Lu Bing Hang ◽

Ting Li Yang

Keyword(s):

Kinematic Analysis ◽

Inverse Kinematics ◽

Algebraic Method ◽

Inverse Kinematic ◽

New Method ◽

One Dimension ◽

Parallel Mechanisms ◽

Simple Method ◽

Inverse Kinematics Problem ◽

Serial Robot

Because the solution to inverse kinematics problem of the general 5R serial robot is unique and its assembly condition has been derived, a simple effective method for inverse kinematics problem of general 6R serial robot or forward kinematics problem of general 7R single-loop mechanism is presented based on one-dimension searching algorithm. The new method has the following features: (1) Using one-dimension searching algorithm, all the real inverse kinematic solutions are obtained and it has higher computing efficiency; (2) Compared with algebraic method, it has evidently reduced the difficulty of deducing formulas. The principle of the new method can be generalized to kinematic analysis of parallel mechanisms.

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A new development of homotopy continuation method, applied in solving nonlinear kinematic system of equations of parallel mechanisms

2015 3rd RSI International Conference on Robotics and Mechatronics (ICROM) ◽

10.1109/icrom.2015.7367874 ◽

2015 ◽

Cited By ~ 4

Author(s):

Amir Salimi Lafmejani ◽

Ahmad Kalhor ◽

Mehdi Tale Masouleh

Keyword(s):

Continuation Method ◽

Homotopy Continuation ◽

System Of Equations ◽

Parallel Mechanisms ◽

Homotopy Continuation Method ◽

Kinematic System ◽

New Development

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New collocation path-following approach for the optimal shape parameter using Kernel method

SN Applied Sciences ◽

10.1007/s42452-021-04231-1 ◽

2021 ◽

Vol 3 (2) ◽

Author(s):

Zouhair Saffah ◽

Abdelaziz Timesli ◽

Hassane Lahmam ◽

Abderrahim Azouani ◽

Mohamed Amdi

Keyword(s):

Shape Parameter ◽

Kernel Method ◽

Continuation Method ◽

Path Following ◽

High Order ◽

Homotopy Continuation ◽

Homotopy Continuation Method ◽

Optimal Value ◽

Rbf Kernel ◽

Order Algorithm

AbstractThe goal of this work is to develop a numerical method combining Radial Basic Functions (RBF) kernel and a high order algorithm based on Taylor series and homotopy continuation method. The local RBF approximation applied in strong form allows us to overcome the difficulties of numerical integration and to treat problems of large deformations. Furthermore, the high order algorithm enables to transform the nonlinear problem to a set of linear problems. Determining the optimal value of the shape parameter in RBF kernel is still an outstanding research topic. This optimal value depends on density and distribution of points and the considered problem for e.g. boundary value problems, integral equations, delay-differential equations etc. These have been extensively attempts in literature which end up choosing this optimal value by tests and error or some other ad-hoc means. Our contribution in this paper is to suggest a new strategy using radial basis functions kernel with an automatic reasonable choice of the shape parameter in the nonlinear case which depends on the accuracy and stability of the results. The computational experiments tested on some examples in structural analysis are performed and the comparison with respect to the state of art algorithms from the literature is given.

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