Optimal motions planning for a GOUGH parallel robot

Afroun, Mohamed; Chettibi, Taha; Hanchi, S.; Dequidt, Antoine; Vermeiren, Laurent

doi:10.1109/med.2008.4602022

Cited by 5 publications

(3 citation statements)

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“…(29) Then the normal vector of the plane of the mid-oscillating circle, H, is denoted by: Since points A and B are in the plane with the normal vector H, then the center of the circular path can be obtained by solving the system of the equations:…”

Section: Investigation Of Motion Error By Circular Interpolationmentioning

confidence: 99%

“…Dash et al [27] presented a numerical technique for path-planning within the workspace of parallel manipulators where isolated singularities have been eliminated based on Grassmann's line geometry and local routing method. Afroun et al [28,29] presented a technique for generating optimal motion for a parallel DELTA robot and Gough parallel robot. In their study, the sequential quadratic programming method was employed for finding the optimal position of the spline control points.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical modelling of linear motion error for Hexarot parallel manipulators

Pedrammehr

Qazani

Asayesh

et al. 2016

Applied Mathematical Modelling

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a b s t r a c tHexarot is a robotic manipulator that belongs to the family of axis symmetric parallel mechanisms. The robot is able to move the robot platform or tool center point in six degrees of freedom (DOF). This paper presents the kinematics model of the robot including the inverse and forward kinematics, and its time derivatives. Then using the kinematics formulations, investigation of the nonlinear motion of the Hexarot robot for a desired linear motion path is performed. For this purpose, the concept of curvature of the robot path is used for measuring the nonlinearity of the actual motion of the robot. The nonlinear motion error of the robot is analyzed for the scenario where the platform moves on a linear path between two arbitrary points of the robot workspace. The effects of different parameters on the nonlinear motion error of the mechanism are demonstrated and strategies for motions with low error values are proposed.

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Section: Investigation Of Motion Error By Circular Interpolationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mathematical modelling of linear motion error for Hexarot parallel manipulators

Pedrammehr

Qazani

Asayesh

et al. 2016

Applied Mathematical Modelling

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“…They presented several compliance mappings, which can be employed during toolpath planning of the developed PKM. Afroun et al 18 first approximated the time evolution of the mobile platform, Cartesian coordinates, and the orientation by cubic spline functions with free control points and then employed the sequential quadratic programming to optimally determine the position of the control points as well as the transfer time. Pateloup et al 19 discussed the optimal location of a trajectory inside the workspace of PKM tool to minimize the machining time.…”

Section: Introductionmentioning

confidence: 99%

Contour maps for developing optimal toolpath and workpiece setup in hexapod machine tools by considering the kinematics nonlinearity

Karimi

Nategh

2016

Proceedings of the Institution of Mechanical Engineers, Part B:

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Contrary to the conventional serial kinematics machine tools, the parallel kinematics machine tools exhibit nonlinear behavior which is a major source of the machining error. This causes even a linearly programmed path to be traversed along a nonlinear path. The resulting error, known here as the kinematic error, should be critically considered during the toolpath planning. The estimation of the maximum kinematic error using the concept of median osculating circle is introduced in this article. The proposed formulation demonstrates that the maximum kinematic error depends on the curvature of the actual trajectory. In order to estimate the curvature, constant curvature contour maps are introduced. These maps depend on the structural parameters of the machine and are recommended to be provided by the machine's manufacturer. The constant curvature contour maps are illustrated to be an effective graphical tool for kinematic error estimation and thus successfully conducting the optimal planning of the toolpath and the workpiece setup. Consequently, it is recommended in this article that the constant curvature contour maps be employed in the format of a database by computer-aided manufacturing systems during toolpath planning and by interpolators during command generation or by a part programmer to optimally setup the workpiece or conduct the toolpath planning such that the least kinematic error occurs during the machining.

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