Determination of optimum geometries for a planar re-configurable machining platform using the LFOPC optimization algorithm

An optimally re-configurable planar Gough–Stewart machining platform

“…Each linear actuator is connected to the fixed base and the moving platform by revolute joints. Two of the three moving platform revolute joints coincide, and as such all three lie in the same ''moving platform line'', while the three fixed base revolute joints lie in the same ''fixed base line'', which is consistent with the geometrical definition of a planar Gough-Stewart platform previously given by the authors [1].…”

“…., n time }. Du Plessis and Snyman [1] describe the details of evaluating this objective function. For the sake of completeness, the three evaluation steps are summarized below.…”

“…In testing the basic optimization methodology in the previous paper [1], 12 inequality constraints of the form C j (X) 6 0, j = 1, 2, 3, . .…”

“…The side constraints limiting the allowable relative distances between the linearly adjustable revolute joints of the fixed base (X 2 and X 5 ) and the moving platform (X 1 ) of the test-model are exactly the same as in [1]. These six side constraints are 0.1 m 6 X 1 6 0.45 m, 0.113 m 6 X 2 6 0.465 m and 0.113 m 6 X 5 6 0.27 m, and account for the first six inequality constraints C j (X) 6 0, j = 1, 2, 3, .…”

“…In a previous paper [1] the current authors proposed a new fundamental numerical optimization methodology, for determining optimum feasible geometries of a planar re-configurable 0094 Gough-Stewart machining platform for kinematically prescribed tool paths. Fig.…”