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

Optimum geometries of a re-configurable planar Gough–Stewart machining platform are determined for kinematically prescribed tool paths. The optimization is done via the Leap-Frog OPtimizer for Constrained problems (LFOPC) by the second author. The five geometrical design variables correspond to the placement of the machine relative to the prescribed path and the positioning of the actuator joints on the base and on the moving platform. The objective is to minimize the dynamic actuator forces required for executing the prescribed path, subject to constraints on the geometry and the ranges of actuator lengths. In presenting the fundamental optimization methodology, relative simple numerical experiments are performed, in order to illustrate the feasibility of the proposed optimization approach to the design problem.