Experiment design in compliant mechanisms and kinematic identification of parallel mechanisms (2010)
This article discusses a procedure for force-displacement modeling compliant mechanisms by using a design of computer experiments methodology -- This approach produces a force-displacement meta-model that is suited for real-time control of compliant mechanisms -- The term meta-model is used to represent a simplified and efficient mathematical model of unknown phenomena -- The meta-modeling of compliant mechanisms is performed from virtual experiments based on factorial- and space-filling design of experiments -- The procedure is used to model the quasi-static behavior of the HexFlex compliant mechanism -- The HexFlex is a parallel compliant mechanism for nano-manipulation that allows six degrees of freedom of its moving stage -- The meta-model of the HexFlex is calculated from experiments with the Finite Element Method (FEM) -- The obtained meta-model for the HexFlex is linear for the range of movement of the mechanism -- The accuracy of the meta-model was calculated conducting a set of computer experiments with random uniform distribution of the input forces -- Three criteria were calculated in each displacement direction (x, y, z, θx, θy, θz) comparing the meta-model prediction with respect to the results of the virtual experiments: 1. maximum of the absolute value of the error, 2. relative error, and 3. root mean square error -- The maximum errors were founded adequate with respect to demanding manufacturing tolerances (absolute errors) and lower than errors reported by other authors (relative errors)