Optimal design of a measurement system for the calibration of a flexible pneumatic actuator

The design of a measurement system to be used for the calibration of a flexible pneumatic actuator is considered. In this extent it is necessary to have an independent measurement system that can measure the position of the end effector. In principle the position of the end effector can be obtained in 3D space, if three distances l₁, l₂ and l₃ from three known points (not in a line) are given. However, in practice the three distances are measured with errors and the corresponding position of the end effector itself is affected by the error. The aim of this work is to define which are the best positions of the points in order to obtain the smallest uncertainties in the determination of the position of the end effector of the flexible pneumatic actuator when the distances l₁, l ₂ and l₃ are known with a given tolerance