Design, manufacturing, and performance verification of a Roberts linkage for inertial isolation

• A procedure for optimal design of a spatial linkage for inertial isolation is presented.
• The a linkage can be applied to inertial isolation of precision devices.
• Linkage design allows iterative precision assembly of mechanism components.
• A CMM is used in unusual way to measure and validate the mechanism performance.
• The design procedure involves an innovative optimisation technique that exploits Zernike polynomials for ensuring mechanism performance.

There are a number of experimental apparati aimed at the measurement of small forces, whose performance is strictly related to the availability of an isolated inertial frame. This means that one component of the apparatus has to be set in free-fall condition along selected degrees of freedom. Such a free-fall condition can be achieved thanks to dedicated mechanisms acting as inertial isolation systems. The present work discusses the optimal design, realization, and testing of an inertial isolation system implemented as a 3-D Roberts linkage. The first part of the work describes the design phase: the optimal calculation of the linkage design parameters is performed through the application of a Nelder–Mead optimization scheme. In order to apply the optimization scheme, the calculation of the linkage kinematics is firstly performed through a variational approach, then the sampled surface describing the linkage trajectory is approximated by a set of Zernike polynomials, which allows to effectively define and calculate the target function for the optimization itself. The second part of the work describes the detailed design and realization of a linkage prototype, and its chararacterization by means of a coordinate measuring machine. The characterization of the device is carried out by exploiting a coordinate measuring machine, which is unusually employed for both driving the linkage moveable part along its two DoF trajectory, and for measuring the resulting error about the nominal trajectory.