Scaling laws for the dynamics and control of flexible-link manipulators

To design and test large flexible manipulators, dynamically equivalent scale model manipulators can be built which will fit inside a conventional research lab. By constructing dynamically equivalent prototypes, all the dynamic properties of the manipulator are scaled, including gravity and flexibility effects. Dimensional analysis is used to determine the nondimensional groups which define the dynamic equivalence conditions for general flexible-link manipulators. The scaling laws for natural frequencies, mode shapes, and friction effects are also presented. An example illustrates how two physically different flexible-link manipulators with two degrees of vibration can be constructed to be dynamically equivalent. The example also illustrates how, with the application of scaled PD controllers, the responses of the two systems can be scaled versions of one another.