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.

Dimensional analysis is used to determine the nondimensional groups which define the dynamic equivalence conditions for rigid-link manipulators. Scaling laws for general actuators and nonlinear controllers are also presented. As an example, simulation results are presented which illustrate how a large two-link elbow manipulator operating on the Moon can be designed by constructing a dynamically equivalent prototype in Earth gravity, and also, how a sliding mode controller designed for the prototype Earth robot can be scaled for implementation on the Moon-based manipulator.

When constructing large robotic manipulators or space structures, it is advisable to begin with a small-scale prototype on which to perform the design, analysis, and debugging. To ensure that the results obtained on the scale-model apply directly to the actual manipulator, it is necessary that the prototype and the original robot are dynamically equivalent. This paper examines the single flexible link (SFL) manipulator. Dimensional analysis is used to identify the nondimensional groups for the SFL. These groups are present in the corresponding nondimensional equations of motion, which are also derived. To account for inherent manufacturing imprecision, tolerances are developed for the nondimensional groups. Scaling laws for continuous-time and discrete-time controllers are developed for dynamically equivalent SFL systems. These theoretical scaling laws are verified experimentally for an H/sub /spl infin// and a PD control strategy.

The nondimensional groups which characterize a group of dynamically equivalent single flexible link (SFL) manipulators are determined. A scaling law for linear rational controllers is developed for dynamically equivalent SFL systems. As an example of the applicability of this theoretical scaling law to even sophisticated control techniques, it is verified experimentally for an H/sub /spl infin// control strategy.