Optimal Actuation of Dynamically Driven Serial and Hybrid Flexure Systems

In this paper, we introduce the principles necessary to guide designers in determining the optimal number and placement of actuators for driving the stage of a general serial or hybrid flexure system at any desired speed. Although the degrees of freedom (DOFs) of a flexure system are largely determined by the location and orientation of its flexure elements, the system’s stage will tend to displace in unwanted directions (i.e., parasitic errors) while attempting to traverse its intended DOFs if it is not actuated correctly. The problem of correctly placing actuators is difficult because the optimal location changes depending on the speed with which the stage is driven. Moreover the issue of correctly actuating the stage of a serial or hybrid flexure system is substantially more complicated than actuating the stage of a parallel system because serial and hybrid systems possess multiple rigid bodies, which greatly enhance the system’s dynamic complexity, and provide a host of alternative options for actuating the system with its intended DOFs. In this paper we review the principles of static and dynamic actuation space and provide the mathematics necessary to apply these spaces to serial and hybrid systems such that designers can rapidly visualize all the ways actuators can be placed to correctly drive any combination of the system’s rigid body constituents such that the system’s stage achieves the desired DOFs with minimal parasitic error at any speed.