Principles of Lossless Adjustable One-Ports

Abstract

This paper explores the possibility of constructing two-terminal mechanical devices (one-ports) which are lossless and adjustable. To be lossless, the device must be passive (i.e., not requiring a power supply) and nondissipative. To be adjustable, a parameter of the device should be freely variable in real time as a control input. For the simplest lossless one-ports, the spring and inerter, the question is whether the stiffness and inertance may be varied freely in a lossless manner. We will show that the typical laws which have been proposed for adjustable springs and inerters are necessarily active, and that it is not straightforward to modify them to achieve losslessness, or indeed, passivity. By means of a physical construction using a lever with moveable fulcrum, we will derive device laws for adjustable springs and inerters which satisfy a formal definition of losslessness. We further provide a construction method which does not require a power supply for physically realizable translational and rotary springs and inerters. The analogous questions for lossless adjustable electrical devices are examined.