‘Perfect’ Spring Equilibrators for Rotatable Bodies

Abstract

A new equilibrator design approach based on system potential energy functions is presented. This approach was used to discover a group of spring equilibrators which perfectly balance a rotatable rigid link at every orientation angle through 360 deg of link rotation. Springs are connected between a rotatable link and ground, where one end of each spring is connected to the rigid link and the other end of each spring is connected to ground. The rigid link is connected to ground by a pin joint and is free to rotate about that joint. The conditions for existence and the design equations for all equilibrators which fall into this category are developed and presented. Three designs appear to offer unique advantages over the infinite number of design options available.