Complete gravity balancing of the general four-bar linkage using linear springs

Abstract

Complete gravity (or static) balancing of the general four-bar linkage through proper mass distribution, also known as counterweight balancing, has been established for several centuries. However, despite extensive research on spring-based balancing techniques for various types of mechanisms, such a method for the complete gravity balancing of the general four-bar linkage remains unavailable. In this paper, we demonstrate that the general four-bar linkage can be completely gravity-balanced using two linear springs or even a single spring. The linkage considered here represents the most general case, where all the link masses are taken into account and can be positioned arbitrarily on their respective links. The balancing design employs the well-known zero-free-length springs and requires no additional auxiliary links. Three design examples illustrate the proposed method for balancing different mass patterns, with different numbers of springs in use. Finally, we show that the method is also applicable for complete balancing of some multi-loop, complex linkages.