SYNTHESIS OF PERFECT SPRING BALANCERS WITH HIGHER-ORDER ZERO-FREE-LENGTH SPRINGS

ABSTRACT Static balancing is a well-known technique in mechanism synthesis to achieve equilibrium throughout the range of motion, for instance to eliminate gravity from the equations of motion. Another application of static balancing is in spring-tospring balancing where the influence of n springs on the mechanism behavior (e.g. input torque) are balanced by m other springs (n and m both non-zero positive integers). In this category of balanced mechanism, design methodology and examples exist based on zero-free-length springs, i.e. linear extension springs in which the force is proportional to the length of the spring, rather than to its elongation. The present paper will present for the first time the design of perfect springto-spring balancers with higher-order zero-free-length springs, i.e. springs in which the force is proportional to a (positive integer) power of its length. A general approach will be given together with four new mechanisms incorporating springs ranging from two third-order springs in the simplest example, to four equal thirteenth order springs plus one first order spring in the most complex example