Spring equilibrator theory for static and dynamic planar machinery

A spring equilibrator design methodology for planar rigid body mechanisms has been developed on the basis of energy exchange between equilibrator elastic potential energy and system gravitational potential and kinetic energy. Theoretically, the developed methodology can be applied to mechanisms including general multi-degree-of-freedom revolute joint kinematic chains and pin-in-slot kinematic pairs.;In static balancing, the concept of perfect balancing, which was previously applied only to revolute joint kinematic chains, has been extended to the equilibration of higher order pin-in-slot kinematic pairs and the mass of springs. Several examples based on the developed equilibrator design approach have been presented, including perfect balancing of a planar skew-pantograph mechanism.;In dynamic balancing, a new concept of harmonic synthesis has been combined with an optimization procedure. The motivation of introducing this new concept is based on the observation that ideal energy matching between kinetic and potential energy is found in a harmonically oscillating pendulum. Examples of dynamic balancing of a pick-and-place robot manipulator and a swinging leg of a walking machine have illustrated the effectiveness of the developed method.