Balancing conditions of the RSS’R, spatial mechanism: An alternative method using natural coordinates

Abstract

Dynamic balancing of rigid body linkages with constant mass links is a traditional but still very active research area in mechanical engineering. It has some difficulties but the initial one is to derive the so-called balancing conditions, that are helpful to obtain different configurations for the balanced mechanism. The objective of this work is to illustrate the application of a general method to find the force and moment balancing conditions of planar and spatial linkages. It is applied for the dynamic balancing of the RSS’R spatial mechanism. The method is based on the use of Natural Coordinates so the whole system is represented only by a set of basic points, avoiding the use of angular coordinates. This facilitates obtaining the expressions for the linear momentum and for the angular momentum required to extract the shaking force and the shaking moment balancing conditions for the linkage. These conditions are interpreted and used to propose different design alternatives which can lead to a convenient design.