Derivation of Input/Output Relationships for the Bennett 6r Linkages Based on the Method of Decomposition

Abstract

The Bennett overconstrained 6R linkages are the double-planar, the double-spherical and the plano-spherical 6R linkages. These mechanisms are obtained by combining simple planar and/or spher-ical mechanisms and then removing one of the common links. This paper presents the derivation of the input/output relationships for these mechanisms using the decomposition method. This method is based on writing the input/output equations for the two imaginary loops comprising the 6R mechanism and then eliminating the imaginary joint variable. It is found that the resulting input/output equations con-tain up to 4th power of trigonometric terms, such as cos4 θ.