Spatial orientations of principal vector planes for inherent dynamic balancing

Abstract

The spatial orientations of the planes defined by principal vectors of the pantograph, the closed 4-principal vector linkage, and the grand 4R four-bar based inherently balanced linkage architecture are investigated in this paper. These principal vector planes form the basis for the synthesis of planar and spatial inherently balanced linkages, i.e. linkages derived with balance as starting point in the design process of which the center of mass is in an invariant point in one of the links. It is shown that a pantograph consists of a single plane of principal vectors, the 4-principal vector linkage consists of three planes of principal vectors, and the grand 4R four-bar based inherently balanced linkage architecture consists of ten planes of principal vectors with four parallel sets. It is shown how the principal vector planes can be used for synthesis by example of a spatial inherently balanced double Bennett linkage.