The Spatial Pantograph and Its Mass Balance

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Abstract

This paper presents the spatial version of the well-known pantograph linkage. While the traditional pantograph is a planar parallelogram linkage with 1 internal degree of freedom (DoF) and four moving links connected with solely revolute pairs, the general spatial pantograph is a linkage with 3 internal DoFs in which the four moving links are connected with spherical joints and two additional out-of-plane links are connected with universal joints. The out-of-plane links constrain the linkage to maintain the essential parallelogram and also constrain all links to move similarly. This is necessary for full controllability and also for inherent force balance, which is obtained for specific conditions on the mass distribution of the links. The force balance conditions are given and also a reduced version of the spatial pantograph linkage with 2 internal DoFs is presented which has five moving links connected with solely universal joints.