Design of one DOF closed-loop statically balanced planar linkage with link-collinear spring arrangement

Several methods have been proposed for reducing the space required for a spanning-spring arrangement in a statically balanced mechanism (SBM) with auxiliary elements. This paper proposed a designing method to overcome the problem traditionally caused by the interference of the spanning-spring arrangement and the use of auxiliary elements. A prismatic joint is required for designing the proposed one DOF, closed-loop, planar linkage with a link-collinear spring arrangement. In our design, two prismatic joints are required for a closed-loop, planar four-link SBM to achieve static balance by deriving the formulation of elastic energy. Moreover, these two prismatic joints should be adjacent and perpendicular to each other. Furthermore, at least one of the prismatic joint must be adjacent to the ground link. On the basis of the design principles of the four-link SBM, a six-link SBM with two independent loops is also discussed. The ground link must be the link connected to the common joints and with the maximum number of ground-adjacent links. And one prismatic joint must be set as the common joint for reducing the number of the prismatic joints from four to three.