Movable Focal-Type 7-Bar Baranov-Truss Linkages

Baranov truss is a structural framework composed of revolute jointed bars. It is also regarded as an Assur kinematic chain (briefly termed AKC) in viewpoint of kinematics. Based on Grübler mobility criterion, these AKCs with zero DoF should be generally unmovable. However, under some specified dimensional constraints, they have the constrained motion. In the paper, we focus on identifying mobility constraints of the simplified planar 7-bar Type-I Baranov-truss (AKC-I) linkage and on synthesizing one novel family of movable focal-type 7-bar linkages. In the beginning, applying the vector-loop approach produces the algebraic relations between structural parameters and angular variables of the simplified 7-bar such linkages. Next, by Sylvester elimination method, we attain one algebraic polynomial, which is function of an input variable only, and propose the mobility dimensional constraints of such truss architecture. Moreover, following the graphical technique for generating Kempe focal linkages, we systematically synthesize eight kinds of new movable focal-type 7-bar Baranov-truss linkages by removing one specified redundant link. These synthesized linkages further confirm the accuracy and availability of the derived mobility dimensional constraints.