Synthesis of Midline to Apex Type Griffis-Duffy Platforms using the Geometric Construction Method

From the viewpoint of mechanism synthesis, Midline to Apex Type Griffis-Duffy Platforms (abbreviated as GDPs), a type of parallel mechanisms with triangle bases and moving platforms are studied. According to motion out-put characteristics of GDPs, an aggregate formed by a series of SSC mechanisms with the same maximal height but different lengths is proposed. Then the GDP is treated as the composition of two 3-SS/C mechanisms constructed from the aggregate, while both of them conform to the compatible conditions of geometry. Contributed by this, once a 3-SS/C mechanism is given, a GDP can be obtained by designing the other obeying the same dimensional constraints. Based on the principle of inversion, the locus of one vertex of the unknown moving platform can be transformed by one side of the known base. With this geometric construction of dimensional constraints, a generalized GDP can be directly synthesized, as a result that three vertices of the moving platform lie on three circular arc loci respectively. This research shows that architecture singular GDP can be achieved by means of synthesis, and also provides a new perspective for the design of robot mechanisms using concise geometrical theorems and intuitive graphical methods.