Classification of Direct Kinematics to 3D3A Generalized Stewart Platform with Equilateral Triangle Platforms

Generalized Stewart Platform is the extended form of Stewart platform of parallel linkages, which is two rigid bodies connected with six constraints. The classification of direct kinematics to 3D3A generalized Stewart platform with equilateral triangle platforms based on symbolic computation is presented. The explicit conditions of the parameters for the generalized Stewart platforms to have a given number of real solutions are given while imposing three angular constraints and three distance constraints in sequence. The appropriate parameters can be selected according to the conditions of the parameters, such that the number of real solutions specified can be obtained.