Design of a Variable-Mobility Linkage Using the Bohemian Dome

A new method is presented for the design of kinematotropic linkages based on 2-DOF kinematic chains that generate more than one surface. As an example of the proposed method, a kinematotropic linkage is obtained by studying a special case of the Bohemian dome which has two different parametrizations constructed by translation of circles and, therefore, two different hybrid kinematic chains can be designed to generate the same Bohemian dome. Each of these hybrid kinematic chains can generate two different surfaces and, thus, can be used in the proposed method. Parametrizations for the secondary surfaces are then obtained and studied. A total of 27 motion branches are found in the configuration space of this kinematotropic linkage. The singularities in the configuration space are further determined using the properties of the surfaces. The resultant linkage offers an explanation of Wholhart's queer-square linkage other than its original paper folding. As part of the analysis of this example, the relationship between the properties of self-intersections in generated surfaces and the configuration space of the generator linkage is studied for the first time, leading to a description of motion branches related to self-intersections of generated surfaces.