Dimensional synthesis of a spatial revolute–revolute–spherical–cylindrical (RRSC) mechanism for motion generation

Abstract. This paper presents a dimensional synthesis method of a spatial revolute–revolute–spherical–cylindrical (RRSC) rigid-body guidance mechanism for motion generation. The inputs into the mechanism, namely the prescribed spatial poses, are analysed, revealing that, after two steps of coordinate transformation, the corresponding coupler points lie on a circle. Based on this finding, an input angle determination method is proposed. The design process for the 21 geometric parameters is then decomposed into four steps: first, obtaining the installation angles, the initial input angle, and the angle between the rotation axes of the input link and coupler link; second, determining the basic dimensional types; third, calculating the remaining parameters based on the relationship between the prescribed poses and the generated coupler points; and, fourth, optimizing the mechanism parameters obtained in the first three steps. This approach assumes rigid links and ideal joints. Through this four-step approach, the design efficiency is significantly improved by reducing the dimensionality of the design problem. Notably, the method accommodates both prescribed- and unprescribed-timing design requirements. Its practicality and effectiveness are demonstrated through numerical examples.