A Formalism for the Analysis and Design of Modular Kinematic Structures

The exploitation of robotic systems with more complex kinematic structures than those of conventional serial chains is widely per ceived as one of the main avenues of development for robotics. The concept encompasses systems of different scales and characteris tics, such as hybrid manipulators, multifingered hands, cooperative robotic arms, walking machines, and so on. The underlying kine matic structure of these systems is the same in the sense that they can be regarded as combinations of modules. In this paper, we aim to provide a framework for systematically identifying, classifying, and combining different modules of such manipulators. Hence, we introduce a formalism that comprises a set of definitions, a symbolic representation of modules, and a set of operations based on the kine matic structure, degree of actuation, and mobility of the modules. The proposed formalism allows us to efficiently analyze and synthe size modular manipulators according to their constituent kinematic modules. Moreover, the foregoing operations can be easily per formed in symbolic form, using commercial software, which makes their implementation generic and more useful. The information that is obtained from these operations provides a data base for either designing an inventory of modules or interchanging modules when an inventory of modules is available to the system. The application of the proposed formalism is demonstrated through a few examples, one of which pertains to a 7-DOF hybrid manipulator with parallel subchains, whose architecture is introduced here for the first time.