Topology and Geometry of Serial and Parallel Manipulators

The evolution of requirements for mechanical products toward higher performances, coupled with never ending demands for shorter product design cycle, has intensified the need for exploring new architectures and better design methodologies in order to search the optimal solutions in a larger design space including those with greater complexity which are usually not addressed by available design methods. In the mechanism design of serial and parallel manipulators, this is reflected by the need for integrating topological and geometric synthesis to evaluate as many potential designs as possible in an effective way. In the context of kinematics, a mechanism is a kinematic chain with one of its links identified as the base and another as the end-effector (EE). A manipulator is a mechanism with all or some of its joints actuated. Driven by the actuated joints, the EE and all links undergo constrained motions with respect to the base (Tsai, 2001). A serial manipulator (SM) is a mechanism of open kinematic chain while a parallel manipulator (PM) is a mechanism whose EE is connected to its base by at least two independent kinematic chains (Merlet, 1997). The early works in the manipulator research mostly dealt with a particular design; each design was described in a particular way. With the number of designs increasing, the consistency, preciseness and conciseness of manipulator kinematic description become more and more problematic. To describe how a manipulator is kinematically constructed, no normalized term and definition have been proposed. The words architecture (Hunt, 1982a), structure (Hunt, 1982b), topology (Powell, 1982), and type (Freudenstein & Maki, 1965; Yang & Lee, 1984) all found their way into the literature, describing kinematic chains without reference to dimensions. However, some kinematic properties of spatial manipulators are sensitive to certain kinematic details. The problem is that with the conventional description, e.g. the topology (the term topology is preferred here to other terms), manipulators of the same topology might be too different to even be classified in the same category. The implementation of the kinematic synthesis shows that the traditional way of defining a manipulator’s kinematics greatly limits both the qualitative and quantitative designs of spatial mechanisms and new method should be proposed to solve the problem. From one hand, the dimension-independent aspect of topology does not pose a considerable problem to planar manipulators, but makes it no longer appropriate to describe spatial manipulators especially spatial PMs, because such properties as the degree