Kinematics of manipulators with parallelism, modularity and redundancy: Analysis and design

A general class of manipulators with hybrid kinematic chains is introduced. These manipulators are modular and can readily lead to kinematically redundant structures. Moreover, they may contain serial subchains as well as subchains of parallel modules, acting in parallel and connecting a base to a common end-effector.; At the onset, a novel formalism is introduced to study modular kinematic structures. This includes some new concepts and definitions. The proposed formalism provides a systematic way to represent a complex hybrid manipulator through a hierarchy of its constituting modules. Next, a formulation is devised to study the instantaneous kinematics of these manipulators. The proposed formulation is general and can be applied to most of the existing parallel and hybrid manipulators. To realize the concept of general hybrid manipulator in practice, a few prototype designs are also introduced. The proposed prototypes are superior to their conventional counterparts in terms of dexterity and the volume of their workspace.; The study is then extended to the theory of hyper-redundant manipulators that comprise, as a subclass, the variable-geometry trusses. A spline-based solution method is proposed for the inverse kinematics of hyper-redundant manipulators. The method is applicable to both extensible and nonextensible cases and includes planar as well as spatial manipulators. Also, a new variable-geometry truss is introduced whose modules themselves are kinematically redundant.; Another practical aspect of redundancy is the use of redundant-sensor data to simplify inherent nonlinear direct kinematics of parallel manipulators. For a six-degree-of-freedom general parallel manipulator, we introduce a formulation of the direct kinematics whereby the positioning and orientation problems are decoupled by introducing two auxiliary parameters in the forms of either two angles or two lengths. This is in accordance with the type of redundant sensors, i.e., rotary or translational, to be used. Moreover, a real-time implementation of extra-sensor data, with a unique direct kinematics solution, is proposed by resorting to an eigenvalue problem. The parallelism in the proposed formulation enables the user to benefit from a parallel-computing environment. Hence, we introduce a parallel-computing algorithm that highly increases the robustness of the computational algorithm.; The concept of kinematic isotropy has been used as a criterion in the design of serial and parallel robotic manipulators. However, all notions adopted to express isotropy in parallel manipulators have been based on the structure of the Jacobian matrices of serial manipulators. Here, we introduce a definition of kinematic isotropy that is well-suited to parallel manipulators. This is done by identifying the special structure of the Jacobian matrices involved in the differential kinematics of such manipulators. This leads to a partitioning of the Jacobian matrices into submatrices with dimensionally homogeneous entries. Moreover, based on the proposed definitions of isotropy and kinematic optimality, a set of conditions is derived that provides a systematic way for the optimum kinematic design of parallel manipulators, with or without structural constraints.