A comparative study 3-DOF parallel manipulators

In this dissertation, a comparative study of 3 degree-of-freedom (DOF) parallel manipulators is presented. These manipulators can be used as stand-alone robotic devices or in the construction of Hybrid Kinematic Machines. The high stiffness and low inertia characteristics associated with the parallel manipulator architecture make it suitable for use in the construction of machine tools.; First, a systematic methodology is employed to enumerate possible architectures of a class of 3-DOF parallel manipulators with three legs and a class of 3-DOF manipulators with four legs. The most promising architectures are then identified by applying certain design criteria.; Closed-form solutions for the forward and inverse kinematics of a few promising 3-DOF 3-legged parallel manipulators are presented. A general method for the Jacobian analysis of limited-DOF parallel manipulators (DOF < 6) is developed by making use of the theory of reciprocal screws. The 6 x 6 Jacobian matrix so developed provides information about both architecture and constraint singularities of limited-DOF manipulators. The 6 x 6 and 3 x 3 Jacobian matrices of the promising 3-legged manipulators are derived.; The most significant drawback of parallel manipulators is their limited workspace. Hence, the workspace of each 3-legged manipulator is maximized with due regard to the quality of workspace. A differential workspace volume is weighted by the inverse of the condition number of the Jacobian at that point. A summation over the entire workspace yields the well-conditioned workspace which is maximized. The stiffness matrices of 3-DOF 3-legged manipulators are derived under the assumption that the actuators are the only source of compliance. The minimum and maximum stiffness at each point in the workspace is computed for each manipulator and plotted to obtain the stiffness mappings.; Next, a class of 3-DOF manipulators with four supporting legs is introduced and a general method to solve the closed-form forward and inverse kinematics of a class of 4-legged manipulators is presented. The kinematics of promising 4-legged manipulators are solved. A general method for the Jacobian analysis of this class of manipulators is developed and Jacobian matrices of promising architectures are derived. The well-conditioned workspace of each architecture is maximized. Stiffness matrices of 4-legged manipulators are derived under the assumption that the actuators are the only source of compliance and their stiffness mappings are obtained.; Finally, a comparison study of 3-DOF manipulators on the basis of well-conditioned workspace and stiffness properties is presented and recommendations for future study are given.