Singularity analysis and design of parallel manipulators

Parallel manipulators are formed when multiple kinematic chains act together on a common object. Such devices include multi-fingered hands, walking machines, cooperating robots, and Stewart platforms. Singularities in the kinematics mappings pose problems for the application of these devices. Geometric methods such as line geometry, screw theory, and Clifford algebras have proven to be important tools in the study of these systems. In this dissertation, the interrelationship between singular configurations and parallel architecture is used to direct the design of manipulators with singularity-free workspaces.; Existing theory for determining singular configurations of parallel manipulators composed of prismatic actuators is based on identifying the lines of action of the actuator forces. At a singularity, these lines of action form a rank deficient line system. It is shown that any parallel manipulator with serial chains attached through passive spherical joints has a Jacobian composed of lines. A detailed example of this analysis for a parallel force-reflecting hand controller is provided to demonstrate a new method for finding analytic conditions using line geometry and to motivate the need for a new formulation.; The Clifford algebra of projective three space is used to represent the workspace of a parallel manipulator as a semi-algebraic manifold called the constraint manifold. Singularities of the manipulator form a submanifold of the constraint manifold and are obtained by setting the determinant of the Jacobian matrix equal to zero. Singularity submanifolds for planar and spatial platform manipulators with prismatic actuators are derived and studied.; Platform manipulator singularities can be avoided by using redundant actuation or by identifying singularity-free regions of the workspace. First, line geometry is used to direct the placement of redundant actuators, and to efficiently solve for the redundant actuator forces. Next, we propose an algorithm that generates parallel manipulator designs with a prescribed singularity-free workspace using constraint manifold synthesis with singularity avoidance criterion. These methods provide a foundation for platform manipulator-design algorithms.