Singularity workspace analyses of serial robot manipulators

A broadly applicable formulation for determining analytical boundary surfaces to the workspaces of robotic end-effectors maneuvering in space is presented. Robotic manipulator workspaces are determined by computing singularity sets due to a row rank deficiency condition of the manipulator's constraint Jacobian. The method is applicable to all serial manipulators that comprise combinations of prismatic and revolute joints. Joint limits in terms of inequality constraints are imposed and taken into account in the formulation.; Geometric entities upon which the manipulator loses one or more degrees of freedom are identified and called singular entities. Geometric singular entities, i.e. curves or surfaces, are analytically represented and parametrized in terms of one or more joint variables. These geometric entities are then intersected to characterize the boundary to the workspace and the interior barriers inside the workspace. A numerical technique based on a continuation method is proposed to determine intersections of general parametric surfaces. The problem of simple bifurcation points, at which the matrices used to compute tracing directions become rank deficient, is addressed and classified into four different cases.; Analytical criteria for admissible output velocities and accelerations of the end-effector on singular entities are presented. Directions of admissible normal movements are also established from the analysis of normal curvatures of singular entities and admissible normal accelerations. Definiteness properties of a quadratic form establish new criteria for determining crossability. For singularity sets that are due to imposed joint limits. two supplementary criteria are derived. These criteria provide a complete treatment of the problem of determining non-crossable singular surfaces and curves inside the workspace.; Dexterity analysis of the manipulator's end-effector at a target point is also presented. Two methods are developed to identify possible orientations of the end-effector. Knowledge of dexterity helps a designer to better understand the orientational capability of robot manipulators.; Implementations of the presented formulation in determining swept volumes of geometric entities moving along others are also discussed. Other applications used in NC machining verification and solid modeling are also addressed. Numerical planar and spatial examples are solved to demonstrate and validate the formulation.