Mathematical models that characterize the kinematic behavior of mechanisms and manipulators have been developed, with joint limits taken into consideration. Joint mobility limitations and actuator length limitations are converted from inequalities to equalities without introducing new variables.; A new algorithm is introduced for finding an initial point on the boundary of a workspace, which is not a trivial task. The algorithm starts from an assembled configuration within the workspace and follows a user-specified direction until an initial point on the boundary is located.; In order to trace all solution curves of continuation equations on the boundary, branch switching is required. An approach to find tangents to branches at simple bifurcation points is presented. An efficient algorithm to find all simple bifurcation points with the same physical configuration, as well as the tangent of branches that emanating from the bifurcation points are presented. A systematic method that can switch branches at bifurcation points and solve for all singular solution sets of continuation equations that define boundaries of workspaces of manipulators is presented.; Interior singular curves are often associated with restrictions on motion control. Properties of output restrictions that exists across such interior singular curves are analyzed. Analytical criteria that characterize the properties are presented.; Finally, the working capability of a spatial Stewart platform, a complicated spatial manipulator, is investigated as an illustration of the numerical algorithms presented.
展开▼
