Workspace Analysis of Multibody Mechanical Systems Using Continuation Methods

Abstract

A new approach to numerical analysis of workspaces of multibody mechanical systems is presented, based on manifold theory and computational continuation methods. Generalized coordinates that define the kinematics of a system are classified and interpreted from an input-output point of view. Boundaries of workspaces, which depend on the classification of generalized coordinates, are defined as sets of points for which Jacobian matrices of the kinematic equations are row rank deficient. This criterion generalizes the conventional determinant criteria for applications with square Jacobian matrices. Numerical methods for tracing families of one dimensional trajectories on a workspace boundary are outlined. Open and closed loop manipulator examples are analyzed, using a manifold mapping computer program.