Abstract: The structures of parallel mechanisms result in a nonlinear relationship between their input and output motions, so a great many nonlinear equations are involved in such questions as the analysis of kinematics, dynamics, workspace space and error, and moving control of parallel kinematic machines. Based on manifold theory and computational continuation methods, a new approach to numerical calculation and analysis of the boundary of solution set of a parameterized nonlinear equation system is introduced. A Jacobian matrix’s row rank deficiency condition is explored as the criterion for the boundary of solution set of a nonlinear equation system. A numerical method for mapping the boundary is developed, and it can directly calculate the boundary of the solution set effectively and rapidly. At last, an example, which is involved in calculating the workspace boundary of a real 4 degree-of-freedom parallel kinematic machine tool, is analyzed numerically. The examina-tion results show that this method is suitable for solving the boundary of a nonlinear equation system, and can be used in analysis, design and control of parallel mechanisms.

Key words: Nonlinear, Parallel mechanism, Solution boundary, arc welding, arc welding process control, information acquisition of welding arc, welding arc monitoring