Motion Control for a Series System of “N” Degrees of Freedom Using Numerically Derived and Evaluated Equations

A numerical method of synthesizing motion considering the dynamics of a system of n degrees of freedom which is applicable to either a linear or nonlinear system is presented. The technique which uses divided differences and Newton’s Fundamental Interpolation Formula shows how interior motion requirements may be controlled, in addition to the consideration of the usual boundary conditions. The inherent problem of obtaining a negligible displacement in a disproportionate period of time at the start and end of motion when only boundary conditions are considered is eliminated. The numerical method is equally well adapted to problems in kinematic synthesis, making it a general purpose tool. It is presented in sufficient detail for computer programming, or the computer program may be obtained from the author.