Kane's Equations for Haptic Display of Multibody Systems

Abstract

The design of a general-purpose multibody simulator that runs in real-time and features haptic display is presented. The repertoire of this simulator includes systems subject to holonomic con-straints, nonholonomic constraints, and notably, systems subject to changing constraints. In contrast to the use of generic equations of motion, Kane's method is used by a computerized symbolic manipulator to produce custom-built, compact, and computationally efficient ordinary differential equations for each virtual system to be simulated. A method is presented whereby new equations, reflecting the presence of a transient constraint, may be formulated on-line by a recombination of terms comprising the nominal equations. This paper also serves as a tutorial introduction to Kane's method and includes a detailed derivation of Kane's equations with a geometric interpretation. An illustrative example featuring changing constraint conditions is developed in the body of the paper while two more examples, chosen to high-light certain features within Kane's method, are presented at the conclusion.