Simplification of Dynamic Equations of a Nonholonomic Motion Transfer Mechanism

Abstract

The dynamic equations of first-order linear non-holonomic systems can be given by quasi-Newton's law. One of the advantages of this method is that quasi-Newton's law obviously depends on the geometric properties of the reduced configuration space of a constrainted system. In the study of control problems, the simplification of dynamic equations is important. In this paper, it is pointed out that the simplification of the dynamic equations of a constrained system may be realized by simplifying the geometric structure of the reduced configuration space of the system. If a set of quasi-coordinates can be found to make the geometric structure of the reduced configuration space of a constrainted system simple, then the dynamic equations given by quasi-Newton's law may also be simple. As an application of this method, the simplification of the dynamic equations of a nonholonomic motion transfer mechanism is studied. By using a set of suitable quasi-coordinates, the dynamic equations of the motion transfer mechanism is reduced to the simplest form.