Acceleration and higher-order analyses solved by extending the superposition principle: The incipient motion technique

The superposition principle, when applicable in the kinematic analysis of a mechanism, makes it possible to relate the studied mechanism with its component structures, and reduces the computation burden by exploiting the relationships among different data sets. Acceleration and higher-order analyses of holonomic or first-order non-holonomic mechanisms, and the velocity analysis of mechanisms with time-dependent (rheonomic) constraints need the solution of linear and non-homogeneous equation systems. The non-homogeneity of these problems forbids the use of the superposition principle to solve them. In this work, a novel kinematic-analysis technique (Incipient Motion Technique) that fully exploits the properties of linear and non–homogeneous equation systems is proposed. This solution technique has advantages similar to the ones of the superposition principle, holds for rheonomus systems, too, is efficient enough to use it in general purpose programs for multibody dynamics analysis, and is simple enough to present it in courses for graduate students.