Mobility analysis part-1

Abstract

One of the most basic topics in the field of mechanism is to obtain the number of degrees of freedom (DOF), namely, the mobility of a mechanism. The most well-known formula for mobility analysis is the Grübler–Kutzbach criterion (G-K criterion). This criterion is based on simple arithmetic and can be successfully used in analyzing almost all planar and some spatial mechanisms. Hence, it became very popular and is currently used by a great number of engineers. However, the G-K criterion fails to analyze many over-constrained mechanisms. Recently, lower-mobility parallel manipulators with various merits have attracted many researchers. Given that most of these mechanisms are over-constrained, the G-K criterion fails to analyze them. Hence, mobility analysis becomes a critical issue. Looking for a unified mobility formula has been one of the hot points in mechanical engineering for about 150 years, and is an open issue up to the present. In the current and subsequent Chapters, a mobility principle based on the screw theory and modified G-K formulas is introduced. Many classical and modern PMs are analyzed by the mobility principle. All the works indicate that the mobility principle is really unified.