Mobility criteria of geared five-bar linkages

Abstract

This article proposes simple Grashof type criteria to identify the full rotatability of geared five-bar linkages and provides a systematic approach to study the effects of the five-bar loop and gear constraint in the mobility of a geared five-bar linkage. A fully rotatable geared linkage must have a C-C (crank-crank) type host five-bar linkage. All fully rotatable geared linkages are grouped into A, B, and C types according to the joint rotation space of their host linkages. In type A linkages, a gear constraint may have any gear ratio and phase angle unless a change-point position exists. In type B linkages, the gear ratio may be a unit or other values but the phase angle must be properly chosen to achieve full rotatability. In type C linkages, the two terminal gears must rotate with the same speed in the same direction relative to the center link between them and have a proper phase angle. Any geared linkage which does not belong to one of these three types does not have full rotatability. A table summarizing the required phase angle conditions for a fully rotatable geared linkage with a unit gear ratio is also presented.