An improved mobility analysis for spherical 4R linkages

Mobility analyses of mechanisms represent an important step in the design process due to the fact that undesired types of motion could be avoided or conditions for achieving a specific mobility can be considered as restrictions for the design. This paper presents an improved mobility analysis for spherical four-bar linkages. As a result of this analysis, a simple, powerful and efficient graphical means of determining the range of travel for the angular motion of all the mechanism's links can be devised. These graphical means are named mobility graphs and they could be considered as workspace atlas of the mechanism. The application of mobility graphs in the design process is illustrated by examples. Also, new assembly conditions for the linkage are presented and they extend those previously reported.