Stretch rotation and complete mobility identification of Watt six-bar chains

Mobility of linkages refers to the problems concerning branch, full rotatability, singularities, and order of motion. This paper uses the stretch and rotation of a four-bar loop to convert a Watt six-bar linkage to an equivalent simple Stephenson linkage. It shows the mobility of a Watt six-bar linkage is affected by a hidden five-bar chain. The equivalency offers a simple and clear visual explanation on the formation of branches and sub-branches and how Watt and Stephenson linkages differ in mobility. The resulting mobility algorithm requires no stretch rotation. The dead center positions in the second four-bar loop are the branch points. It reveals that although a Watt six-bar linkage may have only up to four-branches, a branch may have up to six sub-branches. The results offer a simple algorithm suitable for automated identification of branch, sub-branch, and full rotatability. The algorithm is valid for Watt linkages with or without prismatic joints and is independent of linkage inversions. Examples are presented for illustration.