Kinematic study of the general plane-symmetric Bricard linkage and its bifurcation variations

In this paper, the explicit solutions to closure equations of the plane-symmetric Bricard linkage are derived and a thorough kinematic study of the general plane-symmetric Bricard linkage is conducted with DH matrix method. The derived 5R/4R linkages from this Bricard linkage are introduced. Various bifurcation cases of the plane-symmetric Bricard linkage with different geometric conditions are discussed, which include the bifurcation between two plane-symmetric Bricard linkage motion branches and the bifurcation among equivalent serial kinematic chains with revolute joints and a four-bar double-rocker linkage. Especially the plane-symmetric Bricard linkage that can bifurcate to the Bennett linkage is proposed for the first time. These findings not only offer an in-depth understanding about the kinematics of the general plane-symmetric Bricard linkage, but also bridge two overconstrained linkage groups, i.e., the Bennett-based linkages and Bricard-related ones, to reveal their intrinsic relationship.