Kinematic Study of the Original and Revised General Line-Symmetric Bricard 6R Linkages

In this paper, the solutions to closure equations of the original general line-symmetric Bricard 6R linkage are derived through matrix method. Two independent linkage closures are found in the original general line-symmetric Bricard 6R linkage, which are line-symmetric in geometry conditions, kinematic variables and spatial configurations. The revised general line-symmetric Bricard 6R linkage differs from the original linkage with negatively equaled offsets on the opposite joints. Further analysis shows that the revised linkage is equivalent to the original linkage with different setups on joint axis directions. As a special case of the general line-symmetric Bricard linkage, the line-symmetric octahedral Bricard linkage also has two forms in the closure equations. Their closure curves are not independent but joined into a full circle. This work offers an in-depth understanding about the kinematics of the general line-symmetric Bricard linkages.