The whole family of kinematic structures for planar 2- and 3-DOF fractionated kinematic chains

• A new method to synthesize 2- and 3-DOF fractionated kinematic chains is proposed.
• The method is fully-automatic and isomorphism-free.
• Algorithms for the combination of 2 or 3 non-fractionated graphs are proposed.
• All 2-DOF fractionated chains up to 17 links are obtained for the first time.
• All 3-DOF fractionated chains up to 18 links are obtained for the first time.

Fractionated planar mechanisms, apart from the non-fractionated ones, are also widely used in engineering machinery and various robots, especially those with two or three degrees of freedom (DOFs). This paper proposes an automatic approach to synthesize the whole family of the kinematic structures of 2- and 3-DOF fractionated planar kinematic chains. Isomorphism-free algorithms for the combination of two or three non-fractionated topological graphs are proposed first. Then based on the algorithms and the atlas databases of the topological graphs of non-fractionated mechanisms [H.F. Ding, F.M. Hou, A. Kecskeméthy, Z. Huang, Mech. Mach. Theory 2012 47(1) 1–15], a general approach for the generation of fractionated topological graphs and the corresponding atlas database for 2- and 3-DOF fractionated planar kinematic chains is proposed. Isomorphism identification, one of the most difficult problems in structural synthesis, is rendered unnecessary with this synthesis approach. The whole family of the kinematic structures of 2- and 3-DOF fractionated planar kinematic chains up to seven basic loops is obtained for the first time.