Rotatability Laws for N-Bar Kinematic Chains and Their Proof

This paper presents a thorough proof and adds valuable insight into the theorems [1] concerning the mobility of planar N-bar linkages. The paper includes four parts: the assemblability, the revolvability between two links, the full rotatability, and the classification. The proof is based on the assemblability condition of N-bar linkages and the revolvability condition of an angle. Examples are also provided to further clarify the use of these theorems. In these theorems, Grashof’s Law becomes a very special case.