TSAI–TOKAD (T–T) Graph: The Combination of Non-oriented and Oriented Graphs for the Kinematics of Articulated Gear Mechanisms

Abstract. The non-oriented and oriented linear graph techniques are used for the kinematic analy-sis of bevel-gear trains. In this paper, these two techniques are compared and the weaknesses of each technique are shown. In order to overcome the weaknesses of these techniques a new graph-ical technique called Tsai–Tokad (T–T) graph is introduced incorporating the important feature of the non-oriented graph which helps to determine the transfer vertex and the oriented graph tech-nique. The theory is demonstrated by the kinematic analysis of articulated robotic mechanism used by Cincinnati Milacron T3