Dynamic Modeling of Oblique Crossing 3R Wrist with Virtual Link Method

Based on the theory of graph representation, links of the oblique crossing 3R wrist are devided into carriers and carried links, and contributions of the carried links to the generaliazed inertia forces can be divided into two parts. The first part is due to the motion with the carriers and the second part is due to the motion relative to their carriers. At the same time, the concept of virtual link is introduced to calculate the first part and carriers' generaliazed inertia forces. The second part is derived with Lagrange Equation. At the end, an efficient and systematic dynamic equation in which the coupling effects of carried links can be identified individually and systematically, is developed. This method provides the basis for the design of driving chains and leads to a computer automated analysis for other geared robotic mechanisms.