Over-constraints and a unified mobility method for general spatial mechanisms Part 2: Application of the principle

Abstract

The pre-research on mobility analysis presented a unified-mobility formula and a methodology based on reciprocal screw theory by HUANG, which focused on classical and modern parallel mechanisms. However its range of application needs to further extend to general multi-loop spatial mechanism. This kind of mechanism is not only more complex in structure but also with strong motion coupling among loops, making the mobility analysis even more complicated, and the relevant research has long been ignored. It is focused on how to apply the new principle for general spatial mechanism to those various multi-loop spatial mechanisms, and some new meaningful knowledge is further found. Several typical examples of the general multi-loop spatial mechanisms with motion couple even strong motion couple are considered. These spatial mechanisms include different closing way: over-constraint appearing in rigid closure, in movable closure, and in dynamic closure as well; these examples also include two different new methods to solve this kind of issue: the way to recognize over-constraints by analyzing relative movement between two connected links and by constructing a virtual loop to recognize over-constraints. In addition, over-constraint determination tabulation is brought to analyze the motion couple. The researches above are all based upon the screw theory. All these multi-loop spatial mechanisms with different kinds of structures can completely be solved by following the directions and examples, and the new mobility theory based on the screw theory is also proved to be valid. This study not only enriches and develops the theory and makes the theory more universal, but also has a special meaning for innovation in mechanical engineering.