Configuration analysis of complex multiloop linkages and manipulators

The article offers a simple and efficient method to identify all possible configurations up to 29 types of basic kinematic chains containing up to four independent loops. Basic kinematic chains may be regarded as the basic building blocks of any complex planar linkage. Given the required inputs to any single or multiple degree of freedom linkage, the linkage can always be decomposed into a set of basic kinematic chains. Since the method is capable of identifying all possible configurations of these 29 basic kinematic chains, the article offers the most general and versatile method available so far for the analysis of any complicate linkage composed of these basic kinematic chains. The method can be automated by initiating it with a structure analysis and classification, which identifies the linkage type, the simplest way of coupling among loops, and the complexity of the linkage, and then activating an one-dimensional search algorithm. The search is efficient. It requires no initial guess and does not lead to an erroneous solution. The complexity of analyzing a multiloop linkage may be affected by the choice of the input joints. Using an alternative input joint may lead to different basic kinematic chains and ,therefore, different level of complexity or even different number of configurations. The paper also shows that the number of possible configurations corresponding to a set of inputs given to a multiloop linkage is equal to the product of the numbers of configurations of its basic kinematic chains.