The SOCs Modular Method for Kinematic Analysis of Complicated Parallel Manipulators
This paper presents a simple and systematic modular approach for kinematic analysis of complicated Parallel Kinematic Manipulators (in short, PKMs) which coupled degrees are more than 2. (1) Single open chains (in short, SOCs) may be regarded as the basic modules of a PKM. Any PKM can always be decomposed automatically into a set of ordered SOCs, and these SOCs can also be used to recognize the basic kinematic chains contained in it. (2) The kinematic analysis algorithms and the compatibility conditions of the SOC modules are offered. (3) Directly applying the above SOC kinematic modules, the kinematic equations of a PKM can be automatically established. (4) In order to solve kinematic equations of complicated parallel manipulators which coupled degrees are more than 2, a new searching algorithm which requires no initial guess has been presented. The procedural approach is demonstrated in parallel manipulators.
Z. X. Shi et al., "The SOCs Modular Method for Kinematic Analysis of Complicated Parallel Manipulators", Applied Mechanics and Materials, Vols. 52-54, pp. 834-841, 2011