Structure Synthesis of Rank-Degenerated Serial Mechanisms and Over-Constrained Single-Loop Kinematic Chains

Abstract

Based on the Position and orientation characteristic (POC) equation of serial mechanisms proposed by the author, this paper presents a novel systematic approach for structure synthesis of rank-degenerated serial mechanisms and over-constrained single-loop kinematic chains (KCs) (excluding the Bennett mechanism etc). This approach is totally different from the approaches based on the screw theory and based on the displacement subgroup, and only simple mathematical tools (vector algebra, etc.) are used. Using this approach, the structure types of serial mechanisms with the specified ranks and the specified degree of freedom (DOF) are synthesized firstly. After that, using the structure types of the obtained serial mechanisms, structure types of over-constrained single-loop KCs with the specified ranks and the specified DOF can be generated in a straightforward way. The structure types of the obtained serial mechanisms can be used as branches of parallel mechanisms. The structure types and the ranks of the obtained over-constrained single-loop KCs can be used to calculate the DOF of multi-loop mechanisms. In fact, the systematic approach proposed in this paper is a key component of the systematic approach for structure synthesis of parallel mechanisms.

A Mobility Determination Method for Parallel Platforms Based on the Lie Algebra of SE(3) and Its Subspaces

“…2. Yang and his coworkers [17][18][19][20][21][22] developed a method for the synthesis of kinematic chains, including parallel platforms, that also determines their mobility. At first sight, Yang's method uses neither group theory nor screw theory.…”

“…The intersection of the POC matrices requires 6 linear rules or criteria for rotational elements, and 6 linear rules or criteria for translational elements, [21]. Besides, the POC matrix composition requires 2 linear rules or criteria, and 1 nonlinear rule or criterion for translational elements, [22]. Finally, Yang and his coworkers published a book, [20].…”