The isomorphism identification of reducible performance for parallel mechanisms

In this article, the concept of reducible performance is introduced from the viewpoint of the incidence relationship between kinematic outputs and actuating inputs for parallel mechanisms. The theoretic basis of an eigensystem approach is studied, and practical applications are discussed. Finally, a new matrix is proposed, which contains at least one distinct eigenvalue based on the incidence relationship matrix, and the eigensystem approach is used to identify the isomorphism of the new matrices. By using the proposed matrices, the eigensystem approach is used to identify the isomorphism of reducible performance for heavy-payload manipulators. The results show that the eigensystem approach is effective in the isomorphism identification of reducible performance.

Application of Stiffness Decompositions to Synthesis by Springs

Stiffness decompositions originating from two distinct eigenvalue problems are applied to stiffness synthesis by springs. The resulting free-vector and line-vector syntheses provide a clear geometric explanation of the methods. Numerical examples and algorithms are also provided to verify the results.