Abstract:

To study the displacement mechanism of the spatial five-link RCRCR, dual-number matrices are adopt to set up mathematic model and close-form equation. Firstly, 3×3 unitary matrix and Euler formula are introduced to make some dual-number matrices diagonalizable, then, to find relationships, the primary part and dual part are decomposed to derive a 4th degree input-output polynomial equation with a single unknown by symbolic computation. At last, other middle variables are solved. Numerical example confirms that the numbers of analytical solutions for five-link RCRCR mechanism are 4.

Key words: RCRCR mechanism, displacement analysis, dual-number matrices, unitary matrix, Euler formula