Singularity Analysis of Spatial Mechanisms Using Dual Polynomials and Complex Dual Numbers

Abstract

Complex dual numbers w̌ = x + iy + εu + iεv which form a commutative ring are introduced in this paper to solve dual polynomial equations numerically. It is shown that the singularities of a dual input-output displacement polynomial equation of a mechanism correspond to its singularity positions. This new method of identifying singularities provides clear physical insight into the geometry of the singular configurations of a mechanism, which is illustrated through analysis of special configurations of the RCCC spatial mechanism. Numerical solutions for dual polynomial equations and complex dual numbers are conveniently implemented in the CH language environment for analysis of the RCCC spatial mechanism.