Harry H. Cheng and Sean Thompson
Complex dual numbers w = x + iy + eu + iev which form a commutative ring are for the first time introduced in this paper. Arithmetic operations and functions of complex dual numbers are defined. Complex dual numbers are used to solve dual polynomial equations. 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. Like the dual number, the complex dual number is a useful mathematical tool for analytical and numerical treatment of spatial mechanisms.