Complex dual numbers wˇ = 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.
Complex dual numbers w̌1=x1+iy1+εu1+iεv1 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.
Automatic breast compression devices are commonly fitted to mammographic x-ray sets. The force exerted by these compression devices should be limited and periodically checked. This article describes the design and construction of an instrument for the routine assessment of the force applied by breast compression devices on mammography x-ray sets. Results obtained on four different mammography x-ray units are presented. In addition, data on the effect of compression plate design on compression force is given for one unit. The instrument has proved to be a simple and quick method of monitoring the force applied by the compression plates on mammographic x-ray units.
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