Programming with dual numbers and its applications in mechanisms design

Abstract

Dual numbers are expressed in the form x+ɛy where ɛ2. Dual metanumbers are defined in this paper as DualZero, DualInf and DualNaN. The extended dual plane and the extended finite dual plane are introduced to describe dual numbers and dual metanumbers. Handling of dual numbers in the CH programming language is presented. The I/O, arithmetic and relational operations, and built-in mathematical functions are defined for both dual numbers and dual metanumbers. As a result of polymorphism, the syntaxes of dual arithmetic and relational operations, and built-in dual functions are the same as those for real and complex numbers in the CH programming language. The valid lvalues related to dual numbers in CH are defined. The computation of the motion screw for a rigid-body displacement is used as an example to illustrate the creation of user's dual functions. The efficacy of CH programming with dual numbers is demonstrated by displacement analysis of an RCCC mechanism. For the first time, dual data is handled as a built-in data type in a general-purpose computer programming language. Programming with dual numbers in CH is simpler than in any other computer programming language.