Versor Functions

In this chapter, several different types of versor functions are discussed, which demonstrate interesting relationships between Fourier series of complexvalued functions, coupled twists, space curves in n dimensions, and a special type of polynomial curve, Pythagorean-hodograph (PH) curves. All of these stem from a fundamental versor function F : R ↣ G_p,q dened as F : t 7↣ A(t)N Ã(t) ; N E G_p;q , A : R ↣ G _p,q ; where Gp,q denotes the Clifford group of G_p,q (cf. Sect. 3.3).

The chapter consists of two main parts: a discussion of coupled motors and a discussion of PH curves. Coupled motors occur quite naturally in the treatment of robotic arms and kinematic chains in general [150, 161]. It is shown how this is related to cycloidal curves and Fourier descriptors of planar curves. The discussion of coupled motors is concluded with a brief discussion of space curves in higher dimensions generated through coupled motors.