Kinematic and Dynamic Analysis of Spatial Six Degree of Freedom ...

Chapter 2
SCREW KINEMATICS
In this thesis, the tool used to derive the kinematic equations is called as the screw
theory. In this chapter, the screw theory is explained in detail.
2.1 Definition of a Unit Screw in Space
where
A screw can be described as a dual vector as in figure 2.1.
x
P
L
N
e : the unit vector of screw axis
Figure 2.1 – A unit screw in space
E e +
o
e : moment of e wrt. the origin of fixed coordinate system
w: Clifford operator (w 2 =0)
z
R
o
= we
(2.1)
Equation (2.1) is the definition of a unit screw. Screw algebra is the vector algebra of
this dual vector. A screw can be described using three dual coordinates in space as
o
e
Q M
y
e
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