LIBRARY ı6ıul 0) - Cranfield University

_ p1e0a - pORoba
m31
Ilp!
- poll
(3.24)
where lipl - poll is the norm of the vector that results from subtracting p0 from p1
and is given by
IIP1- pOII = jpiiobor _ pOsoba)2 + piyabd _ pOyýr12 +I plsýr - pos ßr12
(3.25)
The matrix components m12, m22 and m32 form a unit vector which gives the
direction of the Y-axis of the table co-ordinates frame relative to the robot world co-
ordinates frame. Their values are obtained as follows:
m12 = p2Robot
_ p0%obot
Hp2-POII
p2yob" - p0y°ha
m22 IIp2
- pOII
p2Rob« - ARoba
m32 _ IIp2
- poll
(3.26)
(3.27)
(3.28)
where jjp2 - pOjl is the norm of the vector that results from subtracting p0 from p2
and is given by
IIp2- pOII =
J(p20b0e
_ pOR0a)2 +(p2ytd _ pORobd)2 +(p2R° _ pOR ):
(3.29)
The matrix components mi.;, m23 and mjj form a unit vector which gives the
direction of the Z-axis of the table co-ordinates frame relative to the robot world co-
ordinates frame. Their values are obtained by calculating a vector cross product
between the unit vectors that give the directions of the X-axis and the Y-axis of the
table co-ordinates frame relative to the robot's world co-ordinates frame. Equations
(3.30) to (3.32) give their calculated values.
1 13 = m21m32 -
m22m31 (3.30)
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