Page 206 - Electrical Engineering Dictionary

I
to one set of 2 sets of output lines. Compare matrix for adjacent coordinate frames has the
with multiplexer. following form:

demultiplexing the inverse operation of
 
multiplexing that enables the transmission of cos q i − cos α i sin q i sin α i sin q i a i cos q i

i−1  sin q i cos α i cos q i − sin α i cos q i a i sin q i 
two or more signals on the same circuit or A i =  0 sin α i cos α i d i 

communication channel. 0 0 0 1
Denavit–Hartenberg notation a system
denormalized number nonzero number
that describes the translational and rotational
whose leading significand bit is zero and
relationships between adjacent links. The
whose exponent has a fixed value. These
D-H representation results in 4 × 4 homo-
numbers lie in the range between the smallest
geneous transformation matrix representing
normalized number and zero.
each link’s coordinate system at the joint with
respect to the previous link’s coordinate sys-
density estimation statistical methods
tem. The D-H representation of a rigid link
for estimating the probability density from
depends on four geometric parameters as-
a given set of examples.
sociated with each link. Every coordinate
frame is assigned according to the three rules:
density function (DF) an alternative
1. The z i−1 axis lies along the axis of mo-
name for probability density function (PDF).
tion of the ith joint.
2. The z i axis is normal to the z i−1 axis,
density matrix representation for the
and pointing away from it.
wave functions of quantum mechanics in
3. The y i axis completes the right-handed terms of binary products of eigenfunction ex-
coordinate system as required. pansion amplitudes; with ensemble averag-
Referring to the figure, the four D-H param- ing the density matrix representation is con-
eters are defined as follows: venient for phenomenological inclusion of
• q i is the joint angle from the x i−1 axis to the relaxation processes.
x i axis about the z i−1 axis (using the right-
hand rule), density matrix formalism of quantum me-
chanics a mathematical formulation of the
• d i is the distance from the origin of the
theory of quantum mechanics more general
(i − 1)-th coordinate frame to the intersec-
tion of the z i−1 axis with the x i axis along than those based on a description in terms
z i−1 axis, of a wavefunction or a state vector, because
it can treat situations in which the state of
•a i istheoffsetdistancefromtheintersection
the system is not precisely known. The den-
of the z i−1 axis with the x i axis to the origin
sity matrix formalism is often used in laser
of the ith frame along the x i axis (in another
physics and in nonlinear optics, for example,
words it is the shortest distance between the
under situations in which collisional dephas-
z i−1 and z i axes),
ing effects are important.
• α i is the offset angle from the z i−1 to the z i
axis about the x i axis (using the right-hand
dependability system feature that com-
rule).
bines such concepts as reliability, safety,
Forarevolutejointd i , a i , andα i arecalledthe maintainability, performance, and testability.
link parameters or joint parameters and re-
main constant. q i is called the joint variable. dependency a logical constraint between
For a prismatic joint, q i , a i , and α i are the link two operations based on information flow-
parameters and remain constant, while d i is ing among their source and/or destination
the joint variable. The D-H transformation operands; the constraint imposes an ordering

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2000 by CRC Press LLC