
TMC428 DATA SHEET (V. 1.00 / February 12, 2001)
38
Copyright 2000, TRINAMIC Microchips GmbH
M I C R O C H I P S
38
The shape parameter
s
selects one of three functions f
box
(
f
), f
circle
(
f
), f
rhomb
(
f
) respectively a superposition of
two of them. The shape parameter
s
= 0
selects the function f
circle
(
f
) which is the sine function sin(
j
) as
used for sine cosine micro stepping. With this, one gets the unit circle (
r
=1.0) by transformation to
cartesian coordinates {
y
= sin(
j
);
x
= cos(
j
)} as outlined in Figure 16, a shape parameter
s
= +1.0 results
in a box, and a shape parameter
s
= -1.0 results in a rhomb. Other values except those, result in
something between box and circle respectively something between circle an rhomb.
The data values y(i) of the look-up table range from 0 to 63 and the argument i ranges also from 0 to 63.
In the following, natural angles (radians) ranging from (0
=
j
< 2
p
) are used for the description. The three
functions for superposition controlled by the shape parameter
s
are
j
p
j
j
j
p
4
j
p
4
j
j
p
j
=
=
sin(
≥
<
≤
=
2
)
(
)
)
(
2
1
0
2
4
)
(
hom
b
r
circle
box
f
f
if
if
f
All together, these three functions are combined to form the function
0
0
0
)]
(
)
(
[
)
(
)
(
)]
(
)
(
[
)
(
)
(
hom
<
=
>
+
+
=
s
s
s
j
j
s
j
j
j
j
s
j
j
s
for
for
for
f
f
f
f
f
f
f
f
b
r
circle
circle
circle
circle
box
circle
So, the shape parameter
s
selects the type of function and it also provides a continuous transition
between circle and box respectively circle and rhomb. To estimate, what function would be best for a
given type of stepper motor, one can try micro stepping based on different shape parameters
s
by
downloading different micro step tables on-the-fly into the TMC428 during motion of a stepper motor.
For calculation of data for the micro step look-up table of the TMC428, one has to replace
j j
i
ranging
from 0 to
p
/2 for the quarter period by
}
63
,...,
3
=
64
2
=
i
with
i
i
p
j
.
The amplitude of the shape function f
s
(
f
i
) has to be limited to the range of 0.0 to 1.0 respectively to the
range of 0 to 63 for the on-chip RAM as described in the beginning of the micro stepping section.
Partial look-up table initialization option
A partially initialized micro step table may be sufficient, if all stepper motors– except those driven in full
step mode –are proposed to use the same micro step resolution constantly before a single micro step is
processed. But with a partial initialized micro step look-up table, the micro step resolution
must not be
changed
anyway. So, a partially initialized look-up table should be taken into account only, if it is a must
because of small memory of proposed used micro controller. Instead of partial initialization of the look-up
table of the TMC428, initialization the look-up table with a triangular function f
rhomb
(
j
) would be a much
better choice.