User guide
176
6000 Series Programmer's Guide
The table below shows these relationships. The arm is directly driven with a servo motor
having 4096 steps per revolution. The table shows increments of 30 degrees, which is about
341 servo motor steps, or about .524 slave inches measured around the circumference described
by rotation of the arm. The plastic flow is measured with an encoder giving 1000 steps per
inch of flow. To maintain ratios in terms of inches, FOLRD will always be 1000. The required
FOLRN value is simply the inverse of the arm’s horizontal velocity component multiplied by
the number of slave steps per inch. The corresponding ratio in terms of surface speeds is given
in parentheses. The required FOLMD is the number of master steps corresponding to the
horizontal component of slave rotation.
Arm angle,
degrees
Horizontal
component
(in.) = cos(deg)
FOLMD =
1000 * delta cos(deg)
Horizontal vel
component = -sin(deg)
Required FOLRN =
-651.9/sin(deg)
210 -0.866 n/a 0.500 1304 (2:1)
240 -0.500 366 0.866 753 (1.155:1)
270 0.000 500 1.000 652 (1:1)
300 0.500 500 0.866 753 (1.155:1)
330 0.866 366 0.500 1304 (2:1)
The profile that we construct from these number is meant to approximate the inverse sine
function in the last column, but of course, will actually be a series of ramps and constant ratio
segments. Let’s review the Compiled Following Move Distance Calculations to determines
the exact shape and error in the first motion segment( from 210 to 240 degrees). First, we need
to determine if the ramp or constant ratio is first for that segment. Using ratios and distances
in inches, we have:
R1 = 2 ;starting ratio
R2 = 1.155 ;final ratio
D = (2*pi)/12 = .524 ;distance at stamp hinge
FOLMD=.366 ;travel along plastic
We find (R1+R2) * FOLMD/2 = .577, which is greater than D, so the “Ramp First”
equations apply to this segment. Let’s examine the error at the junction between the ramp and
constant ratio portion of this segment.
MD1 = [D - (R2 * FOLMD)] / ( (R1 - R2) / 2) = 0.239 master inches
D1 = 0.5 * (R1 + R2) * MD1 = 0.377 slave inches at circumference = 21.6 degrees
cos(210+21.6) - cos(210) = -0.621 - (-0.866) = 0.245 inches slave horizontal travel
error = horizontal slave travel - master travel = 0.245 - 0.239 = 0.006 inches
A similar calculation may be done for the “elbow” of the next of the next segment, and
symmetry indicates these errors will be the same between 270 and 330 degrees. The error along
intermediate points may be found with linear interpolation of ratio and master distance. In this
case, the errors fall within manufacturing tolerance. If the errors were too large, the travel
could be broken into more segments, each with exactly correct positions and ratios at their
boundaries.
So far, we have only discussed the portion of the profile which lowers and raises the stamp.
During the remainder of the profile, the arm must continue its rotation to bring the stamp to
its starting position in time for the next mold. The mold is 3 inches long, and .4 inches are
needed between molds for strength at the edges. This makes the total master cycle 3.4 inches
long. The total slave cycle must be 4096 steps, so the segments required to bring the arm
around must complete the portions of master and slave cycles not already accounted for. We
will create two segments, which divide the remaining master and slave travels in two, and are
mirror images of each other. The average ratio of these two segments must simply be slave
travel divided by master travel, i.e., (D / FOLMD). As previously determined, the FOLRN value
for the boundaries of the stamping portion of the profile is 638. From this value and the
average ratio, we can calculate the peak FOLRN value.
D = 0.5 * remaining slave = 0.5 * (4096 - 4 * 341) = 1366
FOLMD = 0.5 * remaining master = 0.5 * [1000 * (3.4 - 2 * 0.866)] = 834
peak ratio = FOLRN/1000
0.5 * (FOLRN/1000 + 1304/1000) = average ratio = D
/ FOLMD = 1366 / 834 = 1.638
FOLRN = 1972 (solved from above)