Danaher Motion
06/2005
Appendix B
M-SS-005-03 Rev
E
179
Cartesian Profile
For kinematics parameters of straight-line (
MOVES
) motion (velocity, acceleration,
deceleration), different joint parameters are obtained, depending on where in the robot
working space the starting line is positioned. The further from the origin, the smaller joint
velocities are obtained. Contrary to that, the closer to the origin the point is, the smaller the
inertia and higher the acceleration.
To optimally exploit robot capabilities, execute motions nearer to the origin with smaller
Cartesian velocities to avoid exceeding the maximum joint velocity. Movements near the
limits of the working space are farther from the robot origin and have higher robot inertia.
Lower acceleration must be applied to avoid exceeding the maximum joint values.
You must know at least two values (threshold of arm radius where reduction begins and end
point of reduction at straight arm) for all joints. Limits must be considered for the joint. The
whole Cartesian path and all Cartesian interpolation types (straight, circular, via) must be
considered.
Since joint velocity, acceleration, or jerk values cannot be exceeded, take the minimum of
the commanded Cartesian values (
VTRAN
,
ATRAN
,
DTRAN
,
JERKTRAN
,
VROT
,
AROT
,
DROT
and
JERKROT
) and account for the values in joint-space (
VCRUISE
,
ACC
,
DEC
,
JERK
).
Cruise velocity cannot vary. Use a constant cruise value. Leave the principal profile
acceleration and deceleration phase as it is. Acceleration and deceleration cannot vary
during the constant
ACC
/
DEC
phase. Use the highest acceleration in Cartesian space
possible that allows constant
ACC
/
DEC
phases without exceeding joint values. Acceleration
and deceleration may differ, and must be considered separately (mostly in long distance
moves where conditions vary widely for start and destination position). The same restrictions
apply to
JERK
.
Acceleration, deceleration and jerk reduction must be calculated and anticipated, depending
on payload and arm radius. The parameters for a simple scheme are:
threshold values for payload and arm radius where reduction begins
overall 100% reduction value per robot group
per-joint 100% reduction values
Since payload is static (varying only with tool change), this is easily accomplished in the
application. Use the following two mechanisms for Cartesian profiles:
C
artesian
V
elocity
A
daptation
(CVA) is according to the direction and position of the
movement in the working space. For each path, a point closest to the origin (X=0,Y=0)
is found and the Cartesian velocity of the whole motion is reduced according to the
values of joint velocities at that point.
C
artesian
A
cceleration/
D
eceleration/
J
erk
A
daptation (CADJA), where values of jerk,
acceleration and deceleration are reduced according to the relative distance from the
point of origin in reference to the maximum radius of the robot. The reduction
(
INERTIATHRESHOLD
) is active only from a certain distance (radius). The maximum
reduction value is defined at the final point (the fully stretched arm). For all points
between these two values (INERTIATHRESHOLD = 100%), the reduction value is
linearly interpolated. Acceleration is reduced according to the initial point of the
movement. Deceleration is reduced according to the final point of the movement. The
jerk value is reduced according to the average of the two reduction values (for initial
and final point).
