Danaher Motion
06/2005
Appendix B
M-SS-005-03 Rev
E
171
APPENDIX B
N
ON
-H
OMOGENOUS
G
ROUPS
Non-homogenous groups consist of different axes, both rotary and linear. A feature was
added to support the definition of velocities for non-homogenous groups. In the setup, rotary
and linear axes are declared. The system determines if it is a linear- or rotary-dominant
group. For example, in SCARA robot, there are two rotary axes for the first and second joints
and another rotary axis for the last joint (roll). There is only one linear axis (the Z axis). Such
a system is rotary-dominant.
Another example is the OCP system, which is an XY Gantry system with the last two axes
taken from the SCARA. Here, there are two linear (X & Y) axes and another linear (Z axis)
with just one rotary axis (roll). In this case, the system is linearly-dominant.
Axis setup defines the group behavior. Each axis must be declared whether it is linear or
rotary by setting
POSITIONROLLOVERENABLE
to either zero(0) for linear or one (1) for
rotary.
Kinematics
In non-homogenous groups, commanded velocity is always given according to the group
dominancy type. If the group is linearly-dominant, the velocity (
VCRUISE
,
VFINAL
) is in
linear units (mm/sec). The other non-linear axes are checked in the preparation phase of the
movement. The velocity in these axes cannot exceed the maximum value. If it does, the
overall (group) velocity is reduced.
There is only one exception to this rule. This is when a group movement is issued with only
one axis in motion and all the others are stopped. Then, the given value of the velocity is
taken directly in the units for that axis. For example, having movement on the third axis of
the SCARA robot, the velocity value is in mm/sec.
The same is true for both acceleration and jerk values for group-interpolated motion.
C
OORDINATE
S
YSTEMS
Having different world and joint coordinates make the robot kinematics unique. The world
coordinates are normally perceived as working coordinates of an application. Usually, there
is some form of Cartesian coordinate system originating in the robot base.
Another set of coordinates is added for the orientation of the end-effector (gripper, etc.). The
orientation of a body in space is normally described by three angles. Depending on the
number of degrees of freedom (motors used to actuate the orientation joints), they could be
unequal. The world space coordinates are given by its position part (X, XY or XYZ tupple), in
most cases. In general, it could be anything from sphere coordinates to cylindrical system.
The orientation component can use many forms for describing orientation. The most used
coordinate system for orientation angles are Euler angels: yaw, pitch and roll. The Euler
angles can have two or more variations, according to the order of the accepted rotations
(XYX, XZX etc.).
The joint space of a robot is a relatively simple concept. A joint coordinate is a number
uniquely describing the position of a robot segment relative to the previous robot segment. If
the joint connecting the segment is rotary, the joint coordinates are in degrees of the rotation
angle. If it is linear, the joint coordinates are the linear displacement (millimeters).
