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Planes, Axes and Angles
Circular motion always takes place on a given plane, from a start angle to an end angle. The arc angle is the difference between these angles. The arc axis is the vector perpendicular to the arc plane. In addition, the direction of the motion is either Clockwise (CW) or Counter-Clockwise (CCW). CCW motion is defined by a positive arc angle, while a CW motion is defined by a negative arc angle. For instance, a CCW from angle 10 to 40 is defined as an arc of 30 degrees (CCW). The reverse motion, from 40 to 10 is defined as an arc of -30 degrees (CW).
The following diagram illustrates the arc parameters for a CCW motion.
GPP2 defines three major planes. On each plane, it is important to define the axis which serves as the zero angle, as well as the direction for positive angle motion (CCW).
|
Major Plane |
Angle zero |
Direction of Counter-Clockwise Motion |
|
X-Y |
X axis |
X à Y |
|
Y-Z |
Y axis |
Y à Z |
|
Z-X |
Z axis |
Z à X |
The Z-X axis is defined from Z to X, not the other way around. This is consistent with the way right-hand coordinate systems are defined.
The three major planes are illustrated in the following diagram.
Each major plane may be viewed from both sides. For example, the X-Y plane is typically viewed from the Z axis (from the top). For circular motions, the arc axis is aligned with the Z axis. But the same plane could also be viewed from the -Z axis (from below), in which case the arc axis is reversed.
For the reverse major planes, the meaning of CW and CCW motion is reversed. The following diagram illustrates this duality on the X-Y plane. Consider a motion from the X axis (angle 0) to the Y axis (angle 90). Two tools are shown, one coming from the top, with its orientation vector aligned with the Z axis (0,0,1), while the other coming from the bottom, with its orientation vector aligned with the -Z axis (0,0,-1). It can be clearly seen that the same motion, from 0 to 90, represents a CCW motion for the first tool, and a CW motion for the second.
Angles on a plane are cyclic by nature. Typically, the angles in GPP2 range from -180 to 180. However, GPP2 will also use angles ranging up to 360, in order to keep the definition of CW and CCW motions consistent. Specifically, GPP2 will choose the angles that satisfy the following rules:
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In CCW motion, the end angle is always bigger than the start angle.
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In CW motion, the end angle is always smaller than the start angle.
The following diagram and table shows the angles used by GPP2, as well as how GPP2 presents CW and CCW motions in simple and complex cases:
|
Motion From |
Direction |
Arc Angle |
Start Angle |
End Angle |
|
A à B |
CCW |
90 |
0 |
90 |
|
A à B |
CW |
-270 |
360 |
90 |
|
B à A |
CCW |
270 |
90 |
360 |
|
B à A |
CW |
-90 |
90 |
0 |
|
A à C |
CCW |
180 |
0 |
180 |
|
A à C |
CW |
-180 |
360 |
180 |
|
C à A |
CCW |
180 |
180 |
360 |
|
C à A |
CW |
-180 |
180 |
0 |
|
B à D |
CCW |
180 |
90 |
270 |
|
B à D |
CW |
-180 |
90 |
-90 |
|
D à B |
CCW |
180 |
-90 |
90 |
|
D à B |
CW |
-180 |
270 |
90 |
The direction is defined for the standard arc axis and the standard major planes. When viewing the plane from the reverse direction, all directions are reversed (CW becomes CCW, and vice versa).
Full 360 degrees are supported. The arc angle will be 360 for CCW arcs, and -360 for CW arcs.
In full 360 degrees circles, the end point is the same as the start point. As most post-processors define these variables (X/Y/Z_CURPOS) as modal, they will not be set by this circle (as their value does not change). This will result in no output for the end point. To overcome this, GPP2 will force both the center (X/Y/Z_CENTER) and end point (X/Y/Z_CURPOS) variables to be set on for 360 degree circles.
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