Locations can be specified in two ways in V+, transformations and precision points.
A transformation is a set of six components that uniquely identifies a location in Cartesian space and the orientation of the motion device end-of-arm tooling at that location. A transformation can also represent the location of an arbitrary local reference frame.
A precision point includes an element for each joint in the motion device.
Rotational joint values are measured in degrees; translational joint values are measured in millimeters. These values are absolute with respect to the motion device’s home sensors and cannot be made relative to other locations or coordinate frames.
Chapter 8 Location Variables
Coordinate Systems
Figure 8-1 shows the world coordinate system for an Adept SCARA robot and an Adept Cartesian robot. Ultimately, all transformations are based on a world coordinate system. The V+ language contains several instructions for creating local reference frames, building relative transformations, and changing the origin of the base (world) coordinate frame. Therefore, an individual transformation may be relative to another transformation, a local reference frame, or an altered base reference frame.
Different robots and motion devices will designate different locations as the origin of the world coordinate system. See the user’s guide for Adept robots or the device module documentation for AdeptMotion VME systems to determine the origin and orientation of the world coordinate frame.
Figure 8-1. Adept Robot Cartesian Space
adept
+Z
+X
+Y +X
+Y +Z
Chapter 8 Location Variables
Transformations
The first three components of a transformation variable are the values for the points on the X, Y, and Z axes. In an Adept SCARA robot, the origin of this
Cartesian space is the base of the robot. The Z axis points straight up through the middle of the robot column. The X axis points straight out, and the Y axis runs left to right as you face the robot. The first robot in Figure 8-1 on page 181 shows the orientation of the Cartesian space for an Adept SCARA robot. The location of the world coordinate system for other robots and motion devices depends on the kinematic model of the motion device. For example, the second robot in Figure 8-1 shows the world coordinate frame for a robot built on the Cartesian
coordinate model. See the kinematic device module documents for your particular motion device.
When a transformation is defined, a local reference frame is created at the X, Y, Z location with all three local frame axes parallel to the world coordinate frame.
Figure 8-2 on page 183 shows the first part of a transformation. This trans-formation has the value X = 30, Y = 100, Z = 125, yaw = 0, pitch = 0, and roll = 0.
Chapter 8 Location Variables
Figure 8-2. XYZ Elements of a Transformation
The second three components of a transformation variable specify the orientation of the end-of-arm tooling. These three components are yaw, pitch, and roll. These elements are figured as ZYZ' Euler values. Figures 8-3 through 8-5 demonstrate how these values are interpreted.
Yaw
Yaw is a rotation about the local reference frame Z axis. This rotation is not about the primary reference frame Z axis, but is centered at the origin of the local frame of reference. Figure 8-3 on page 184 shows the yaw axis with a rotation of 30°.
Note that it is parallel to the primary reference frame Z axis but may be centered at any point in that space. In this example, the yaw value is 30°, resulting in a transformation with the value (X = 30, Y = 100, Z = 125, yaw = 30, pitch = 0, and roll = 0).
Z
X Y
z
x y
y = 100
x = 30
z = 125
Chapter 8 Location Variables When you are using a robot, the local frame of reference defined by the XYZ components is located at the end of the robot tool flange. (This local reference frame is referred to as the tool coordinate system.) In Figure 8-3, the large
Cartesian space represents a world coordinate system. The small Cartesian space represents a local tool coordinate system (which would be centered at the motion device tooling flange).
Figure 8-3. Yaw Z
X
Y
30°
Z
X Y
Chapter 8 Location Variables
Pitch
Pitch is defined as a rotation about the local reference frame Y axis, after yaw has been applied. Figure 8-4 on page 186 shows the local reference frame with a yaw of 30° and a pitch of 40°.
Chapter 8 Location Variables For example, deflection of a wrist joint is reflected in the pitch component. The movement of a fifth axis on a SCARA robot is reflected in the pitch component. In this example, the motion device end of arm tooling has a pitch of 40°, resulting in a transformation with the value (X = 30, Y = 100, Z = 125, yaw = 30, pitch = 40, and roll = 0). This location can be reached only by a mechanism with a fifth axis. Pitch is represented as ±180°, not as 360° of rotation. Thus, a positive rotation of 190° is shown as –170°.
Figure 8-4. Pitch
40°
PITCH Y-axis of local reference frame (after applying yaw)
Z
X
Y
X
Y
30°
Z
Chapter 8 Location Variables
Roll
Roll is defined as a rotation about the Z axis of the local reference frame after yaw and pitch have been applied. Figure 8-5 shows a local reference frame in the primary robot Cartesian space and the direction roll would take within that space.
In this example the transformation has a value of X = 30, Y = 100, Z = 125, yaw = 30, pitch = 40, and roll = 20. This location can be reached only by a mechanism with fifth and sixth axes.
Figure 8-5. Roll Z
X
Y 20°
ROLL
Z-axis of local reference frame (after applying yaw and pitch)
40°
30°
Z
X
Y
Chapter 8 Location Variables
Special Situations
When the Z axes of the local and primary reference frames are parallel, roll and yaw produce the same motion in the same plane, although the two motions may be in different directions. This is always the case with a four-axis SCARA robot.
The system automatically reflects rotation of the quill in the roll component of a transformation variable, and the yaw component is forced to 0°. In a SCARA robot equipped with a fifth axis, rotation of the quill is reflected in the yaw
component and motion of a rotating end-effector (sixth axis) is reflected in the roll component.
Notice in Figure 8-2 on page 183 that the local reference frame points straight up.
This corresponds to a situation where the end of arm tooling points straight back along the third axis. In a mechanism not equipped with a 360° wrist, this is an impossible position. For a four-axis SCARA, this component must point straight down (pitch = 180°). For a mechanism with a fifth axis, this component must be within the range of motion of the fifth axis.
NOTE: When thinking about a transformation, remember that the rules of ZYZ' Euler angles require that the orientation components be applied in order after the local reference frame has been defined.
After calculating the Cartesian components and placing a local reference frame with x, y, and z axes parallel to the primary reference frame X, Y, and Z axes, the orientation components are applied in a strict order—yaw is applied first, then pitch, and, finally, roll.
Chapter 8 Creating and Altering Location Variables