Table of Contents
Advertisement
Axis-Angle
The Base Coordinate
System
(Please refer to the
figure 1)
Tool Coordinate
System
(Please refer to the
Rx / Ry / Rz representation also, using 3 values to represent the
pose (but not three rotation angles), which is the product of a
three-dimensional rotation vector [x, y, z] and a rotation angle [phi
(scalar)].
The characteristics of the axis angle:
Assume the rotation axis is [x, y, z], and the rotation angle is phi.
Then the representation of the axial angle:
[Rx, Ry, Rz] = [x * phi, y * phi, z * phi]
Note:
1. [x, y, z] is a unit vector, and phi is a non-negative value.
2. The vector length (modulus) of [Rx, Ry, Rz] can be used to
estimate the rotation angle, and the vector direction is the rotation
direction.
3. If you want to express reverse rotation, invert the rotation axis
vector [x, y, z], and the value of phi remains unchanged.
4. Using phi and [x, y, z] can also derive the attitude representation
as unit quaternion q = [cos (phi / 2), sin (phi / 2) * x, sin (phi / 2) *
y, sin (phi / 2) * z].
For example:
The vector of the rotation axis represented by the base coordinate
system is [1, 0, 0], and the rotation angle is 180 degrees (π), then
the axis angle representation of this pose is [π, 0, 0].
The rotation axis is [0.707, 0.707, 0] and the rotation angle is 90
degrees (π / 2), then the axis angle posture is [0.707 * (π / 2), 0.707
* (π / 2), 0].
The base coordinate system is a Cartesian coordinate system
based on the mounting base of the robotic arm and used to
describe the motion of the robotic arm.
(Front and back: X axis, left and right: Y axis, up and down: Z axis)
Consists of tool center point and coordinate orientation. If the TCP
offset is not set, the default tool coordinate system is located at
flange center.
For tool coordinate System based motion: The tool center point is
10
Advertisement
Table of Contents
