User Manual

12
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XYZXYZ
A
B
RRRR =,,
Note: γ corresponds to roll; β corresponds to pitch; α corresponds
to yaw.
Axis-Angle
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
(please refer to the
figure 1)
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)
Tool Coordinate
Consists of tool center point and coordinate orientation. If the TCP