Euler Angles
Euler angles are a set of angles used to define the orientation of a rigid body in a 3D space. In any reference frame, the orientation of a rigid body can be represented by three angles of rotation about the axes of the reference frame. Euler angles can be described using different conventions, each offering multiple representations, depending on the coordinate system defining the rotation and the sequence of the three rotations.
Supported Euler Angle Conventions
The table below lists the correspondence between common Euler angle representations and the applicable robot brands. Euler angles displayed in both Mech-Vision and Mech-Viz follow Representation 1, while the software communication commands transmit corresponding Euler angle conventions.
Representation 1 |
Representation 2 |
Euler angle convention |
Applicable common robot brands |
X→Y→Z |
yaw, pitch, roll(WPR/RPY) |
sxyz(Static XYZ) |
FANUC，YASKAWA，DENSO，DOBOT，AUBO，HANS， JAKA，MELFA，FR，ROKAE，SIASUN，TM，ELITE， STEP，HYUNDAI，FLEXIV，DELTA，TOPSTAR，CGXI |
Z→Y'→X'' |
yaw, pitch, roll(WPR/RPY) |
rzyx(Rotated ZYX) |
ABB，KUKA，NACHI，EFORT，EPSON，ESTUN，INOVANCE |
Z→Y'→Z'' |
OAT |
rzyz(Rotated ZYZ) |
KAWASAKI，QJAR，COMAU，DOOSAN |
X→Y'→Z'' |
\ |
rxyz(Rotated XYZ) |
TURIN，STAUBLI，ADT |
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Euler angle conventions beginning with S (Static) describe the rotation of an object based on a fixed coordinate system. Assume a fixed coordinate system {A} and an object coordinate system {B} in space. Before rotation, the coordinate systems {A} and {B} coincide. First rotate the coordinate system {B} around the X-axis of {A} by an angle of γ, then around the Y-axis of {A} by an angle of β, and finally around the Z-axis of {A} by an angle of α to obtain the object’s final pose.
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Euler angle conventions beginning with R (Rotated) describe the rotation of an object based on the object’s own coordinate system. For example, Z→Y'→Z'' means “first rotate around the Z-axis, then round the new Y-axis, and finally around the new Z-axis”.