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. According to the coordinate system defining rotation and the sequence of the three rotations, Euler angles can be classified into various types, each with multiple representations.
Supported Euler Angle Conventions
The table below lists the correspondence between common Euler angle representations and the applicable robot brands. Euler angles are displayed in Representation 1 in the Mech-Vision and Mech-Viz, while the software communication commands transmit corresponding Euler angle conventions.
Representation 1 |
Representation 2 |
Euler angle convention |
Applicable and 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 a body-fixed 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 a body-fixed 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”.