Coordinate Systems in Vehicle Dynamics Blockset

Vehicle Dynamics Blockset™ uses these coordinate systems to calculate the vehicle dynamics and position objects in the 3D visualization environment.

Environment	Description	Coordinate Systems
Vehicle dynamics in Simulink®	The right-hand rule establishes the X-Y-Z sequence and rotation of the coordinate axes used to calculate the vehicle dynamics. The Vehicle Dynamics Blockset 3D simulation environment uses these right-handed (RH) Cartesian coordinate systems defined in the SAE J670[2] and ISO 8855[3] standards: Earth-fixed (inertial) Vehicle Tire Wheel The coordinate systems can have either orientation: Z-down — Defined in SAE J670[2] Z-up — Defined in SAE J670[2] and ISO 8855[3]	Earth-Fixed (Inertial) Coordinate System Vehicle Coordinate System Tire and Wheel Coordinate Systems
3D visualization engine	To position objects and query the 3D visualization environment, the Vehicle Dynamics Blockset uses a world coordinate system. You can also set the coordinate system of the actors in the visualization environment.	Coordinate Systems for 3D Visualization

Earth-Fixed (Inertial) Coordinate System

The earth-fixed coordinate system (X_E, Y_E, Z_E) axes are fixed in an inertial reference frame. The inertial reference frame has zero linear and angular acceleration and zero angular velocity. In Newtonian physics, the earth is an inertial reference.

Axis	Description
XE	The XE axis is in the forward direction of the vehicle. The XE and YE axes are parallel to the ground plane. The ground plane is a horizontal plane normal to the gravitational vector.
YE
ZE	Vertical, positive downward, parallel to gravitational vector. To transform from the Z-down orientation to the Z-up orientation apply a positive rotation of 180 degrees on the X-axis.

Vehicle Coordinate System

The vehicle coordinate system axes (X_V, Y_V, Z_V) are fixed in a reference frame attached to the vehicle. The origin is at the vehicle sprung mass.

Z-Down Orientation

Axis	Description
XV	The XV axis points forward and is parallel to the vehicle plane of symmetry.
YV	The YV axis is perpendicular to the vehicle plane of symmetry. In the Z-down orientation: YV axis points to the right ZV axis points downward
ZV

Tire and Wheel Coordinate Systems

The tire coordinate system axes (X_T, Y_T, Z_T) are fixed in a reference frame attached to the tire. The origin is at the tire contact with the ground.

The wheel coordinate system axes (X_W, Y_W, Z_W) are fixed in a reference frame attached to the wheel. The origin is at the wheel center.

Z-Up Orientationa	Z-Down Orientation
a Reprinted with permission Copyright © 2008 SAE International. Further distribution of this material is not permitted without prior permission from SAE.

Axis	Description
XT	XT and YT are parallel to the road plane. The intersection of the wheel plane and the road plane define the orientation of the XT axis.
YT
ZT	ZT points: Upward in the Z-up orientation Downward in the Z-down orientation
XW	XW and YW are parallel to the wheel plane: XW is parallel to the local road plane. YW is parallel to the wheel-spin axis.
YW
ZW	ZW points: Upward in the Z-up orientation Downward in the Z-down orientation

Other coordinate systems

Z-Up Orientation with Radii and Deflection Defined	TYDEX H-Coordinate System with Z-up Orientation

Coordinate Systems for 3D Visualization

The 3D visualization environment uses the world coordinate system to position the objects and query the environment. You can set the coordinate system of actors for precise transformations in the environment.

3D Environment Coordinate System

The 3D visualization environment uses a world coordinate system with axes that are fixed in the inertial reference frame.

Axis	Description
X	Forward direction of the vehicle Roll — Right-handed rotation about X-axis
Y	Extends to the right of the vehicle, parallel to the ground plane Pitch — Right-handed rotation about Y-axis
Z	Extends upwards Yaw — Left-handed rotation about Z-axis

Actor Coordinate Systems

To set the coordinate system of the actor use the Coordinate system parameter in the Simulation 3D blocks. These are the coordinate systems for actor transformation in the 3D environment.

Coordinate System	Block Setting	Description
World coordinate system	Default	The world uses the Unreal Engine® coordinate system. The Unreal Engine coordinate system is a left-handed Cartesian coordinate system, in m and rad. Axes X-axis points away from the viewer. Y-axis points to the right. Z-axis points upward. Rotation Roll — Clockwise rotation about X-axis Pitch — Clockwise rotation about Y-axis Yaw — Counterclockwise rotation about Z-axis
MATLAB® coordinate system	MATLAB	The MATLAB coordinate system is a right-handed Cartesian coordinate system with Z-up orientation, in m and rad. Axes X-axis points away from the viewer. Y-axis points to the left. Z-axis points upward. Rotation Roll — Clockwise rotation about X-axis Pitch — Clockwise rotation about Y-axis Yaw — Clockwise rotation about Z-axis
ISO 8855 standard coordinate system	ISO8855	The ISO 8855 [2] (Simulink 3D Animation) standard coordinate system is a right-handed Cartesian coordinate system with Z-up orientation, in m and deg. Axes X-axis points away from the viewer. Y-axis points to the left. Z-axis points upward. Rotation Roll — Clockwise rotation about X-axis Pitch — Clockwise rotation about Y-axis Yaw — Clockwise rotation about Z-axis
X3D ISO standard coordinate system	VRML	The X3D ISO standard coordinate system is a right-handed Cartesian coordinate system with Y-up orientation, in m and rad. Axes X-axis points away from the viewer. Y-axis points upward. Z-axis points to the right. Rotation Roll — Clockwise rotation about X-axis Pitch — Clockwise rotation about Y-axis Yaw — Clockwise rotation about Z-axis
SAE coordinate system	SAE or AERO	The SAE J670 standard coordinate system is a right-handed Cartesian coordinate system with Z-down orientation, in m and rad. This is defined in the SAE J670[1] (Simulink 3D Animation) standard. This coordinate system is used for aerospace applications. For more information, see Body Coordinates (Aerospace Blockset). Axes X-axis points away from the viewer. Y-axis points to the right. Z-axis points downward. Rotation Roll — Clockwise rotation about X-axis Pitch — Clockwise rotation about Y-axis Yaw — Clockwise rotation about Z-axis

References

[1] Gillespie, Thomas. Fundamentals of Vehicle Dynamics. Warrendale, PA: Society of Automotive Engineers, 1992.

[2] Vehicle Dynamics Standards Committee. Vehicle Dynamics Terminology. SAE J670. Warrendale, PA: Society of Automotive Engineers, 2008.

[3] Technical Committee. Road vehicles — Vehicle dynamics and road-holding ability — Vocabulary. ISO 8855:2011. Geneva, Switzerland: International Organization for Standardization, 2011.

[4] Unrau, H.-J., and Zamow J. TYDEX-Format: Description and Reference Manual. Release 1.3, 1997.