Joint (no mass, no inertia) that describes an ideal rolling wheel (rolling on the plane z=0)


This information is part of the Modelica Standard Library maintained by the Modelica Association.

A joint for a wheel rolling on the x-y plane of the world frame. The rolling contact is considered being ideal, i.e. there is no slip between the wheel and the ground. This is simply gained by two non-holonomic constraint equations on velocity level defined for both longitudinal and lateral direction of the wheel. There is also a holonomic constraint equation on position level granting a permanent contact of the wheel to the ground, i.e. the wheel can not take off.

The origin of the frame frame_a is placed in the intersection of the wheel spin axis with the wheel middle plane and rotates with the wheel itself. The y-axis of frame_a is identical with the wheel spin axis, i.e. the wheel rotates about y-axis of frame_a. A wheel body collecting the mass and inertia should be connected to this frame.


To work properly, the gravity acceleration vector g of the world must point in the negative z-axis, i.e.

inner Modelica.Mechanics.MultiBody.World world(n={0,0,-1});

Parameters (2)



Type: Radius (m)

Description: Wheel radius


Value: StateSelect.always

Type: StateSelect

Description: Priority to use generalized coordinates as states

Connectors (1)


Type: Frame_a

Description: Frame fixed in wheel center point. x-Axis: upwards, y-axis: along wheel axis

Used in Components (1)



Ideal rolling wheel on flat surface z=0 (5 positional, 3 velocity degrees of freedom)