Navigation:  Library > Iconic Diagrams > Mechanical > Translation > 3DSmallRotation >


Previous pageReturn to chapter overviewNext page


Iconic Diagrams\Mechanical\Translation\3DSmallAngles


Domains: Continuous. Size: 6D. Kind: Iconic Diagrams (Translation,Rotation).


This is a model of a 6 degree of freedom body. It is the equivalent of the 2D-body model. The first three degrees of freedom in this model are represented by a single mass and the last three degrees of freedom by a rotational inertia. The 3D-body has to be connected to at least three orthogonal 3D-points, which define the reaction forces.


The model has a preferred velocity out causality. The corresponding constitutive equations then contain an integration. The model can also have the non-preferred force out causality. The constitutive equations then contain a differentiation. Because any number of connections can be made, successive ports are named P1, P2, P3 etc. 20-sim will automatically create equations such that the resulting force P.F is equal to the sum of the forces of all connected ports P1 .. Pn. The velocities of all connected ports are equal to P.v


P.F = sum(P1.F, P2.F, ....)

P.v = P1.v = P2.v = ....


velocity out causality (preferred):


I = [1/M;1/M;1/M;1/J[1];1/J[2];1/J[3]];

P.v = I.*int(P.F);


force out causality:


I = [1/M;1/M;1/M;1/J[1];1/J[2];1/J[3]];

P.F = I-1.*ddt(P.v);





Port with 6 degrees of freedom. Any number of connections can be made.



preferred velocity out






Mass [kg].

Moment of inertia for three axes [kgm2]



A body has to be connected to 3D-points with at least three orthogonal nonzero offsets to prevent it from free rotation.
A 3D-body has to be connected to at least three orthogonal 3D-point models to prevent it from free motion.
Flipping or rotating the model does not change the direction of applied forces or measured directions. Preferably leave the orientation as it pops up on the screen.
It is not possible in 20-sim to use vector elements with mixed units. Therefore element number 4 to 6 will be displayed with units [m/s] and [N] although it really is [rad/s] and [Nm]!