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Iconic Diagrams\Mechanical\Translation\3DSmallAngles

Implementations

XYZ

Use

Domains: Continuous. Size: 1-D/6-D. Kind: Iconic Diagrams (Translation,Rotation).

Description - X

A point model forms the connection between the single degree of freedom part of a system and the center of mass of a 3D-body.

The 3D-point-X model is the equivalent of the 2D-point-X model. It describes the translation of force in x-direction to a force in 6 degrees of freedom. Because there are three rotational degrees of freedom, the 3D-point-X model has two offsets, YP and ZP.

The single degree of freedom port p_in describes the connection in x-direction and the 6 degree of freedom port P_out describes connection with the 3D-body.

P_out.F[1] = p_in.F;

P_out.F[2] = 0;

P_out.F[3] = 0;

P_out.F[4] = 0;

P_out.F[5] = ZP*p_in.F;

P_out.F[6] = -YP*p_in.F;

p_in.v = P_out.v[1] - YP*P_out.v[6]

+ ZP *P_out.v[5];

// x-direction

// y-direction

// z-direction

// x-rotation

// y-rotation

// z-rotation

// x-direction

As can bee seen from the equations, a nonzero offset YP or ZP (distance from center of mass) in a 3D-point will result in a momentum. Therefore a 3D-body has to be connected to 3D-points with at least three orthogonal nonzero offsets to prevent it from free rotation.

The equations also show that the y-direction and z-direction are not affected by the 3D-point-X model. Therefore each 3D-body has to be connected to at least three orthogonal 3D-point models to prevent it from free motion.

Interface - X

Ports	Description
p_in P_out[3]	Translation port with one degree of freedom (x [m]). Port with 6 degrees of freedom.
Causality
fixed force out P_out fixed velocity out p_in
Parameters
YP ZP	Distance (y-direction) between connection and center of mass [m]. Distance (z-direction) between connection and center of mass [m].

Description - Y

A point model forms the connection between the single degree of freedom part of a system and the center of mass of a 3D-body.

The 3D-point-Y model is the equivalent of the 2D-point-Y model. It describes the translation of force in x-direction to a force in 6 degrees of freedom. Because there are three rotational degrees of freedom, the 3D-point-Y model has two offsets, XP and ZP.

The single degree of freedom port p_in describes the connection in x-direction and the 6 degree of freedom port P_out describes connection with the 3D-body.

P_out.F[1] = 0;

P_out.F[2] = p_in.F;

P_out.F[3] = 0;

P_out.F[4] = -ZP*p_in.F;

P_out.F[5] = 0;

P_out.F[6] = XP*p_in.F;

p_in.v = P_out.v[2] + XP*P_out.v[6]

- ZP *P_out.v[4];

// x-direction

// y-direction

// z-direction

// x-rotation

// y-rotation

// z-rotation

// y-direction

As can bee seen from the equations, a nonzero offset XP or ZP (distance from center of mass) in a 3D-point will result in a momentum. Therefore a 3D-body has to be connected to 3D-points with at least three orthogonal nonzero offsets to prevent it from free rotation.

The equations also show that the x-direction and z-direction are not affected by the 3D-point-Y model. Therefore each 3D-body has to be connected to at least three orthogonal 3D-point models to prevent it from free motion.

Interface - Y

Ports	Description
p_in P_out[3]	Translation port with one degree of freedom (x [m]). Port with 6 degrees of freedom.
Causality
fixed force out P_out fixed velocity out p_in
Parameters
XP ZP	Distance (x-direction) between connection and center of mass [m]. Distance (z-direction) between connection and center of mass [m].

Description - Z

A point model forms the connection between the single degree of freedom part of a system and the center of mass of a 3D-body.

The 3D-point-Z model is the equivalent of the 2D-point-X model. It describes the translation of force in z-direction to a force in 6 degrees of freedom. Because there are three rotational degrees of freedom, the 3D-point-Y model has two offsets, XP and YP.

The single degree of freedom port p_in describes the connection in x-direction and the 6 degree of freedom port P_out describes connection with the 3D-body.

P_out.F[1] = 0;

P_out.F[2] = 0;

P_out.F[3] = p_in.F;

P_out.F[4] = YP*p_in.F;

P_out.F[5] = -XP*p_in.F;

P_out.F[6] = 0;

p_in.v = P_out.v[3] - XP*P_out.v[5]

+ YP *P_out.v[4];

// x-direction

// y-direction

// z-direction

// x-rotation

// y-rotation

// z-rotation

// y-direction

As can bee seen from the equations, a nonzero offset XP or YP (distance from center of mass) in a 3D-point will result in a momentum. Therefore a 3D-body has to be connected to 3D-points with at least three orthogonal nonzero offsets to prevent it from free rotation.

The equations also show that the x-direction and y-direction are not affected by the 3D-point-Z model. Therefore each 3D-body has to be connected to at least three orthogonal 3D-point models to prevent it from free motion.

Interface - Z

Ports	Description
p_in P_out[3]	Translation port with one degree of freedom (x [m]). Port with 6 degrees of freedom.
Causality
fixed force out P_out fixed velocity out p_in
Parameters
XP YP	Distance (x-direction) between connection and center of mass [m]. Distance (y-direction) between connection and center of mass [m].

Description - XYZ

A point model forms the connection between the single degree of freedom part of a system and the center of mass of a 3D-body.

The 3D-point-XYZ model is a combination of the 3D-point-X model, the 3D-point-Y model and the 3D-point-Z model. It describes the translation of force in x-direction, y-direction and z-ditrection to a force in 6 degrees of freedom. Because there are three rotational degrees of freedom, the model has three offsets, XP, YP and ZP.

The single degree of freedom ports p_inx, p_iny and p_inz describes the connection in x-direction, y-direction and z-direction and the 6 degree of freedom port P_out describes connection with the 3D-body.

P_out.F[1] = p_inx.F;

P_out.F[2] = p_iny.F;

P_out.F[3] = p_inz.F;

P_out.F[4] = YP*p_inz.F - ZP*p_iny.F;

P_out.F[5] = -XP*p_inz.F + ZP*p_inx.F;

P_out.F[6] = XP*p_iny.F - YP*p_inx.F;

p_inx.v = P_out.v[1] - YP*P_out.v[6] + ZP *P_out.v[5];

p_iny.v = P_out.v[2] + XP*P_out.v[6] - ZP *P_out.v[4];

p_inz.v = P_out.v[3] - XP*P_out.v[5] + YP *P_out.v[4];

// x-direction

// y-direction

// z-direction

// x-rotation

// y-rotation

// z-rotation

// x-direction

// y-direction

// z-direction

As can bee seen from the equations, a nonzero offset XP, YP or ZP (distance from center of mass) in a 3D-point will result in a momentum. Therefore a 3D-body has to be connected to 3D-points with at least three orthogonal nonzero offsets to prevent it from free rotation.

Interface - XYZ

Ports	Description
p_inx p_iny p_inz P_out[3]	Translation port with one degree of freedom [m]. Translation port with one degree of freedom [m]. Translation port with one degree of freedom [m]. Port with 6 degrees of freedom.
Causality
fixed force out P_out fixed velocity out p_in
Parameters
YP XP theta	Distance (y-direction) between connection and center of mass [m]. Distance (x-direction) between connection and center of mass [m]. Angle of impact of the single degree of freedom port [rad].

Note

•	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]!