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Iconic Diagrams\Mechanical\Translation\3DSmallAngles

Implementations

X

Y

Z

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]!