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TwoDPoint

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TwoDPoint

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Iconic Diagrams\Mechanical\Translation\2DSmallAngles

Implementations

X

Y

theta

XY

Use

Domains: Continuous. Size: 1-D/2-D. Kind: Iconic Diagrams (1D Translation, 2D Planar).

Description - X

TwoDPoint models are used to connect 1D models to TwoDBodies. They indicate a 1D force or torque that is applied in a certain direction, onto a body. The TwoDPoint-X model forms the connection between the single degree of freedom in x-direction and the center of mass of a body. Consider the example below, where force F in x-direction (single degree of freedom) is pushing upon a body (three degrees of freedom) at an offset YP from the body center of mass.

2DBody1

To create such a construct the TwoDPoint-X model is used:

2DPoint-X

The TwoDPoint-X model describes the transformation of force in x-direction to a force in three degrees of freedom. The single degree of freedom port p_in describes the connection in x-direction and the three three degree of freedom port P_out describes connection with the 2D-body (x, y and q).

P_out.F[1] = p_in.F;

P_out.F[2] = 0;

P_out.F[3] = -p_in.F * YP;

 

p_in.v = P_out.v[1] - YP * P_out.v[3];

// x-direction

// y-direction

// rotation

 

// x-direction

 

Interface - X

Ports

Description

p_in

P_out[3]

1D Translation port (x).

2D Port with three degrees of freedom (x, y, q).

Causality

 

fixed force out P_out

fixed velocity out p_in

 

Parameters

 

YP

Distance (y-direction) between connection and center of mass [m].

 

 

Description - Y

TwoDPoint models are used to connect 1D models to TwoDBodies. They indicate a 1D force or torque that is applied in a certain direction, onto a body. The TwoDPoint-Y model forms the connection between the single degree of freedom in y-direction and the center of mass of a body. Consider the example below, where force F in y-direction (single degree of freedom) is pushing upon a body (three degrees of freedom) at an offset XP from the body center of mass.

2DBody2

To create such a construct the 2D-point-Y model is used:

2DPoint-Y

The 2D-point-Y model describes the transformation of force in y-direction to a force in three degrees of freedom. The single degree of freedom port p_in describes the connection in y-direction and the three three degree of freedom port P_out describes connection with the 2D-body (x, y and q).

P_out.F[1] = 0;

P_out.F[2] = p_in.F;

P_out.F[3] = p_in.F * XP;

 

p_in.v = P_out.v[2] + XP * P_out.v[3];

// x-direction

// y-direction

// rotation

 

// y-direction

Interface - Y

Ports

Description

p_in

P_out[3]

1D Translation port (y).

2D Port with three degrees of freedom (x, y, q).

Causality

 

fixed force out P_out

fixed velocity out p_in

 

Parameters

 

XP

Distance (x-direction) between connection and center of mass [m].

 

 

Description - theta

TwoDPoint models are used to connect 1D models to TwoDBodies. They indicate a 1D force or torque that is applied in a certain direction, onto a body. The TwoDPoint-Theta model forms the connection between the single degree of freedom rotation and the center of mass of a body. Consider the example below, where torque (single degree of freedom) is acting on a body (three degrees of freedom).

2DBody4

To create such a construct the TwoDPoint-Theta model is used:

2DPoint-theta

The TwoDPoint-Theta model describes the transformation of a single rotation to a rotation of the 2D-body. The single degree of freedom port p_in describes the connection to the single degree rotation the three three degree of freedom port P_out describes connection with the 2D-body (x, y and q).

P_out.F[1] = 0;

P_out.F[2] = 0;

P_out.F[3] = p_in.T;

 

p_in.omega = P_out.v[3];

// x-direction

// y-direction

// rotation

 

// rotation

 

Interface - theta

Ports

Description

p_in

P_out[3]

1D Rotation port (q).

2D Port with three degrees of freedom (x, y, q).

Causality

 

fixed force out P_out

fixed velocity out p_in

 

 

Description - XY

TwoDPoint models are used to connect 1D models to TwoDBodies. They indicate a 1D force or torque that is applied in a certain direction, onto a body. The TwoDPoint-XY model forms the connection between a single degree of freedom in arbitrary direction and the center of mass of a body. Consider the example below, where force F (single degree of freedom) is pushing upon a body (three degrees of freedom) with an arbitrary angle theta at an offset XP and YP from the body center of mass.

2DBody3

To create such a construct the TwoDPoint-XY model is used:

2DPoint-XY

The TwoDPoint-XY model describes the transformation of a one degree of freedom force in an arbitrary direction to a force in three degrees of freedom. The single degree of freedom port p_in describes the connection in the arbitrary direction and the three three degree of freedom port P_out describes connection with the 2D-body (x, y and q).

 

Fx = cos(theta)*p_in.F;

Fy = sin(theta)*p_in.F;

 

P_out.F[1] = Fx;

P_out.F[2] = Fy;

P_out.F[3] = Fy * XP - Fx * YP;

 

p_in.v = cos(theta)*P_out.v[1] +

sin(theta)*P_out.v[2] +

XP * sin(theta)* P_out.v[3] -

YP * cos(theta) * P_out.v[3];

// arbitrary-direction

// arbitrary-direction

 

// x-direction

// y-direction

// rotation

 

// arbitrary-direction

 

Interface - XY

Ports

Description

p_in

P_out[3]

1D Translation port in arbitrary direction.

2D Port with three degrees of freedom (x, y, q).

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 TwoDBody has to be connected to at least three unequal TwoDPoint models to prevent it from free motion (rotation & translation).
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.