Encyclopaedia Index

Contents:
(a) General
(b) Examples

### (a) General

This chapter explains how the motion of objects can be described via In-Form statements without the use of MOF data files. Unlike the latter, which require explicit pre-computation of the co-ordinates of the object at each time step, In-Form specifies the co-ordinates implicitly by way of "(MOVOB" statements which use special POS and OFFSET functions.

The (MOVOB" statement has the following format:

`MOVOB of VR_OBJ_NAME is SPECIAL_FUNCTION() with PARENT=PARENT_NAME)`
where VR_OBJ_NAME is the name of a VR object name which is connected to a appropriate object-related coordinate system for which the current attributes are set.

The special In-Form flag "withPARENT=PARENT_NAME" determines the positio of the current object in the family hierarchy of objects.

The OFFSET function describes the hierarchy part of the attribute settings, i.e. the way in which the motion of one object depends on that of another.

OFFSET is a special In-Form function for declaring the frames of reference of object-related coordinate systems. Each new OFFSET function declares a new frame coordinate system and describes its position relative to its parent system. OFFSET has next format

```

OFFSET(Xorigin, Yorigin, Zorigin)

```

where Xorigin, Yorigin, Zorigin are formulas for calculation of coordinates of the origin position of the rotation axis relative to its parent.

POS is a special In-Form function which describes the co-ordinates of position of moving object in appropriate object-related co-ordinate system. POS has the following format

```

POS(Xpos, Ypos, Zpos, Xang, Yang, Zang)

```

where

Xpos, Ypos, Zpos are formulas for calculation of X, Y, Z co-ordinates of the position of moving VR object in meters.

Xang, Yang, Zang are formulas for setting the rotation angle of moving VR object about X, Y, Z axis in degrees.

Each formula can contain the TIM variable which is current time in seconds at the current time step.

Probably hereafter the new special In-Form functions will be created in addition:

```

VEL(Xvel, Yvel, Zvel, Xrot, Yrot, Zrot)

```

where

Xvel , Yvel, Zvel are formulas for setting the X, Y, Z linear velocity components of moving VR object, m/s;

Xrot, Yrot, Zrot are formulas for setting the rotation velocities of moving VR object about X, Y, Z axis, 1/s.

```

ACC(Xacc, Yacc, Zacc, Xracc, Yracc, Zracc)

```

where

Xacc, Yacc, Zacc are formulas for setting the acceleration of linear motion of moving VR object in X, Y, Z directions, m/s^2; Xracc, Yracc, Zracc are formulas for setting the acceleration of rotation motion of moving VR object about X, Y, Z axis, 1/s^2.

### (b) Examples of In-Form use for MOFOR attributes settings

.
1. #### Elementary motion: linear movement

The task is to provide the attributes for a simple motion of a 2D rectangular object called "BLOCK" with uniform velocity of 3m/s in Z-direction of computational domain starting from a given initial, stationary position of the object.

The description the hierarchy part is not mandatory as there is only one moving object. Therefore it is enough to define the Z position of moving object in each time step.

```

(MOVOB of BLOCK is POS(0, 0, 3*TIM, 0, 0, 0))

```

The movement is along Z-axis. The initial position and the sizes of the BLOCK are specified in the Q1 file. Z co-ordinates of moving BLOCK object are described as

Z velocity component[m/s] * current time[s].

2. #### Composite movement: rolling block

The hierarchy part is described as follows:

```

(MOVOB of CHAM is OFFSET(0&0&0))

(MOVOB of BLOCK is OFFSET(0.55&0.9&0) with PARENT=CHAM)

```

The OFFSET defines the position of the rotation axis relative to the root frame: it places the Z-axis in the middle of BLOCK initial position.

The movement is along X-axis and the rotation about Z-axis. X co-ordinates of moving BLOCK object and rotation angles are described as

```

(MOVOB of BLOCK is POS(0.5*tim&0&0&0&0&-30*tim))

```

3. #### Independent motions: crossing paths

The case exemplifies the setting-up the attributes for the independent movements of two objects following their own linear trajectories in 2D, X-Y, computational space.

The movement of the first object, called SPHERE1, starts from its stationary position at the west-south corner and follows a prescribed parabolic trajectory. The velocity of SPHERE1 is 10 m/s and is defined by interaction of gravitation force.

The second object, SPHERE2, starts at east-south corner of the domain and follows the linear trajectory crossing the one from right to left. It has the constant velocity component of -10 m/s in X-direction and 3 m/s in Y-direction.

The description the hierarchy part is not mandatory as two moving objects move inside one root co-ordinates system. Therefore it is enough only to define the position of moving objects in each time step.

The movement of SPHERE1 object is along diagonal of XY plane. X and Y co-ordinates of moving object are described as

```

vel=10.; gravt=9.81

(MOVOB of SPHERE1 is POS(tim*:vel:&tim*:vel:-0.5*:gravt:*tim^2&0&0&0&0))

```

The movement of SPHERE2 object is along X-axis from right to left. X co-ordinates of moving object are described as

```

(MOVOB of SPHERE2 is POS(-tim*:vel:&0&0&0&0&0))

```

4. #### Connected objects: falling of a cracked wall

The case exemplifies the setting-up the attributes for the connected movements of two objects following their relative rotation in 2D, Y-Z, computational space.

The movement of the first object, called BLOCK, starts from its stationary position as a vertical wall with its base placed next to the middle of the bottom domain boundary. BLOCK is allowed to fall. It does so by rotating clockwise about X-axis of its south-high corner. The angular velocity of the fall is 75 degrees per second.

Initially, the second smaller object, TIP, sits stationary on the top of BLOCK and can be regarded as a part of the wall. Once the whole wall starts to fall, it cracks and TIP begins to move in opposite direction by rotating counterclockwise about X- axis of the north-low corner of the BLOCK. The angular velocity of the TIP relative to the BLOCK is 180 degree per second.

The hierarchy part is described as follows:

```

(MOVOB of BLOCK is OFFSET(0&0&2.1))

(MOVOB of TIP is OFFSET(0&2.5&-0.5) with PARENT=BLOCK)

```

Two frames are defined: BLOCK is a parent joint, and TIP is the BLOCK's child.

The OFFSET of BLOCK defines the position of the rotation axis relative to the root frame: it places the origin of parent related co-ordinate frame at the south-high corner of BLOCK initial position.

The OFFSET of TIP defines the position of the rotation axis relative to the BLOCK frame: it places the origin of its co-ordinate frame at the north-low corner of BLOCK initial position.

The movement of BLOCK object is a rotation clockwise about X plane. Rotation angle is described as

```

(MOVOB of BLOCK is POS(0&0&0&75*tim&0&0))

```

The movement of SPHERE2 object is a rotation counterclockwise about X plane. X co-ordinates of moving object are described as

```

(MOVOB of TIP is POS(0&0&0&-180*tim&0&0))

```

5. #### Stirred reactor

The impellor design considered here consists of a ROD, mounted on rotating vertical SHAFT, and two PADDLEs, which stir the flow. As the impeller rotates it forces the surrounding fluid in part to rotate with it. The design with rotating paddles is used in order to promote mixing, and perhaps chemical reaction also.

The task of the exercise is to provide the attributes for connected movements of SHAFT-ROD-PADDLEs assembly following their relative rotation in 3D computational space. The angular velocity of the shaft is 60 rpm.

The hierarchy part is described as follows:

```

(MOVOB of CHAM is OFFSET(0&0&0))

(MOVOB of SHAFT is OFFSET(0.15&0.25&0.25) with PARENT=CHAM)

(MOVOB of ROD is OFFSET(0&0&0) with PARENT=SHAFT)

(MOVOB of PADDLE1 is OFFSET(0&0&0) with PARENT=ROD)

```

Four frames are defined: SHAFT is a parent joint, and ROD, PADDLE1 and PADDLE2 are the SHAFT's children.

The OFFSET of SHAFT defines the position of the rotation axis relative to the ROOT frame: it places the origin of parent related co-ordinate frame at the middle of the SHAFT bottom face of its initial position.

The ROD and PADDLEs rotate about the same axis and has no freedom to move relatively to SHAFT. The OFFSETs of ROD and both PADDLEs are zero.

The movement of SHAFT object is a rotation clockwise about X plane. Rotation angle is described as

```

(MOVOB of SHAFT is POS(0&0&0&360*tim&0&0))

```