Assembly data for intake valve in database

Part name Part number Assembly Coordinates to

to be assembled position be assembled

Intake valve 1 (dx, dy, dz) (cx, cy, cz)

Intake valve 1 (dx, dy, dz) (cx, cy, cz)

Intake valve 1 (dx, dy, dz) (cx, cy, cz)

Intake valve 1 (dx, dy, dz) (cx, cy, cz)

Total 4

u ¼ cos 1½ðdirection1Þðdirection2Þ& should be rotated into D1. In Fig. 18, D1, D2 and D3 directions

(1) are as follows:

That is, the angle between directions of two reference surfaces is equal to the arccosine of the scalar product of them. The program first calls the intake valve from the database and selects a planar surface as reference surface on it. In Fig. 17, reference planar surface selected of the intake valve is given. All the assembly procedures of the intake valve will be con-ducted through this reference surface.

Intake valves designed with different angle in Fig. 18 should be positioned to assembly direction. Assembly direction predefined in the database of the intake valve is direction D1 (0, 0, 1). The user can draw the intake valve in any angle such as D2 and D3. In this case, the direction of the reference surface of the intake valve is investigated. If the direction of the reference surface is different from assembly direction predefined in the database, the program calculates the angle between directions of two reference surfaces and rotates the intake valve according to the calculated angle. Since real assembly direction is D1, Directions D2 and D3

D1 ¼ ½0; 0; 1&; D2 ¼ ½0; 0:707; 0:707&;

D3 ¼ ½0; 0:866; 0:5&

The scalar product of two directions can be obtained as

D1D2 ¼ ð0;    0:707; 0:707Þð0; 0; 1Þ; D1D2 ¼ 0:707;

D1D3 ¼ ð0; 0:866; 0:5Þð0; 0; 1Þ; D1D3 ¼ 0:5

By applying the formula (1) b and a are obtained:

a ¼ cos 10:707; a ¼ 45 ; b ¼ cos 10:5; b ¼ 60

According to above calculations, the angle between D1 and D2 directions is 458 and, the angle between D1 and D3 directions is 608. After the angle between two directions is calculated, rotation direction and axis should be determined. To rotate the intake valve which has direction D2 into direction D1, directions D1 and D2 are checked. Directions D1 and D2 respectively are [0, 0, 1] and [0, 0.707, 0.707]. Since directions D1x and D2x are the same, rotation axis must be x

 axis. Rotation direction is related to the sign of y axis of direction D2. Because D2y is 0.707, the sign of y axis of direction D2 is ( ). Therefore, the intake valve which has direction D2 is rotated in clockwise. The intake valve which has direction D2 should be rotated 458 around x axis in clockwise. In this way, the intake valve which has direction D3 should be rotated 608 around x axis in counter clockwise, because the sign of y axis of direction D3 is (+). After the intake valve is positioned, STEP file of the intake valve is generated again. Because updated local origin to be used as base point in the assembly belonging to reference surface is determined from the last STEP file. The program holds the intake valve from the base point and assembles it according to data represented in Table 1. This data has been predefined in the database as assembly information. According to Table 1, four intake valves are assembled into the assembly file with respect to assembly position.