0075

Item 0075

DESIGN: Power Train - Frame - Offset Conversion

Objective:

Computer program to convert between helicopter coordinates and engine coordinates. Not working properly.

Drawing:

FORM: Power Train - Frame

Notes:

See folder on bookmark on Analytic Geometry and folder on Geometry

Translation:

The distance from drive train mast junction to center of engine base; in drive train coordinate system.

Back is positive.

Starboard is positive.

Up is positive.

Rotation:

X-axis	Straight back is 0 degrees.	Viewed downward; positive is CCW.
Y-axis	Straight up is 0 degrees.	Viewed from back; positive is CCW.
Z-axis	Straight ?? is 0 degrees.	Viewed from port side; positive is CCW.

Offset of Engine Origins from Power Train's Origin:

From Drive Train:

	Port	Starboard	Rotation
X (station)	= 8.5977"	= 8.5977"	12.5
Y (side)	= -1.1961"	= 1.1961"
Z (elevation)	= 17"	= 17"	15

Nomenclature:

Cartesian coordinates:

Descartes:

X	Length "abscissa"	(for x-coordinate)
Y	Width "ordinate"	(for y-coordinate)
Z	Height "altitude"	(for z-coordinate)

Angle with X-axis is called "bearing", or "heading" or "phi" or 'theta'

Euler:

Here the direction angles;

alpha α (roll) {about positive x-axis},

beta ß (pitch) {about positive y-axis},

gamma γ (yaw) {about positive z-axis}

are the angles that the vector makes with the positive x-, y- and z-axes, respectively. In formulas, it is usually the direction cosines that occur, rather than the direction angles.

Yaw	about	Z	to get Euler angle	"phi"	φ Φ
Roll	about	X	to get Euler angle	"theta"	θ Θ
Pitch	about	Z	to get Euler angle	"psi"	ψ Ψ

Quadrants:

1^st	(+,+)	2:00 to 3:00 o'clock
2^nd	(-,+)	3:00 to 6:00 o'clock
3^rd	(-,-)	6:00 to 9:00 o'clock
4^th	(+,-)	9:00 to 12:00 o'clock

Views:

Plan	(view is top down)	Plane XY
Side	(view is port to starboard)	Plane ZX
End	(view is tail to nose)	Plane ZY

Matrix & Determinant:

The element in the i th row and j th column is called the (i,j) th element and is denoted by a_ij.

Note- row then column.

Element is also called coefficient, or coordinate or entry.

I think matrix multiplication is row vector multiplied by column vector.

Basic Shape of Frame:

The basic frame shape is to consist of a tetrahedron (i.e. 4 joined triangles).

The hard points (mounting points) will be at the 3 corners of the one face which attaches to the back of the seat.

Cartesian Coordinate System:

Axes:

Roll axis	(abscissa)	X
Pitch axis	(ordinate)	Y
Yaw axis	(altitude)	Z

Coordinate Planes:

xy-coordinate plane

yz-coordinate plane

xz-coordinate plane

Origin:

Point 0,0,0

Orientation:

Turn the plane through a certain amount of yaw to get the Euler angle labeled phi.

Then turn it through a certain amount of roll to get the Euler angle labeled theta.

(Yes, this contradicts the labels used to describe location in

spherical coordinates.) Finally, turn it through a certain amount of

yaw again to get the Euler angle labeled by the Greek letter psi. Even

though you never turned the plane through a pitch, you can get a

pitch, in effect, by doing the right yaw, roll, and yaw.

Definitions:

Translation: A translation is a straight-line movement of an object from one position to another.

Rotation:

Transformation: A transformation associates to each point a different point in the same coordinate system.

Homogeneous coordinates

Cartesian coordinates

Substitution (Change of coordinates) relates the coordinates of a point in one coordinate system to those of the same point in a different coordinate system.

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Last Revised: December 12, 2000