L

The length of the line from point 2 to point 9, k is k = r tan(|i)

The length of the line from point 2 to point 10, L is

The coordinates of point 9 are No = (k+L) * cos a . + N9

E9 = (k+L) * cos (3a+j + E2 V9 = (k+L) * cos Ya+j + V2

The coordinates of point 10 are

N10 = L * cos aa+j + N2 E10 = L * cos (3a+j + E2 V10 = L * cos ya+j + V2

The length of line t+z and its direction cosines are ^

N9-N4 E9-E4 V9-V4

The distance from point 9 to point 8, t, and the coordinates of point 8 4/

are r

N8 = t * cos at+z + N9 E8 = t*cosßt+z + E9 V8 = t * cos yt+2 + V9

The length of line u from point 10 to point 8 and the direction cosines of 10^ u and m are u u = a/(N8 - N10)2 + (Eg - E10)2 + (V8 - V10)2

Selecting the length of line m to be unity, the coordinates of point 12 are

N12 = 1 * cos otj + N8 E12 = 1 * cos pj + E8 V12 = 1 * cos y^ + V8 The coordinates of point 11 which lies one unit directly above point 8 are

The length of line q from point. 11 to point 12 and the direction cosines of q are q = V(N12 - Nn)2 + (El2 - En)2 + (V12 - vn)2

The angle 5 between line n and line q is l2-l2-q2 8 = acos(- 2 * i * q )

The length of y, point 8 to point 14 is y = 1 * tan(S)

The law of sines gives the length of the line p, from point 11 to point 14

The coordinates of point 14 are

The direction cosines of line y are cos ay =

The tool face rotation angle y which is the angle between the z and y is y = acos( cos a cos a. + cos B cos B. + cos y cos 7. )