Elements of descriptive geometry, with applications to isometric projection and othe forms of one-plane projection; a text-book for colleges and ingineering schools by O. E. Randall.

42

DESCRIPTIVE GEOMETRY

103. Problem 41. Given the straight line [M= 0, 1, 6; N= 0,
6, 6] and the point 0 = 3, 4, - 2; required to revolve the point 0
about M-N as an axis through arcs of 60 degrees and 90 degrees.
104. Problem 42. Given two inter-,,, \ secting straight lines, one of which is,i\, perpendicular to H and the other oblique
O,,N, to.;to I; required to revolve the latter about
~. H, the former as an axis.,......., Analysis and Construction. In Fig.:: - l52 let M-N (m,-n,, m'-n') represent the
* I V. line perpendicular to H, and let M-O
i -/ \. (m,-o,, m'-o) represent the line oblique
A/ \5 to H.
l/o' l&o" \o' Since the point 1M, in the line M-O,
is also in the axis 11-N, it will not
~n ~ move during revolution.
FIG. 52 Any other point, as 0, in 2-0 will
move as explained in Problem 36.
When the line M-0 occupies such a position that its horizontal
projection falls at m,-o,,, the vertical projection of 0 will fall at o",
and the vertical projection of the line
in this position will fall at m'-o".
In the same way the two projections
of 1-0 in any position of the circuit
may be found.
105. Problem 43. Given two intersect- o,,n ----—," \
ing straight lines one of which is perpen- G ' O, L
dicular to V and the other oblique to V;
required to revolve the latter about the '
former as an axis. m '
Analysis and Construction. In Fig. 53
let -N (m,-n,, m'-nl) represent the line.perpendicular to V, and let 3M-0 (m,-ot, F
FIG. 53'
m'-o') represent the line oblique to V.
For the same reasons presented in Section 104, f, which is a
point in the axis, will remain stationary, and 0 will move as
indicated in the diagram.